Upon the above-mentioned units the system of time-reckoning will be based. The days are joined into months and the months into years; only more rarely are the seasons interposed as regular units of time. The system is like a chain the links of which run into one another without gaps: each link is equivalent, or as nearly as possible equivalent, to every other link of the same class, and therefore need only be given a name and counted, not necessarily conceived in the concrete, although this is not excluded. This is the only genuine system, a system of _continuous time-reckoning_, which excludes all gaps in the chain and all links of indeterminate length. The relation between the larger and the smaller units may be treated in various ways, chiefly on account of the fact that the smaller units do not divide exactly into the larger. Sometimes the smaller units may be fitted into the larger as subdivisions of the latter, so that they constitute the links of the chain formed by the larger unit. The inequality referred to shews then that the units vary to some extent in number or size (year of 365 or 366 days, of 12 or 13 lunar months, lunar month of 29 or 30 days). In that case the beginnings of the larger unit and of the first of the smaller units coincide. Thus in our year New Year’s Day and the first day of the first month coincide, but the length of the months varies somewhat. This is an inheritance from the lunisolar year, in which also New Year’s Day and the first day of the first month coincided and the length of the month varied between 29 and 30 days, but in addition the year varied between 12 and 13 months. This mode of reckoning, in which the smaller units are contained in the larger as subdivisions of them, will be termed the _fixed_ method. But where the smaller units do not exactly divide into the larger, both may also be counted independently of one another without being equalised. A case in point is our week, which is reckoned without reference to the year, so that every year begins with a different day of the week. This method of reckoning we shall term the _shifting_ method. It is less systematic than the fixed method, and we shall therefore expect to find it play a greater part in earlier times than at the present day.