Lunar calendar

“ 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. ”

“ If the series is repeated once, at the end of 810 months, or about 661⁄2 years, the eclipse calendar will be behind the average eclipse season .78 days, and the lunar calendar will be in advance of the synodical revolutions of the moon only .22 days. ”

“ The excess of the solar year beyond the lunar, employed in the calendar to signify the moon’s age at the beginning of the year. The common solar year consisted of 365 days and the lunar year only 354 days, the difference is eleven; whence, if a new moon fall on the first day of January in any year, the moon will be eleven days old on the first day of the following year, and [Pg 86] twenty-two days old on the first of the third year. The numbers eleven and twenty-two are therefore the epacts of those years respectively. ”

“ On the other hand, when the time by which the new moons anticipate the lunar cycle amounts to a whole day, which, as we have seen, it does in 308 years, the new moons will arrive one day earlier, and the epacts must consequently be increased by unity. Thus the epacts 11, 22, 3, 14, &c., in consequence of the lunar equation, become 12, 23, 4, 15, &c. In order to preserve the uniformity of the calendar, the epacts are changed only at the commencement of a century; the correction of the error of the lunar cycle is therefore made at the end of 300 years. ”

“ CALENDAR REGULATION. 1. THE INTERCALATION. The circumstance that the lunar months are among almost all peoples named from the phases of Nature involves the necessity of an agreement between the two really incommensurable periods given by the sun and the moon. This problem is the central point of the older scientific chronology. We shall now investigate more closely how the problem has arisen, and what has been its development among the primitive peoples.
Where there is only a series of less than twelve months, the problem of calendar regulation does not exist. ”

“ It became apparent as the world progressed that use of the moon was very unsatisfactory for this purpose, as the calendar became complicated and confusion resulted, owing to the difference between the lunar and solar years. This condition remained until the reign of Caesar, when that monarch determined to establish a more satisfactory method of reckoning time. With the aid of an eminent astronomer, he completely revised the calendar, using the revolution of the earth around the sun as the standard for the length of a year. ”

“ The Lunar cycle, or the cycle of the moon, is a period of nineteen years, after which the new and full moons fall on the same days of the year as they did nineteen years before. This cycle was invented by Meton, a celebrated astronomer of Athens, and may be regarded as the masterpiece of ancient astronomy. In nineteen solar years there are 235 lunations, a number which, on being divided by nineteen, gives twelve lunations, with seven of a remainder, to be distributed among the years of the period. ”

“ The counting that is important for the calendar is that according to the days of the lunar month, but in this the primitive peoples hold to the concrete phenomenon of the moon. The habit of reckoning in this fashion may however be partly responsible for the fact that among certain peoples [323] every day of the month has not been given a name, but the days are counted from certain points of departure, such as new moon, full moon, etc. Very rarely do we meet with a genuinely calendrical use of the tally. ”

“ In ancient times ceaseless efforts were made to adjust the months to the measure of the year, but we have practically given up the attempt, and in our calendar the lunar months shift along as they will, while the ordinary months are periods of a certain number of days, having no relation to the movements of the moon. ”

“ At a comparatively early period, however, the phases of the moon attracted attention, and became the basis of calendars. Lunar calendars are found among savage and half-civilized tribes of various grades of culture in Polynesia, Africa, Asia, and the Americas, and were retained for a time by most ancient civilized peoples. Later observation included the movements of the sun; it is only among advanced peoples that festivals are connected with equinoxes and solstices. ”

“ By registering, therefore, the exact days of any cycle at which the new or full moons occurred, such a calendar would show on what days these events would occur in any other cycle; and, since the regulation of games, feasts, and fasts, has been made very extensively, both in ancient and modern times, according to new or full moons, such a calendar becomes very convenient for finding the day on which the new or full moon required takes place. Suppose, for example, it were decreed that a festival should be held on the day of the first full moon after the Vernal equinox. ”

