(M265) Thus we infer with some probability that the sacred Twelve Days or Nights at midwinter derive their peculiar character in popular custom and superstition from the circumstance that they were originally an intercalary period inserted annually at the end of a lunar year of three hundred and fifty-four days for the purpose of equating it to a solar year reckoned at three hundred and sixty-six days. However, there are grounds for thinking that at a very early time the Aryan peoples sought to correct their lunar year, not by inserting twelve supplementary days every year, but by allowing the annual deficiency to accumulate for several years and then supplying it by a whole intercalary month. In India the Aryans of the Vedic age appear to have adopted a year of three hundred and sixty days, divided into twelve months of thirty days each, and to have remedied the annual deficiency of five days by intercalating a whole month of thirty days every fifth year, thus regulating their calendar according to a five years’ cycle.(781) The Celts of Gaul, as we learn from the Coligny calendar, also adopted a five years’ cycle, but they managed it differently. They retained the old lunar year of three hundred and fifty-four days divided into twelve months, six of thirty days and six of twenty-nine days; but instead of intercalating twelve days every year to restore the balance between lunar and solar time they intercalated a month of thirty days every two and a half years, so that in each cycle of five years the total number of intercalary days was sixty, which was equivalent to intercalating twelve days annually. Thus the result at the end of each cycle of five years was precisely the same as it would have been if they had followed the old system of annual intercalation.(782) Why they abandoned the simple and obvious expedient of annually intercalating twelve days, and adopted instead the more recondite system of intercalating a month of thirty days every two and a half years, is not plain. It may be that religious or political motives unknown to us concurred with practical considerations to recommend the change. One result of the reform would be the abolition of the temporary king who, if I am right, used to bear a somewhat tumultuary sway over the community during the saturnalia of the Twelve Days. Perhaps the annually recurring disorders which attended that period of license were not the least urgent of the reasons which moved the rulers to strike the twelve intercalary days out of the year and to replace them by an intercalary month at longer intervals.