Just as our mathematicians find no difficulty either in foretelling or retrospecting eclipses to a minute, so does the ancient "sixty" cycle, which the Chinese have from time immemorial used for computing or noting days and years, enable them, or for the matter of that ourselves, to calculate back unerringly any desired day. Thus, suppose the 1st January, 1908, is the 37th day of the perpetual cycle of sixty days; then, if the Chinese historians say that an eclipse took place on the first day of the new moon, which began the 9th Chinese month of the year corresponding in the main to our 800 B.C., and that the 1st day of the moon was also the 37th day of the sixty-day perpetual cycle, all we have to do is to take roughly six cycles for each year, six thousand cycles for each thousand years, allowing at the same time two extra cycles every third year for intercalary moons, and then dealing with the fractions or balance of days. If our calculation does not bring the two 37th cyclic days together accurately, we must of course go into the question of how and when the Chinese calendars were altered, a subject that will be treated of in a subsequent chapter. It must be remembered that there can never be any question of so much as a whole year being involved in the balance of error; for, with the Chinese as with us, one year, whenever modified, always means that space of time, however irregularly computed at each end of it, within which two solstices and two equinoxes have taken place, Voltaire, in the article on "China" of his Universal Dictionary, remarks that "of 32 ancient Chinese eclipses, 28 have been identified by Western mathematicians"; and M. Edouard Chavannes, who has given a great deal of time and labour to working out the mysteries of the Chinese calendar, does not hesitate to claim accuracy to the very day (29th August) for the eclipse of the sun recorded in the Book of Odes (as re-edited by Confucius) as having taken place on the 28th cyclic day of the beginning of the both moon in 776 B.C. (i.e. of--775). This eclipse is of course not recorded in the "Springs and Autumns," which begins with the year 722 B.C. The Chou dynasty, which came into power in 1122, for the second time put back the year a month because the calendar was getting confused. That is, they made what we should call January begin the legal year instead of February; or the still more ancient March; but some of the vassals either used computations of their own, or kept up those handed down by the two dynasties previous to that of Chou: hence in the Confucian histories, as expanded, there are frequent discrepancies in consequence of events apparently copied from the records of one vassal state having been reported to the historian of a second vassal state without steps having been taken to adjust the different new years. CHAPTER VI THE ARMY