Any further advance can only be made by way of hypothesis. Thus the sabbath of the times before the Exile was either, as later, the last day of a seven-day period that was shifting in relation to the lunar month, or else it was something different. Both statements are hypotheses. And if it was something different we are driven to a still further hypothesis in order to decide what it was. The suggestion most in favour is that it was the day of full moon. The sabbath is said to be the second principal day of the course of the moon simply because sabbath and new moon are always mentioned together in the days before the Exile. But this obviously proves nothing. It has further been stated that the sabbath must be a fixed day of the lunar month, since otherwise it would sometimes coincide with the day of new moon; but evidently the expression ‘new moon and sabbath’, however formally interpreted, does not in itself exclude such a coincidence. Further sabbath and _shabattu_ are the same word, and consequently a second hypothesis is that ‘sabbath’ as well as _shabattu_ means the day of full moon. The proof is only binding if the word in itself must mean ‘full moon’; the etymology however is disputed, so that it gives no help. It is not difficult to establish a general fundamental sense which will fit in both with the festival-day of full moon and of the seven-day period. On the ground of the researches here carried out, however, we may put a question a satisfactory answer to which is demanded by the hypothesis just mentioned:--How is it possible for a period which forms a fixed subdivision of the lunar month to become detached from the moon and be made into an independent period shifting in relation to the lunar month? And there will still be a preliminary question to get rid of, viz. how has the septenary period arisen from the day of full moon, the 15th day of the month? The answer will be, I suppose, that the 14th, not the 15th, was taken as the day of full moon and that Babylonian influence introduced the septenary division, so that the name of one of the septenary days, the 14th, has been carried over to the rest. But since in the legislation of the Exile the great festivals were appointed for the 15th, it is clear that this day, and not the 14th, was at that time taken as the day of full moon. The question whether any late Babylonian speculation in numbers may have exercised a determinative influence upon the Jewish legislation must be decided by experts. From the unsatisfactory answer to the preliminary question I return to the main question. A shifting reckoning of this kind can only be understood chronologically as a breaking away from the concrete phenomena of Nature, an incomplete calculation being established instead of the empirical observation, as was the case, for instance, with the Egyptian shifting year, put in place of the solar year, and bringing with it months of thirty days in the place of lunar months.