Hitherto we have observed the division of the month into small and the smallest phases of the moon, in which three or at most four days have the same name, and are numbered in order that they may be distinguished. Other peoples count the days beginning at the principal moon-phases. The Central Eskimos can determine the days of the month very accurately from the age of the moon[699], the terms are unfortunately not given. So also for the Kaigan of N. W. America names of the nights reckoned from the phases of the moon are quoted; unfortunately only very confused and inaccurate information could be obtained, and only 14 names are given:—1, new moon; 2, ‘second sleep’, etc., up to 9, full moon or ‘great moon’, the third night after which is ‘the first night after the full moon’[700]. For the inhabitants of southern Formosa the bare and therefore almost useless statement is made that they reckon according to the age of the moon[701]. Of the Wagogo of what was formerly German East Africa we are told that the phases of the moon and the numbers of the nights serve as more accurate determinations of time. For instance, the third night after the next appearance of the moon will be the day following the third night after the moon’s appearance, and therefore the fourth of a month, since the crescent is visible exactly on the first day of a month[702]. Unfortunately we are not told what phases, other than the new moon, serve as starting-points for the reckoning. The same remark applies to an account for Sumatra. The Central Sumatran Expedition has proved that names for days of the week and for months are unknown among the Rawa and the Djambi Kubu of Djipati Mando. The people count by the phases of the moon, and say e. g. the 1st, 2nd, 3rd day of the moon[703].
These accounts are unfortunately of little use, since they say too little about the method of the counting. Even when a complete list of the days or nights of the month does seem to be forthcoming (the Wagogo, the Kubu), it generally happens that the counting proceeds from several starting-points, so that the month is divided up into smaller divisions. This is natural, since primitive peoples not only possess small capacity for counting but also prefer to keep the concrete phenomenon in view. It has already been pointed out that the counting frequently begins at the two most prominent phases, the new and the full moon; by this means the month is divided into the two corresponding halves of the waxing and the waning moon, or in respect of the appearance or non-appearance of the moon in the evening and early night into the light and the dark halves. The difference between these halves follows from direct observation of nature, and they are therefore known even to peoples which do not count the days, e. g. the inhabitants of Buin[704], the Germanic tribes, and others. In Swedish the distinction between ny and nedan, i. e. the time of the waxing and of the waning moon, is still known. The Masai, besides a full list of the days of the month, have a second reckoning according to the light and the dark halves of the month[705]. The Hindus and the civilised peoples of S. E. Asia reckon in the same way: of these systems of time-reckoning the Hindu has exercised a powerful influence. Avesta shews the same reckoning. In the old Gallic calendar of Coligny each month is divided into two sharply distinguished halves. The Romans indeed, in the form of their calendar known to us, reckoned so many days before the Kalends (the first day of the month), the Nones (the 5th or 7th), and the Ides (the 13th or 15th), but before their calendar settled into its curious and quite irrational historic form the Kalendae must have been the day of the new moon, which was publicly proclaimed, and the Idus the day of full moon. The Nonae are secondary: the word simply means the ninth (day), i. e. before the Ides, which position the day occupies in the inclusive reckoning employed. The Greek reckoning in decades is well-known, but in earlier times a bipartite division of the month appears. Homer divides the month into ἱστάμενος and φθίνων (‘rising’ and ‘fading’), Hesiod once mentions a ‘thirteenth day of the rising moon’[706].
We have seen above how to the phases of the new and the full moon that of the waning moon is added as a third. When the gradual development of the moon is regarded—as is done when numbers are used—and not the particular shape of it appearing on a certain day, we also get three periods, since between the waxing and the waning occurs the full moon, and this, although not in the strictest sense, lasts longer than a day, and unlike the waxing and the waning moon remains in the sky the whole night long. The time of full moon therefore appears as a third independent period between the waxing and the waning. The impulse to a tripartite division hereby given clashed with the decimal system of enumeration of most peoples; as a rule the counting was suspended at the basal series of numbers. In this manner we may account for the not uncommon phenomenon that only ten months are numbered, the two others being called by special names[707]. Thus arises the division of the month into three decades, in which however the last decade may vary between 9 and 10 days.
The division into decades is not so common as the halving of the month. The Zuñi of Arizona divide the month into three decades, each of which is called a ‘ten’[708]. The Ahanta of the western Gold Coast divide the moon-month into three periods, two of ten days each, the third—which lasts until the new moon appears—of about 9½ days (more correctly, no doubt, varying between 9 and 10 days). The Sofalese of East Africa must have done the same, since de Faria says that they divided the month into 3 decades and that the first day of the first decade was the feast of the new moon[709]. The Masai, who number either the days of the whole month consecutively or the days of its two halves, nevertheless give special prominence to the initial days of the decades (alongside of other notable days), and call them negera[710].
