That the quadripartite division of the month should be practically non-existent among primitive peoples is easily to be understood in view of the considerations already mentioned. Unlike the halving it is not based upon any very clearly distinguishable phases, nor is there in the phases any such suggestion of a quadripartite division as is offered for a tripartite. The shape of the moon on the 8th or the 22nd day differs very little from that of the previous and the following days, and does not constitute a turning-point like the full moon. From the phases of the moon no quadripartite division can arise: the brightest phase of all, the full moon, has an unnatural position in such a division. It can only be understood as a halving of the halves of the month, and this presupposes that the moon’s variation in light is regarded as a unity and divided into parts. The primitive peoples however start not with the abstract unity but with the concrete phases, proceeding at first quite unsystematically, and only subsequently combining them into a system. The quadripartite division therefore is in its very nature a numerical system. That it has penetrated so profoundly into our natures that even ethnological scholars and travellers are not always able to get away from it, is due to the connexion with the seven-day week, which is regarded as a division of the month, and also to the fact that we so seldom take any notice of the concrete phenomena of the heavens. The quadripartite division must therefore be described as not original (the case is different when the time of the moon’s invisibility is added as a fourth phase to the three already mentioned). To the best of my knowledge it appears first in Babylonia[718], and gains ground together with the _sabattu_, i. e. the appointing of every seventh day of the month as tabooed: it has become common among us on account of the seven-day week, which was conceived as a division of the month. In reality the tripartite division is also the natural one, since it arises from the concrete phenomenon of the moon, and not from any division of the month into parts consisting of a certain number of days. Here the full moon takes its proper place, which it misses in the quadripartite division. The limitation of the divisions to a definite number of days is secondary throughout. CHAPTER VI. THE MONTHS.