The Moon by us to you her greeting sends, The correction of this inaccuracy, however, was not pursued separately, but was combined with another object, the securing a correspondence. between the lunar and solar years, the main purpose of all early cycles. Sect. 5.-Invention of Lunisolar Years. THERE are 12 complete lunations in a year; which according to the above rule, would make 354 days, leaving 12 days of difference between such a lunar year and a solar year. It is said, that at an early period, this was attempted to be corrected by interpolating a month of 30 days every alternate year; and Herodotus relates a conversation of Solon, implying a still ruder mode of intercalation. This can hardly be considered as an advance in the knowledge of the motions of the heavens. 19 The first cycle which produced any near correspondence of the reckoning of the moon and the sun, was the Octaëteris, or period of 8 years: 8 years of 19 9 B. i. c. 15. 354 days, together with 3 months of 30 days each, make up 2922 days; which is exactly the amount of 8 years of 365 days each. Hence this period would answer its purpose so far as the above lengths of the lunar and solar cycles are exact; and it might assume various forms, according to the manner in which the intercalary months were distributed. The customary method was to add a thirteenth month at the end of the third, fifth, and eighth year of the cycle. This period is ascribed to various persons and times; probably different persons proposed different forms of it. Dodwell places its introduction in the 59th olympiad, or in the 6th century, B. C.: but Ideler thinks the astronomical knowledge of the Greeks of that age was too limited to allow of such a discovery. This cycle, however, was imperfect. The duration of 99 lunations is something more than 2922 days; it is more nearly 29231; hence in 16 years there was a deficiency of 3 days, with regard to the motions of the moon. This cycle of 16 years (Heccodecaeteris), with 3 interpolated days at the end, was used, it is said, to bring the calculation right with regard to the moon; but in this way the origin of the year was displaced with regard to the sun. After 10 revolutions of this cycle, or 160 years, the interpolated days would amount to 30, and hence the end of the lunar year would be a month in advance of the end of the solar. By terminating the lunar year at the end of the preceding month, the two years would again be brought into agreement: and we have thus a cycle of 160 years 20. This cycle of 160 years, however, was calculated from the cycle of 16 years; and was probably never used in civil reckoning; which the others, or at least that of 8 years, appear to have been. The cycles of 16 and 160 years, were corrections of the cycle of 8 years; and were readily suggested, when the length of the solar and lunar periods became known with accuracy. But a much more exact cycle, independent of these, was discovered and introduced by Meton", 432 years B. C. This cycle consisted of 19 years, and is so correct and convenient, that it is in use among ourselves to this day. The time occupied by 19 years, and by 235 lunations, is very nearly the same; (the former time is less than 6940 days by 91⁄2 hours, the latter by 7 hours.) Hence, if the 19 years be divided into 235 months, so as to agree with the changes of the moon; at the end of that period the same succession may begin again with great exactness. In order that 235 months, of 30 and 29 days, may make up 6940 days, we must have 125 of the former, which were called full months, and 110 of the latter, which were termed hollow. An artifice was used in order to distribute 110 hollow months among 6940 days. It will be found that there is a hollow month for each 63 days nearly. Hence if we reckon 30 20 Geminus, Ideler. 21 Ideler Hist. Unters. p. 208. days to every month, but at every 63d day leap over a day in the reckoning, we shall, in the 19 years, omit 110 days; and this accordingly was done. Thus the 3d day of the 3d month, the 6th day of the 5th month, the 9th day of the 7th, must be omitted, so as to make these months hollow.' Of the 19 years, seven must consist of 13 months; and it does not appear to be known according to what order these seven years were selected. Some say they were the 3d, 6th, 8th, 11th, 14th, 17th, and 19th; others, the 3d, 5th, 8th, 11th, 13th, 16th, and 19th. The near coincidence of the solar and lunar periods in this cycle of 19 years, was undoubtedly a considerable discovery at the time when it was first accomplished. It is not easy to trace the way in which such a discovery was made at that time; for we do not even know the manner in which men then recorded the agreement or difference between the calendar day and the celestial phenomenon which ought to correspond to it. It is most probable, that the length of the month was obtained with considerable exactness, by the observation of eclipses, at considerable intervals of time from each other; for eclipses are very noticeable phenomena, and must have been very soon observed to occur only at new and full moon 22. 22 Thucyd. vii. 50. Ἡ σεληνη εκλειπει· ετυγχανε γαρ πανσεληνος ουσα. iv. 52. Του ήλιου εκλιπες τι εγενετο περι νουμηνιαν. ii. 28. Νουμηνία κατα σεληνην (ώσπερ και μονον δοκεῖ εἶναι γιγνεσθαι δυνατον) ὁ ἥλιος εξελιπε μετα μεσημβριαν και παλιν επληρώθη, γενομενος μηνοειδης και αστερων τινων εκφανέντων. VOL. I. K The exact length of a certain number of months being thus known, the discovery of a cycle which should regulate the calendar with sufficient accuracy, would be a business of arithmetical skill, and must depend, in part, on the existing knowledge of arithmetical methods; but in making the discovery, a natural arithmetical sagacity was probably more efficacious than method. It is very possible that the cycle of Meton is correct more nearly than its author was aware, and more nearly than he could ascertain from any evidence and calculation known to him. It is so exact that it is still used in calculating the new moon for the time of Easter; and the Golden Number, which is spoken of in stating such rules, is the number of this cycle corresponding to the current year 23. Meton's cycle was corrected a hundred years later (330 B. C.), by Calippus, who discovered the error of it by observing an eclipse of the moon six years before the death of Alexander 24. In this corrected period, four cycles of 19 years were taken, and a day left out at the end of the 76 years, in order to make allowance for the hours by which, as already observed, 6940 days are greater than 19 years, and than 235 lunations: and this Calippic period is used 23 The same cycle of 19 years has been used by the Chinese for a very great length of time; their civil year consisting, like that of the Greeks, of months of 29 and 30 days. The Siamese also have this period. (Astron. Lib. U. K.) 24 Delamb. A. A. p. 17. |