“ Then, too, regarding the moon as a timekeeper, we must not forget the service that it renders in furnishing a division of time intermediate between the day—which is measured by the earth’s rotation—and the year, which is defined by the earth’s orbital revolution. Notwithstanding the survival of lunar reckoning in our religious services, we, in our time and country, scarcely need a moon to mark our months ”

“ We have already seen that tables were constructed showing on what days each new moon would fall in the whole lunar cycle, but, though they would in nineteen years fall upon the same day of the month, they fell about an hour and a half earlier in the day, and this in sixteen cycles, or about three hundred and twelve years, would make a difference of one day. As these tables were published by ecclesiastical and secular authority, and could not be changed without such authority, another method was resorted to to find the times of the moon without the use of these tables. ”

“ The moons of the civil year are also distinguished by their place in the cycle of sixty; and as the intercalary moons are not reckoned, for the reason before stated, namely, that during one of these lunations the sun enters into no new sign, there are only twelve regular moons in a year, so that the cycle is renewed every five years. Thus the first moon of the year 1873 being the first of a new cycle, the first moon of every sixth year, reckoned backwards or forwards from that date, as 1868, 1863, &c., or 1877, 1882, &c., will also commence a new lunar cycle of sixty moons. ”

“ It might seem, that, since the moon rotates on her axis in about twenty-seven days, the lunar day ought to be twenty-seven days long, instead of twenty-nine. There is, however, a solar, as well as a sidereal, day at the moon, as on the earth; and the solar day at the moon is longer than the sidereal day, for the same reason as on the earth. During the solar day the moon must make both a synodical rotation and a synodical revolution. ”

“ If we now find this inconspicuous part of the heavens equally honoured by several nations in very ancient times, we shall be led to think either that these nations, independently of each other, happened to observe and mark out the sun’s annual course through the heavens at exactly the same date, and therefore chose the same point as marking the winter solstice; or we must suppose that they derived their calendar and knowledge of the Zodiac from observations originally made by some one civilized race. ”

“ Thus by neglecting the invisible one, which would properly be called 28, 29 or 30, and which falls in the great interval between keunòngs 1 and 23, we get exactly one keunòng for each lunar month. This makes the calculation extremely easy, but it is obvious that as we advance we shall in time arrive at a month in which the keunòng we obtain by observation falls on a different date from that which the series would lead us to expect. It is in fact at the end not of a lunar, but a solar year, that the keunòngs revert to nearly the same interval of time separating them from the preceding new moon. ”

“ Our correspondent's notion that the moon's cycle begins with a new moon on the 1st of January, is probably derived from this, that the calendar is so contrived that for a very long period the years which have 1 for their golden number, have a new moon near the 1st of January, either on it, or within a day of it. ”

“ There is no reason to suppose that the day of full moon could become detached from the genuine lunar month, and such a process would seem still more strange since the day of new moon remained a genuine new-moon day. On the other hand the development of market and rest-day into a day of taboo is everywhere natural, and is attested in the above examples from Africa ”

“ Again, so that the fourteenth day of the paschal moon may be correctly found, and that the age of the moon may be truly announced to the faithful every day from the martyrology, according to the ancient custom of the Church, we decree:
that the golden number is to be removed from the calendar and in its place is to be substituted a cycle of epacts, regulated (as we have said) by a certain rule of the golden number, to make sure that the new moon and the paschal fourteenth day of the moon will always retain their true places. ”

“ Our calendar to-day is a purely solar one; our months are twelve in number, but of purely arbitrary length, divorced from all connection with the moon; and to us, the Saros cycle does not readily leap to the eye, for eclipses [123] of sun or moon seem to fall haphazard on any day of the month or year. ”

“ The ordinary clocks show time by the mean, not the real, sun: and it was always laid down that Easter depends on the opposition (or full moon) of the mean sun and moon, not of the real ones. Thus we see that, were the Calendar ever so correct as to the mean moon, it would be occasionally false as to the true one: if, for instance, the opposition of the mean sun and moon took place at one second before midnight, and that of the real bodies only two seconds afterwards, the calendar day of full moon would be one day before that of the common almanacs. ”