each, Mercury i68 of 13 years each, and the Moon 113 of 19 years each, 

 the fractions being neglected. On a certain day of this period, the planets, 

 inclusive of the Moon and the Sun, occupied the same sign of the Zodiac, 

 and, 1072 years later, the same planets were united in the opposite sign. 

 These combined attractive powers may perhaps have caused the accelera- 

 tion and retardation of the moon, each lasting 1072 years. By the way, 

 during 2146 years the fixed stars proceed nearly 30°, a whole sign of the 

 Zodiac. This important combined planetary period is not mentioned by 

 Prof. Newcomb. 



Furthermore, the latter makes the older eclipses in Ptolemy's Almagest, 

 as computed by Hartwich according to Hansen's Lunar Tables (Astrono- 

 mische Nachricten, 1S60, n. 1241), the groundwork of his new Tables, the 

 terminus a quo. But Ptolemy's eclipses are linked to Ptolemy's Historical 

 Canon, which does not contain one correct date prior to a.d. 80, as has 

 been demonstrated in extenso in these Transactions, vol. iii. p. 401. All 

 astronomers from Alphonsus's age to La Hire, Lalande, Burckhardt, and 

 Damoiseau, based their Tables on the same eclipses (particularly since 

 Petavius's DoctHna Temportim, Paris, 1627, was believed to have con- 

 firmed Ptolemy's Historical Canon), because nobody was able to restore 

 the true history and chronology of the ancient nations, for want of mathe- 

 matical certainties. At present things are changed. For since Ptolemy 

 and Petavius, in whose days chronology was in its infancy, a great many 

 chronological resources, as reliable as the Multiplication Table, have come 

 to light, which put beyond question that Ptolemy's eclipses, apart from 

 those observed by himself, belong to other years than the Alexandrian 

 astronomer fancied. We specif}' once more a great many planetary con- 

 figurations, referring historical events in controversy to certain years; 

 conjunctions of planets ; new and full moons observed on certain days, 

 observations of the equinoxes and solstices on certain days and hours; a 

 number of formerly unknown ancient eclipses, referred to certain days 

 and hours ; the Greek and Hebrew solar calendars ; the inscriptions which 

 compare certain days of solar months with those of lunar months ; the 

 four seasons of the Greeks, the true epochs of their Olympian, Pythian, 

 Isthmian, and Nemean games; the Apis periods, and the like. By means 

 of so many infallible arguments it has been brought to light that the whole 

 Historical Canon of Ptolemy down to Titus is absolutely erroneous, and 

 that the older eclipses in the Almagest have not been observed, but, by 

 Ptolemy's computations, referred to wrong years. Now whoever, at pres- 

 sent, intends to construct correct Lunar Tables by means of the eclipses 

 in the Almagest, is morally bound before all to demonstrate both that 

 the said eclipses belong really to the same years and days to which the 

 Almagest refers them, and that my new chronology of the ancient 

 eclipses is nonsense. 



To this the astronomers like to object that Ptolemy's eclipses, if com- 

 puted by the best Tables in existence, those of Hansen, agree pretty well 

 with our Tables, and consequently, so they say, Ptolemy's eclipses must 



