Scholars who investigated the calendars of the Incas of Peru and the Mayas of Yucatan wondered at the calendar of 360 days; so did the scholars who studied the calendars of the Egyptians, Persians, Hindus, Chaldeans, Assyrians, Hebrews, Chinese, Greeks, or Romans. Most of them, while debating the problem in their own field, did not suspect that the same problem turned up in the calendar of every nation of antiquity.
Two matters appeared perplexing: a mistake of five and a quarter days in a year could certainly be traced, not only by astronomers, but even by analphabetic farmers, for in the short span of forty years— a period that a person could readily observe—the seasons would become displaced by more than two hundred days. The second perplexity concerns the length of a month. "It seems to have been a prevailing opinion among the ancients that a lunation or synodical month lasted thirty days."49 In many documents of various peoples, it is said that the month, or the "moon," is equal to thirty days, and that the beginning of such a month coincides with the new moon.
Such declarations by ancient astronomers make it clear that there was no such thing as a conventional calendar with an admitted error;
epigomena." He refers to the 360 gods in the "theology of Orpheus," to the 360 eons of the gnostic genii, to the 360 idols before the palace of Dairi in Japan, to 360 statues "surrounding that of Hobal," worshiped by the ancient Arabs, to the 360 genii who take possession of the soul after death, "according to the doctrine of the Christians of St. John," to the 360 temples built on the mountain of Lowham in China, and to the wall of 360 stadia "with which Semiramis surrounded the city" of Babylon. This material did not convey to its collector the idea that an astronomical year of 360 days had been the reason for the sacredness of the number 360. 49
Medhurst, The Shoo King.
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as a matter of fact, the existence of an international calendar in those days is extremely unlikely.
After centuries of open sea lanes and international exchange of ideas, no uniform calendar for the whole world has as yet been devised: the Moslems have a lunar year, based on the movements of the moon, which is systematically adjusted every few years to the solar year by intercalation; many other creeds and peoples have systems of their own containing many vestiges of ancient systems. The reckoning of months as equal to thirty and thirty-one days is also a relic of older systems; the five supplementary days were divided among the old lunar months. But at robin-bobin
present the almanac does not ascribe an interval of thirty days between two lunations or a period of 360 days for twelve lunations.
The reason for the universal identity of time reckoning between the fifteenth and the eighth centuries lay in the actual movement of the earth on its axis and along its orbit, and in the revolution of the moon, during that historical period. The length of a lunar revolution must have been almost exactly 30 days, and the length of the year apparently did not vary from 360 days by more than a few hours.
Then a series of catastrophes occurred that changed the axis and the orbit of the earth and the orbit of the moon, and the ancient year, after going through a period marked by disarranged seasons, settled into a "slow-moving year" (Seneca) of 365 days, 5 hours, 48 minutes, 46
seconds, a lunar month being equal to 29 days, 12 hours, 44 minutes, 2.7 seconds, mean synodical period.
Disarranged Months
As a result of repeated perturbations, the earth changed from an orbit of 360 days' duration to one of 365/4 days, the days probably not being exactly equal in both cases. The month changed from thirty to twenty-nine and a half days. These were the values at the beginning and at the end of the century of "the battle of the gods." As a result of the perturbations of this century, there were intermediary values of the year and the month. The length of the year probably ranged between 360 and 365/4 days, but the moon, being a smaller (or
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weaker) body than the earth, suffered greater perturbations from the contacting body, and the intermediate values of the month could have been subjected to greater changes.
Plutarch declares that in the time of Romulus the people were "irrational and irregular in their fixing of the months," and reckoned some months at thirty-five days and some at more, "trying to keep to a year of 360 days," and that Numa, Romulus' successor, corrected the irregularities of the calendar and also changed the order of the months. This statement suggests the question: Might it not have been that during the period between consecutive catastrophes the moon receded to an orbit of thirty-five or thirty-six days' duration?
If, in the period of confusion, the moon actually changed for a while to such an orbit, it must have been an ellipse or a circle of a radius larger than before. In the latter case, each of the four moon phases must have been of nine days' duration. It is of interest, therefore, to read that in many sagas dealing with the moon, the number nine is used in measures of time.1
A series of scholars found that nine days was for a while a time period of many ancient peoples: the Hindus, the Persians,2 the Raby-lonians,3 the Egyptians,4 and the Chinese.5 In religious traditions, literature, and astrological works, seven days and nine days compete as the measure of the month's quarter.
In the time of the Homeric epics, the nine-day week became prevalent in the Greek world. The seven-day week and the nine-day
1 "The number nine occurs conspicuously in so many sagas which, for other reasons, I recognized to be moon sagas, that I am convinced that the holiness of this number has its origin in its very ancient application in time division." The author of this passage (E. Siecke, Die Liebesgeschichte des Himmels, Vnter-suchungen zur indogermanischen Sagenkunde [1892]) did not suppose a change in the nature of the lunar cycles, and also was not aware of the work of the scholar referred to in the following footnote, yet he was forced to believe that nine was connected with a time subdivision of a month.
2 A. Kaegi, "Die Neunzahl bei den Ostarien." in the volume dedicated to H. Schweizer-Sidler (1891).
3 Kugler, "Die Symbolik der Neunzahl," Babylonische Zeitordnung, p. 192.
* E. Naville, Transactions of the Society of Biblical Archaeology, IV (1875), 1-18. B Roscher, Die enneadischen und hebdomadischen Fristen und Wochen, Vol. XXI, No. 4, of Abhandlungen der philol.-histor. Klasse der Kgl. sachs. Ges. der "Wissenschaften (1903).
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robin-bobin
week are both found in Homer.6 The Romans, too, retained the recollection of a time when the week had been of nine days' duration.7
The change from a seven-day phase to a nine-day phase is found in the traditions of the peoples of Rumania, Lithuania, and Sardinia, and among the Celts of Europe, the Mongols of Asia, and the tribes of West Africa.8
In order to explain this strange phenomenon in time reckoning, obviously connected with the moon, the suggestion was made that, in addition to the seventh-day phase of the moon, a nine-day phase was also observed, which is a third part of the month.9 But this idea must be rejected, because a third part of a month of twenty-nine and a half days would more nearly be ten days and not nine.10 Besides, the quarter-month phases are easily observable periods during which the moon increases from new moon to half moon, to full moon, and then decreases accordingly; but a nine-day period falls between these phases.
Therefore, and in view of the vast material from many peoples, we conclude that at one time during the century of perturbations, for a period between two catastrophes, the moon receded to an orbit of thirty-five to thirty-six days' duration. It remained on such an orbit for a few decades until, at the next upheaval, it was carried to an orbit of twenty-nine and a half days' duration, on which it has proceeded since then.