regulation of the calendar[1187]. On the other hand the priests also have observed the stars and used their stellar science principally for sooth-saying, as e. g. in Hawaii and in Babylonia. But neither does this lead to any improvement of the calendar, since the religion must keep to the existing lunisolar calendar, although in one case of the most far-reaching importance the astrology arose from it. The improving of the calendar, the object of which must be, after the full development of the lunisolar, to return to the solar calendar, in order that the calendar may be better adapted to the needs of practical life, becomes henceforth the task of the lay scientific astronomer. CHAPTER XV. CONCLUSION. 1. SUMMARY OF RESULTS. _The concrete nature of the time-indications._ Any genuine system of time-reckoning must admit of numerical treatment, i. e. it must consist of divisions of which the length is strictly limited and which, when they belong to the same order, are as far as possible of the same length. A numerical conception is abstract and not primitive; even the power of counting is little developed among primitive peoples in general, and among the lowest peoples it is extremely limited. Counting is abstract, the primitive man clings to the concrete phenomena of the outer world. In matters of chronology, therefore, he finds his way not by counting but by referring to the concrete phenomena the recurrence of which in definite succession experience has taught him to expect. The first time-indications are therefore not numerical but concrete. Their character clearly appears e. g. when ‘a sun’ is said for ‘day’, and ‘a sleep’ for ‘night’; the hours of day are denoted by the concrete phenomena of the twilight, dawn, sunrise, etc., and the equally concrete position of the sun or the occupations of the day. The lunar month is usually called ‘a moon’, and its days are denoted by the phases and position of the moon. The year is originally neither a period of time nor the circle of the seasons (which is first gradually developed under the influence of agriculture in particular), but the produce of the year: e. g. it embraces the time between sowing and harvest, and is often not a complete year in our sense. Only gradually does the year develop into the period of time that elapses between a season and the recurrence of the same season, or more rarely between a phase of a star and the return of the same phase. From the latter period the genuine solar year has arisen. The seasons are composed of occupations and of climatic and other natural phenomena, and still preserve this concrete relationship and are therefore not definitely limited in duration. This relationship is also extended to the moons, which for their determination are not numbered but are brought into connexion with a natural phase and named accordingly, so that the twelve to thirteen months of the year can be fixed as regards position and succession.