as the circle of changes of the seasons is designated by the word year. The lunar changes are, indeed, more obvious to the sense, and strike a more careless person, than the annual; the moon, when the sun is absent, is almost the sole natural object which attracts our notice; and we look at her with a far more tranquil and agreeable attention than we bestow on any other celestial object. Her changes of form and place are definite and striking to all eyes; they are uninterrupted, and the duration of their cycle is so short as to require no effort of memory to embrace it. Hence it appears to be more easy, and in earlier stages of civilization more common, to count time by moons than by years. The words by which this period of time is designated in various languages, seem to refer us to the early history of language. Our word month is connected with the word moon, and a similar connection is noticeable in the other branches of the Teutonic. The Greek word μ in like manner is related to unvŋ, which though not the common word for the moon, is found in Homer with that signification. The Latin word mensis is probably connected with the same group." The month is not any exact number of days, being more than 29, and less than 30. The latter number was first tried, for men more readily select numbers possessing some distinction of regularity. It existed for a long period in many countries. A very few months of 30 days, however, would suffice to derange the agreement between the days of the months and the moon's appearance. A little further trial would show that months of 29 and 30 days alternately, would preserve, for a considerable period, this agreement. The Greeks adopted this calendar, and, in consequence, considered the days of their month as representing the changes of the moon: the last day of the month was called čvŋ kaì véa, “the old and new," as belonging to both the waning and the reappearing moon :18 and their 17 Cicero derives this word from the verb to measure: "quia mensa spatia conficiunt, menses nominantur;" and other etymologists, with similar views, connect the above-mentioned words with the Hebrew manah, to measure (with which the Arabic word almanach is connected). Such a derivation would have some analogy with that of annus, &c., noticed above: but if we are to attempt to ascend to the earliest condition of language, we must conceive it probable that men would have a name for a most conspicuous visible object, the moon, before they would have a verb denoting the very abstract and general notion, to measure. 18 Aratus says of the moon, in a passage quoted by Geminus, p. 38: *Αιει δ ̓ ἄλλοθεν ἄλλα παρακλίνουσα μετωπὰ Ειρῃ, ὁποστάτη μήνος περιτέλλεται ἡὼς. As still her shifting visage changing turns, By her we count the monthly round of morns. festivals and sacrifices, as determined by the calendar, were conceived to be necessarily connected with the same periods of the cycles of the sun and moon. "The laws and the oracles," says Geminus, "which directed that they should in sacrifices observe three things, months, days, years, were so understood." With this persuasion, a correct system of intercalation became a religious duty. The above rule of alternate months of 29 and 30 days, supposes the length of the months 29 days and a half, which is not exactly the length of a lunar month. Accordingly the Months and the Moon were soon at variance. Aristophanes, in "The Clouds," makes the Moon complain of the disorder when the calendar was deranged. Οὐκ ἄγειν τὰς ἡμέρας Οὐδὲν ὀρθῶς, ἀλλ ̓ ἀνω τε καὶ κάτω κυδοιδοπᾶν CHORUS OF CLOUDS. The Moon by us to you her greeting sends, Shuffle her days, and turn them topsy-turvy: And that the gods (who know their feast-days well) By your false count are sent home supperless, And scold and storm at her for your neglect.19 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 (of 29 days to a lunation) would make 354 days, leaving 124 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 19 This passage is supposed by the commentators to be intended as a satire upon those who had introduced the cycle of Meton (spoken of in Sect. 5), which had been done at Athens a few years before "The Clouds" was acted. 20 B. i. c. 15. intercalation. This can hardly be considered as an improvement in the Greek calendar already described. The first cycle which produced any near correspondence of the reckoning of the moon and the sun, was the Octaeteris, or period of 8 years: 8 years of 354 days, together with 3 months of 30 days each, making up (in 99 lunations) 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 three 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 2923; hence in 16 years there was a deficiency of 3 days, with regard to the motions of the moon. This cycle of 16 years (Heccadecaeteris), 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." This cycle of 160 years, however, was calculated from the cycle of 16 years; and it 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, 22 432 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; 21 Geminus. Ideler. 22 Ideler, Hist. Unters. p. 208. THE GREEK ASTRONOMY. (the former time is less than 6940 days by 94 hours, the latter, by 74 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 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 some 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.23 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 would 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 23 Thucyd. vii. 50. ̔Η σελήνη ἐκλείπει· ἐτύγχανε γὰρ πανσέληνος οὖσα. iv. 52. Τοῦ ἡλίου ἐκλιπές τι ἐγένετο περὶ νουμηνίαν. ii. 28. Νουμηνίᾳ κατὰ σελήνην (ὥσπερ καὶ μόνον δοκεῖ εἶναι γίγνεσθαι δυνατὸν) ὁ ἡλίος ἐξέλιπε μετὰ μεσημβρίαν καὶ πάλιν ἐν ἐπληρώθη, γενόμενος μηνοειδὴς καὶ ἀστέρων τινῶν ἐκφανέντων. 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.24 Meton's Cycle was corrected a hundred years later (330 в. c.), by Calippus, who discovered the error of it by observing an eclipse of the moon six years before the death of Alexander.25 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 in Ptolemy's Almagest, in stating observations of eclipses. The Metonic and Calippic periods undoubtedly imply a very considerable degree of accuracy in the knowledge which the astronomers, to whom they are due, had of the length of the month; and the first is a very happy invention for bringing the solar and lunar calendars into agreement. The Roman Calendar, from which our own is derived, appears to have been a much less skilful contrivance than the Greek; though scholars are not agreed on the subject of its construction, we can hardly doubt that months, in this as in other cases, were intended originally to have a reference to the moon. In whatever manner the solar and lunar motions were intended to be reconciled, the attempt seems altogether to have failed, and to have been soon abandoned. The Roman months, both before and after the Julian correction, were portions of the year, having no reference to full and new moons; and we, having adopted this division of the year, have thus, in our common calendar, the traces of one of the early attempts of mankind to seize the law of the succession of celestial phenomena, in a case where the attempt was a complete failure. Considered as a part of the progress of our astronomical knowledge, improvements in the calendar do not offer many points to our observation, but they exhibit a few very important steps. Calendars which, belonging apparently to unscientific ages and nations, possess a great degree of accordance with the true motions of the sun and moon (like "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.) 25 Delamb. A. A. p. 17. |