2« The Jerusalem Talmud, Tractate Sanhedrin I, 19a. 27 Daniel 2 : 21.
2* G. Thibaut, p. xlvii of his translation of die Panchasiddhantika, the astronomical work of Varaha Mihira (Benares, 1889).
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background of the fixed stars, are about five days too short for Saturn, over five days too short for Jupiter, eleven days too short for Mars, eight or nine days too short for Venus, less than two days too short for Mercury. In a solar system in which the earth revolves around the sun in 360
days, the synodical periods of Jupiter and Saturn would be about five days shorter than they are at present, and that of Mercury less than two days shorter. But Mars and Venus of the synodical table of Varaha Mihira must have had orbits different from their present ones, even if the terrestrial year was only 360 days.
Calendric changes in India were effected in the seventh century: at that time, as in China also, the ten-month year was supplanted by a twelve-month year.29
In the eighth century a calendar reform was made in Egypt. We have already referred to a cataclysm during the reign of the Pharaoh Osorkon II of the Libyan Dynasty; another disturbance of a cosmic nature took place a few decades later, still in the time of the Libyan Dynasty.
In the fifteenth year of the reign of Sosenk III "there occurred a remarkable prodigy of uncertain nature, but in some way connected with the moon." 30 The contemporaneous document written by the royal son, the high priest Osorkon, reads: "In the year 15, fourth month of the third season, 25th day, under the majesty of his august father, the divine ruler of Thebes, before heaven devoured (or: not devoured) the moon, great wrath arose in this land."31 Soon thereafter Osorkon "introduced a new calendar of offerings." 32 The mutilated condition of the inscription makes it impossible to determine the exact nature of the calendric reform.33
It appears that the same or a similar disturbance in the movement of the moon is the subject of an Assyrian inscription, which specks
29 A. del Mar, The Worship of Augustus Caesar, p. 4. so Breasted, Records of Egypt, IV, Sec.
757.
31 Ibid., Sec. 764. See controversy in Zeitschrip fiir agyptische Sprache, VI (1868).
32 Breasted, Records of Egypt, IV, Sec. 756.
»3 A. Erman, Zeitschrip fiir agyptische Sprache, XLV (1908), 1-7.
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of the moon being obstructed on its way. "Day and night it was handicapped. In its august station it did not stand." Because of the duration of the phenomenon, it is concluded that "it could not mean an eclipse of the moon."34 The reference to the moon's unwonted position also precludes such an interpretation.
At the end of the eighth or the beginning of the seventh century before the present era, the people of Rome introduced a calendar reform. In the preceding section we referred to Ovid's statement in Fasti concerning the reform of Romulus, who divided the year into ten months, and the reform robin-bobin
of Numa, who "prefixed" two months. Plutarch's "Life of Numa" contains the following passage, part of which has already been quoted: "He [Numa] applied himself, also, to the adjustment of the calendar, not with exactness, and yet not altogether without careful observation. For during the reign of Romulus, they had been irrational and irregular in their fixing of the months, reckoning some at less than twenty days, some at thirty-five, and some at more; they had no idea of the inequality in the annual motions of the sun and moon, but held to the principle only, that the year should consist of three hundred and sixty days." 35
Numa reformed the calendar, and the "correction of the inequality which he made was destined to require other and greater corrections in the future. He also changed the order of the months."
38
Numa was a contemporary of Hezekiah.37
In the second half of the seventh century before the present era, the length of the new month and the new year was calculated by the Greeks.
Diogenes Laertius regarded Thales the Milesian, one of the "seven sages of antiquity," as the man who discovered the number of days in the year and the length of the seasons. In his Life of Thales he wrote: "He was the first to determine the sun's course from solstice to 34 P. Jensen, Die Kosmologie der Babylonier, p. 39.
35 Plutarch, Lives, "The Life of Numa" (transl. B. Perrin). 36 Ibid. 37 Cf. Augustine, The City of God, Bk. XVIII, Chap. 27.
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solstice." And again: "He is said to have discovered the seasons of the year and to have divided it into 365 days." 38 He was "the first to predict eclipses of the sun and to fix the solstices." 30
Thales is said to have written two treatises, one "On the Solstice" and the other "On the Equinox," neither of which is extant.
If the natural year always was what it is now, it is very strange that this discovery should have been attributed to a sage who lived as late as the seventh century, when Egypt and Assyria were already very old kingdoms, and when the dynasty of David was in its last decades. The longest and shortest days of the year, and thus the length of the year, are easily determined by the length of the shadow. Thales is said to have been born in the first year of the thirty-fifth Olympiad or —
640. The progress of culture would hardly leave to one and the same person the calculation of the days in a year, which is a simple matter, and the calculation of forthcoming eclipses, which is an advanced achievement. Similarly, the fact, as stated by Plutarch and Diogenes Laertius, that Solon, another sage of the same period, adjusted the months to the motion of the moon after finding that the time from one new moon to another is half a day shorter than thirty days, must be understood as an adjustment of the calendar to the new order in nature. The span of time from one new moon to another is a natural time division, almost as easily observable as day and night; primitive peoples, unable to read and write, know that the period is less than thirty days.
On the other side of the globe, the people of Peru reckoned time from the day of the last cataclysm, and this method of computation was in use when the Europeans reached that country in the beginning of the sixteenth century.40
After the last cataclysm, the times and the seasons were computed anew. King Inti-Capac-Yupanqui ordered astronomical observations and calculations to be made, the result of which was a calendar re-38 Diogenes Laertius, Lives of Eminent Philosophers (English transl. R. D. Hicks, 1925).
39 Ibid.; see also Herodotus i. 74. 40 Brasseur, Manuscrit Troano, p. 25.
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form, and the year, previously of 360 days, "was changed to 365 days and 6 hours." "
"This Ynca appears to have been the first to order and settle ceremonies. ... He it was who established the twelve months of the year, giving a name to each, and ordaining the ceremonies that were to be observed in each. For although his ancestors used months and years counted by the quipus, yet they were never previously regulated in such order until the time of this lord." 42
robin-bobin
"All Toltec histories mention an assembly of sages and astrologers that was convoked in the city of Huehue-Tlapallan for the purpose of working on the correction of the calendar, and the reforming of the computation of the year, which was recognized as erroneous and which had been employed until that time." *3
Half a meridian away, across the Pacific Ocean, a calendar was introduced in Japan in —660, and the reckoning of years in that country starts from that year.
In China, the astronomer Y-hang in the year —721 announced to the Emperor Hiuen-tsong that the order of the sky and the movements of the planets had changed which made it impossible to predict eclipses; and he referred to other authorities who asserted that in the time of Tsin the planet Venus used to move 40 degrees to the south of the ecliptic and eclipse the star Sirius. Y-hang explained that the course of the planet Venus changed in the days of Tsin. **