Among the Greeks the division into decades displaced the older bisection. Of the names of the decades the first and third refer to the concrete form of the moon: μὴν ἱστάμενος, older ἀεξόμενος[711], literally ‘the appearing, waxing moon’, and μὴν φθίνων, ‘the waning moon’. For originally μήν must here have had the sense of ‘moon’ which the etymology suggests. The second decade was called μὴν μεσῶν, ‘the month at the middle’: the epithet shews that μήν here means ‘month’, and not ‘moon’. This name is therefore younger than the two others, which must once have been used to describe the two halves of the month, and do so still in Homer[712].
The custom of reckoning on the fingers or on a notched stick has doubtless lent assistance to the counting of the days of the month. The Wa-Sania make a notch in a stick for every day, and when the month is ended they put this stick aside and begin a new one[713]. At the southern corner of Lake Nyassa the days are counted by means of pieces of wood threaded on a string[714]. A complete enumeration of the days however only exists among highly developed peoples who have discarded a more concrete time-reckoning in favour of an abstract system, just as the civilised peoples of modern Europe abandoned the Roman system of time-reckoning, which was still often used in the Middle Ages (though indeed it had long since departed from its concrete basis), in favour of a simple enumeration of the days of the month.
Finally a couple of curious East African reckonings of the days of the month are to be mentioned, although they are not primitive but have a lengthy development behind them. A common feature of both is that the day of the new moon is already the fourth day, so that the counting of the days begins with the moon’s invisibility, which can hardly have been the original practice. The Wadschagga divide the month into four parts the days of which are numbered, the first and third parts consisting of ten days each, and the second and fourth of five days each. Accordingly they begin to count the new moon at ‘the fourth day, which brings the moon’, the day on which the slender delicate crescent of the moon first reappears after sunset: for the rites of this day see [above, p. 153]. On the fourth day of the second division (the eleventh after new moon) they say that ‘the moon turns to the back of the house’: when twilight falls it is already seen beyond the culmination-point. The fourth day of the third division (the 16th after new moon) is called ‘the day that brings the moon up from below’ (i. e. from the eastern horizon), where ‘it appears like a pot’; the fourth day of the last division is called ‘the four, which dismisses the moon’, and the first of the first division, when the moon vanishes, ‘the one, which floats away the moon so that it is no longer visible’: it ‘tramples into pieces the days of the God’[715]. The natural phases of the moon therefore make themselves felt in spite of the counting. With this, as is so often the case, is connected a fully developed superstition concerning the days of the month. The Masai in ordinary life reckon their moon-months as consisting of 30 days, and number the days from 1 to 30 or 29. Besides this there is a second way of counting which begins at the 16th and reckons the days of darkness (en aimen). Further, special prominence is given to certain days and groups of days, e. g. to the 4th, the new-moon day, hence called also ertaduage duo olaba, ‘the moon is to be seen’, to the 15th, ol gadet, i. e. the rising moon ‘looks over’ to the sun which has not yet set, and to the concluding day, the eng ebor olaba, ‘the brightness of the moon’, but especially to the days of the dark half of the month, en aimen. The 16th is called ol onjori, ‘the greenish day’, the 17th, ol onjugi, ‘the red’, 18 to 20, es sobiaïn, 21 to 23, nigeïn, 27 etc., en aimen nerok, ‘the black darkness’. The people also emphasise the concluding days of the decades[716]. The natural foundation afforded by the phases of the moon therefore appears very clearly: the only noteworthy feature is that the days of the moon’s invisibility are included in the division which is called ‘the brightness of the moon’. An outside influence must no doubt be assumed. Among the Masai also the selection of lucky and unlucky days is common.
The starting-points in the counting of the days of the month also afford evidence for the question as to which phases of the moon are the oldest, and were already utilised for this purpose. Both the methods of counting and the phases themselves are based upon a bisection or trisection of the month: to this were then added other phases, originally quite unsystematically. Among us the quarters of the moon are common; but of their use among primitive peoples I have found only a single instance. Of the Papuans of the Indian Archipelago it is stated that they divide the month into four parts according to the phases of the moon: paik baleo, the new moon, paik jouwar, the first quarter, paik plejif, the waning of the moon, and paik imar, the old moon[717]. It must not, of course, be taken for granted that these phases are of equal length, as ours are.
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.