The Jewish calendar on this system would have consisted of ordinary months, alternately 29 and 30 days in length. The intercalary months would have contained alternately 30 or 31 days, and once in every century one of the ordinary months would have had an additional day. Or, what would come to very much the same thing, this extra day might have been added at every alternate Jubilee. By combining these two numbers of Daniel some cycles of extreme astronomical interest have been derived by De Cheseaux, a Swiss astronomer of the eighteenth century, and by Dr. H. Grattan Guinness, and Dr. W. Bell Dawson in our own times. Thus, the difference between 2,300 and 1,260 is 1,040, and 1,040 years give an extremely exact correspondence between the solar year and the month, whilst the mean of the two numbers gives us 1,780, and 1,780 lunar years is 1,727 solar years with extreme precision. But since these are not given directly in the Book of Daniel, and are only inferential from his numbers, there seems no need to comment upon them here. It is fair, however, to conclude that Daniel was aware of the Metonic cycle. The 2300-year cycle gives evidence of a more accurate knowledge of the respective lengths of month and year than is involved in the cycle of 19 years. And the latter is a cycle which a Jew would be naturally led to detect, as the number of intercalary months contained in it is seven, the Hebrew sacred number. The Book of Daniel, therefore, itself proves to us that king Nebuchadnezzar was perfectly justified in the high estimate which he formed of the attainments of the four Hebrew children. Certainly one of them, Daniel, was a better instructed mathematician and astronomer than any Chaldean who had ever been brought into his presence. We have the right to make this assertion, for now we have an immense number of Babylonian records at our command; and can form a fairly accurate estimate as to the state there of astronomical and mathematical science at different epochs. A kind of "quasi-patriotism" has induced some Assyriologists to confuse in their accounts of Babylonian attainments the work of times close to the Christian era with that of many centuries, if not of several millenniums earlier; and the times of Sargon of Agadé, whose reputed date is 3800 B.C., have seemed to be credited with the astronomical work done in Babylon in the first and second centuries before our era. This is much as if we should credit our predecessors who lived in this island at the time of Abraham with the scientific attainments of the present day.