SAROS, NEROS, SOSOS. These names are from the fragments left of Berosus, who says that the Chaldttans bad three astronomical periods so called, the saros of 3600 years, the,neros of 600 years, and the sows of 60 years. Of the two latter we know nothing more, and as to the saros, the duration given by Berosus is either entirely wrong, or else subsequent writers have taken another Chaldean period, which is neither of the three above, and applied the term saros to it. Geminus (ch. 15) mentions that the Chaldoeans had found a period of 669 months, or 19,756 days (so the text stands after an emendation by Bouillaud). Ptolemy mentions the same period, and Pliny (lib. it, c. 13) remarks relative to it, that eclipses return again after a period of 223 (the third of 669) months; but the text here again was corrupt, until Halley (' Phil. Trans.,' No. 194) restored the true reading, which was afterwards confirmed by manuscripts. To complete the mis fortunes of this period, Suidas has the word Saros, but it was omitted from his Lexicon either by mistake or faultiness of manuscripts, until Dr. Pearson restored it (' Exp. of the Creed,' 1083, fol. 59, according to Weidler), and even then it gives 222 months instead of 223, which was again corrected by Halley. In the time of Riccioli, ()minus and Ptolemy were the authorities cited on this period, and the name Saros was not applied to it. Many writers (Costard for example) confound it with the Metonic period of 235 lunations, which is a totally different thing : others again, as Geminus, and even Riccioli, appear to consider it as a period for the determination of the lunation or month; and perhaps the assertion made by some others, that the Chaldmans were in possession of the Metonic cycle, may be another confusion between the latter and the saros.
Leaving the authorities on the subject, we know [3IooN] that 223 average intervals between full moon and full moon make up very nearly 242 nodical months, or passages of the moon from one node to the same again. Now since -the eclipses entirely depend upon the manner in which the full and new moons take place relatively to the node, it is obvious that if 223 lunations were exactly 242 nodical months, and if the sun's and moon's orbits were truly circular, and their motions uniform, all the eclipses of one set of 223 Inflations would be produced again precisely in the same order during the next 223; that is, if there were (say) an eclipse of the sun during the 47th lunation, reckoning from a given full moon, there would necessarily be another in the (47 + 223)rd, or the 270th lunation, and so on.
All these suppositions are near enough to the truth to make this sequence of eclipses very nearly take place. For since 223 lunations make sidereal months, anomalistic months, and 241.999 nodical months, it is obvious that at the end of a saros the moon is in the same position with respect to the sun, nearly in the same part of the heavens, nearly in the same part of her orbit, and very nearly indeed at the same distance from her node as at the beginning of the period. Now 223 lunations make 6585.32128 days,
or 6585 days, 7 hours, 42 minutes, and 38 seconds; or 18 years (of 365 days), 15 days, 7 hours, 40 minutes, and 38 seconds. Consequently a Bares of five leap years is 18 years, 14 days, and one of four leap years is 18 years, days, nearly. The Chaldrean period is 6585i days; and to avoid fractions they appear to have put together three such periods, making 19,756 days, and 669 lunations. From what has been said above, it might be inferred that the rotation of the moon's node is made in nearly a saros ; and in fact that revolution does take 18'6 years.
It is to be observed, however, that the end of each Baron is not in the same part of the day as the beginning, which is of consequence as to the solar eclipses, though not so as to the lunar, and still more does the inexactness of the period affect the former. For a saros contains 241.998659 mean nodical revolutions ; so that if the moon be in her node at the beginning of a saros, she will want '001341 of a revolution of being in her node at the end of it. This is about 29', nearly the moon 'a diameter, which makes it sometimes happen that a lunar eclipse which takes place in a certain lunation of one saros does not take place in the same lunation of the next, and very often causes the same as to a solar eclipse. And the effect must be that at last the eclipse of any lunation is destroyed, by the accumulation of these errors of 29' each time. Nor do the circumstances of one Bares pre cisely resemble those of another until a longer period of about 746 such periods has elapsed. But in the same manner that eclipses are removed out of one lunation by the inexactness of the period, they are carried into another. There are about 70 eclipses in each same, 30 lunar and 40 solar.
The Metonic cycle of 235 lunations gives 255'021 nodical months, is not near enough to a whole number to produce anything like a return of similar eclipses. But it is, as explained [Moon], near enough to an exact number of years to restore the full moons to the same days of the year, or the preceding or following days. The Metonic cycle is a that is, portions of time measured from a given epoch, and each equal to 19 years, are used in chronology. But the Saros is not a chronological period, but only a portion of time with any arbitrary commencement. Hence the student most not look in works on chronology for any information upon it.
(Riccioli, Alm. Nov. ; Weidler, Hist. Agron. ; Bouillaud, Astron.
; Ferguson's Astronomy.)