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Olympiads by alternate periods of fifty and forty-nine lunar months,280 which added together make up eight solar years, seems to prove that the Olympic cycle of four years was really based on a cycle of eight years, from which it is natural to infer that in the beginning the Olympic, like the Pythian, games may have been octennial instead of quadriennial.281 Now we know from the testimony of the ancients themselves that the Greeks instituted the eight-years' cycle for the purpose of harmonising solar and lunar time.282 They regulated their calendar primarily by observation of the moon rather than of the sun; their months were lunar, and their ordinary year consisted of twelve lunar months. But the solar year of three hundred and sixty-five and a quarter days exceeds the lunar year of twelve lunar months or three hundred and fifty-four days by eleven and a quarter days, so that in eight solar years the excess amounts to ninety days or roughly three lunar months. Accordingly the Greeks equated eight solar years to eight lunar years of twelve months each by intercalating three lunar months of thirty days each in the octennial cycle; they intercalated one lunar month in the third year of the cycle, a second lunar month in the fifth year, and a third lunar month in the eighth year.283 In this way they, so to say, made the sun and moon keep time together by reckoning ninety-nine lunar months as equivalent to eight solar years; so that if, for example, the full moon coincided with the summer solstice in one year, it coincided with it again after the revolution of the eight years' cycle, but not before. The equation was indeed not quite exact, and in order to render it so the Greeks afterwards found themselves obliged, first, to intercalate three days every sixteen years, and, next, to omit one intercalary month in every period of one hundred and sixty years.284 But these corrections were doubtless refinements of a later age; they may have been due to the astronomer Eudoxus of Cnidus, or to Cleostratus of Tenedos, who were variously, but incorrectly, supposed to have instituted the octennial cycle.285 There are strong grounds for holding that in its simplest form the octennial cycle of ninety-nine lunar months dates from an extremely remote antiquity in Greece; that it was in fact, as a well-informed Greek writer tell us,286 the first systematic attempt to bring solar and the lunar time into harmony. Indeed, if the Olympiads were calculated, as they appear to have been, on the eight years' cycle, this of itself suffices to place the origin of the cycle not later than 776 b. c., the year with which the reckoning by Olympiads begins. And when we bear in mind the very remote period from which, judged by the wonderful remains of Mycenae, Tiryns, Cnossus and other cities, civilisation in Greek lands appears to date, it seems reasonable to suppose that the octennial cycle, based as it was on very simple observations, for which nothing but good eyes and almost no astronomical knowledge was necessary,287 may have been handed down among the inhabitants of these countries from ages that preceded by many centuries, possibly by thousands of years, the great period of Greek literature and art. The supposition is confirmed by the traces which the octennial cycle has left of itself in certain ancient Greek customs and superstitions, particularly by the evidence which points to the conclusion that at two of the oldest seats of monarchy in Greece, namely Cnossus and Sparta, the king's tenure of office was formerly limited to eight years.288

      The motive for instituting the eight years' cycle was religious, not practical or scientific.

      We are informed, and may readily believe, that the motive which led the Greeks to adopt the eight years' cycle was religious rather than practical or scientific: their aim was not so much to ensure the punctual despatch of business or to solve an abstract problem in astronomy, as to ascertain the exact days on which they ought to sacrifice to the gods. For the Greeks regularly employed lunar months in their reckonings,289 and accordingly if they had dated their religious festivals simply by the number of the month and the day of the month, the excess of eleven and a quarter days of the solar over the lunar year would have had the effect of causing the festivals gradually to revolve throughout the whole circle of the seasons, so that in time ceremonies which properly belonged to winter would come to be held in summer, and on the contrary ceremonies which were only appropriate to summer would come to be held in winter. To avoid this anomaly, and to ensure that festivals dated by lunar months should fall at fixed or nearly fixed points in the solar year, the Greeks adopted the octennial cycle by the simple expedient of intercalating three lunar months in every period of eight years. In doing so they acted, as one of their writers justly pointed out, on a principle precisely the reverse of that followed by the ancient Egyptians, who deliberately regulated their religious festivals by a purely lunar calendar for the purpose of allowing them gradually to revolve throughout the whole circle of the seasons.290

      In early times the regulation of the calendar is largely an affair of religion.

      Thus at an early stage of culture the regulation of the calendar is largely an affair of religion: it is a means of maintaining the established relations between gods and men on a satisfactory footing; and in public opinion the great evil of a disordered calendar is not so much that it disturbs and disarranges the ordinary course of business and the various transactions of civil life, as that it endangers the welfare or even the existence both of individuals and of the community by interrupting their normal intercourse with those divine powers on whose favour men believe themselves to be absolutely dependent. Hence in states which take this view of the deep religious import of the calendar its superintendence is naturally entrusted to priests rather than to astronomers, because the science of astronomy is regarded merely as ancillary to the deeper mysteries of theology. For example, at Rome the method of determining the months and regulating the festivals was a secret which the pontiffs for ages jealously guarded from the profane vulgar; and in consequence of their ignorance and incapacity the calendar fell into confusion and the festivals were celebrated out of their natural seasons, until the greatest of all the Roman pontiffs, Julius Caesar, remedied the confusion and placed the calendar of the civilised world on the firm foundation on which, with little change, it stands to this day.291

      The quadriennial period of games and festivals in Greece was probably arrived at by bisecting an older octennial period.

      On the whole, then, it appears probable that the octennial cycle, based on considerations of religion and on elementary observations of the two great luminaries, dated from a very remote period among the ancient Greeks; if they did not bring it with them when they migrated southwards from the oakwoods and beechwoods of Central Europe, they may well have taken it over from their civilised predecessors of different blood and different language whom they found leading a settled agricultural life on the lands about the Aegean Sea. Now we have seen reasons to hold that the two most famous of the great Greek games, the Pythian and the Olympian, were both based on the ancient cycle of eight years, and that the quadriennial period at which they were regularly celebrated in historical times was arrived at by a subdivision of the older octennial cycle. It is hardly rash, therefore, to conjecture that the quadriennial period in general, regarded as the normal period for the celebration of great games and festivals, was originally founded on elementary religious and astronomical considerations of the same kind, that is, on a somewhat crude attempt to harmonise the discrepancies of solar and lunar time and thereby to ensure the continued favour of the gods. It is, indeed, certain or probable that some of these quadriennial festivals were celebrated in honour of the dead;292 but there seems to be nothing in the beliefs or customs of the ancient Greeks concerning the dead which would suggest a quadriennial period as an appropriate one for propitiating the ghosts of the departed. At first sight it is different with the octennial period; for according to Pindar, the souls of the dead who had been purged of their guilt by an abode of eight years in the nether world were born again on earth in the ninth year as glorious kings, athletes, and sages.293 Now if this belief in the reincarnation of the dead after eight years were primitive, it might certainly furnish an excellent reason for

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