The Semites brought about the necessary adjustment, not by leap-years, but by the insertion of an additional month. For example, eight solar years have a total of 2920 days, not counting the addition days of leap years. The same number of days make up ninety-nine lunar months, or, in other words, eight lunar years and three intercalary months, are equal to eight solar years. Thus, in eight years, three additional months must be introduced, making the number of days almost equal with the days of eight solar years, except for a small discrepancy, caused by the additional day in leap year. When these additional days had reached the number of thirty, they could be accounted for by the introduction of a further additional month. In regulating these points, the equinoxes were of the utmost importance, and, in the second place, the ceremonial oblation of the first fruits. If it was evident that the month Nisan would terminate before the vernal equinox—its beginning and middle had to precede the equinox, as well as the _quarta decima lunæ_—and if the barley was not in ear by the 14th, then it was considered the discrepancy had to be set right. This was done by prolonging the last month of the expiring year, Adar, for twenty-nine days longer than usual. In other words, an additional month was added to the year, designated merely as Veadar. This was the intercalary month. This, happening thrice in eight years, brought the lunar and solar years into agreement by a very simple expedient. The equinox could be controlled by help of the Zodiac, for, on the 20th March, the sun enters Aries, and, on the 23rd September, Libra. Had the Jews followed out this method scientifically, _i.e._, had the introduction of the intercalary months followed fixed laws and been ruled by astronomical observations and calculations, then, though still difficult, it would have been possible to make the Jewish Calendar synchronise with others. But the introduction of these additional days was, so to speak, arbitrary and dependent upon the good pleasure of the priests. Thus we can never say for certain that such and such a year was a leap year with the Jews, and accordingly no date in the past can with certainty be made to synchronise with a date in the Julian or any other Calendar.[106]