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.

The system of time-reckoning, the continuous counting of the time-units, represents the final point of the development. It is our object to investigate the preceding stages, both systematic and unsystematic. Certain important ideas which frequently recur must however first be clearly set down. The time-reckoning in the proper sense of the term is preceded by time-indications which are related to concrete phenomena of the heavens and of Nature. Since these indications depend upon the concrete phenomenon, their duration fluctuates with the latter, or rather the duration does not stand out by itself but the phenomenon as such is exclusively regarded: the time-indication is not durative, like the link in any system of time-reckoning, but indefinite, or, to borrow a grammatical term, aoristic. And setting aside these finer distinctions we also find that the phenomena to which the time-indications are related are of fluctuating and very unequal duration. Since the duration is indeterminate and fluctuating, and the time-indications are not limited one by the other but overlap and leave gaps, they cannot be numerically grouped together. Here we ought really to speak not of a time-reckoning in the proper sense, but only of time-indications. But since the word ‘time-reckoning’ has become naturalised, this method may be described as the discontinuous system of time-reckoning, because the time-indications do not stand in direct relation to other time-indications but are related only to a concrete phenomenon, and through that to other time-indications, so that they are of indeterminate length and cannot be numerically grouped together.

If the number of dawns, suns, autumns, or snows that has passed since a certain event took place, or will elapse before a certain event is to take place, be indicated, the time that has passed or is to pass will be defined, because the dawn or the sun recurs once in the day, and an autumn or a snow, i. e. winter, once in the year. This is the oldest mode of counting time. It is not the units as a whole that are counted, since the unit as such had not yet been conceived, but a concrete phenomenon recurring only once within this unit. It is the pars pro toto method so extensively used in chronology, and by this name we shall call it[1].

Since it must now be regarded as the natural course of development that the systematic has gradually arisen out of the unsystematic, and that the indication of concrete phenomena following one another in the regular succession of Nature has preceded the abstract numerical indication of time offered by our calendars, the origin of the time-reckoning must be sought not in any one system, however simple, but in the discontinuous or pars pro toto time-indications which are related to concrete phenomena.

Our task is now to make clear the nature of these discontinuous and pars pro toto time-indications, since from them proceeds, as order is ever evolved out of chaos, the continuous time-reckoning, the calendar.

CHAPTER I.
THE DAY.

For primitive man the day is the simplest and most obvious unit of time. The variations of day and night, light and darkness, sleeping and waking penetrate at least as deeply into life as the changes following upon the course of the year, such as heat and cold, drought and rainy seasons, periods of famine and plenty. But for the primitive intellect the year is a very long period, and it is only with difficulty and at a later stage that it can be conceived and surveyed as a whole. Day and night, on the other hand, are short units which immediately become obvious. Their fusion into a single unit, the day of 24 hours, did not take place till later, for this unit as we employ it is abstract and numerical: the primitive intellect proceeds upon immediate perceptions and regards day and night separately.

Evidence for this fact is furnished by most languages, which are as a rule without any proper term for day and night together, the circle of 24 hours. In writing English one sadly misses the Swedish dygn, which has exactly the required significance. The German Volltag is an artificial and not very happy compound. The Greeks also formed a learned and rare (though good) compound, νυχθήμερον. The usual method is to make use of a term according to the pars pro toto principle. This principle, which we meet here at the outset and shall come across more and more frequently in the course of the following pages, is of great importance for the development of time-reckoning since it shews how the original time-indication is discontinuously related to a concrete phenomenon, and only slowly and at a later period develops into a continuous numerical unit of time.