402 TRANS. ST. LOUIS ACAD. SCIENCE. 



otherwise reporters, of what earlier eye-witnesses had perceived. Thus 

 Livy, Cicero, and others, mention the eclipses recorded in the Annates 

 Max/mi, and this great work, still existing in Tiberius's days, contained 

 all remarkable events of Roman history which the annalists of the Capitol 

 had, day by day, once recorded. The classical authors, moreover, were 

 reasonable and honest men ; they were able to speak truth, and willing to 

 do it. What would they have gained by telling falsehoods, by improvising 

 eclipses which nobody had seen, or by referring them to wrong years, sea- 

 sons, days, and hours? Of this character are, for instance, Thucydides, 

 Xenophon, Aristophanes, Herodotus, Pindar, Plutarch, Josephus, Philos- 

 tratus, the Roman chroniclers, Livy, Cicero, Tacitus, Pliny, and the like. 

 All these ancient authors deserve confidence as long as the impossibility 

 of their traditions is not clearly demonstrated. This is and must be the 

 stand-point of all historians. 



Formerly, it is true, the eclipses in Ptolemy's Almagest were considered 

 to be the most reliable ones, but erroneously; for, Ptolemy, 140 A.c, had 

 not, with his own eyes, observed those ancient eclipses; and their particu- 

 lars are not the result of Babylonian observations, but the fruits of Ptole- 

 my's computations, as will be seen below. Had Babylonian astronomers 

 themselves observed the minutes of those eclipses, the times and magnitudes 

 of the latter, as specified in the Almagest, would agree with each other 

 and with the classic eclipses. Instead of this, careful computations of Ptol- 

 emy's 19 lunar eclipses, by means of Hansen's Lunar Tables, have brought 

 to light that one of them finished prior to the rising of the moon, and that 

 another obscuration of the moon amounted only to a quarter of an inch, 

 which nobody would have perceived with the naked eye. Paradoxes 

 similar to these are coming. Granting that the Babylonian eclipses were 

 exactly described in Ptolemy's Almagest; granting that Hansen was right 

 in deducing from the same eclipses the secular accelerations of the moon's 

 motions and other elements of his Tables, — how is it that the latter do not 

 correspond with the ascertained Roman and Greek eclipses? The obscu- 

 ration of the sun in — 400, July 1, e.g., which was, according to the Annates 

 Maximi, a total one in Rome, amounted, according to Hansen"s theory, to 

 2' 34" only. How came it to pass that all the Lunar Tables, from Ptole- 

 my down to Damoiseau, based both on the Almagest and modern obser- 

 vations, proved incorrect some years after their construction ? The reason 

 is that the terminus a quo, the Babylonian eclipses in the Almagest were 

 wrong ones ; that Ptolemy had referred them to wrong years; that the 

 longitudes of the moon, her Nodes and Apsides, were in 721 B.C. other 

 ones than those determined by means of the Almagest. 



In short, it is evident that, in establishing a true theory of the moon's 

 motions, either the eclipses in the Almagest or else those in the Classics 

 must be given up. Tertium non datur. It is true that, sometimes, the 

 astronomers determined the dates of Greek and Roman eclipses a priori, 

 and in spite of the actual history and chronology, and only by the instru- 

 mentality of Lunar Tables based on the eclipses in the Almagest ; but this 



