Several sources give the words in which the qalammas made known the re-distribution: they are affected by later views but must contain a kernel of truth, since they shew difficulties which are not even noticed by the authorities. According to Kalby the expression runs simply:—“The safar of this year is declared holy”, or “free”; according to Ibn Ishaq:—“O God, I declare one of the two months called safar, namely the first, to be free, and I postpone the other till next year.” What is meant by postponing safar II until the next year is unexplained and unexplainable. Since the year begins with safar I, and the proclamation takes place in dhu-l-hijja, safar II already belongs to the next year. Safar II is in itself not holy, so that here there can be no question of a changing of the holy character of the month. But if by the expression safar safar I is understood, matters become clear. Safar I is doubled: I a is an intercalary month, and therefore not holy, and belongs as a thirteenth month to the current year; I b begins the new year and is holy. “I remove safar (viz. I b) to next year” is an incorrect but intelligible way of saying that the new year begins with this month. In the Qâmûs the expressions runs:—“O God, I am authorised to move the months or to leave them in their places and confirm them, and none can blame me or put me to my defence. O God, I declare the first safar to be free, and the second holy. The same do I determine in respect of the two rajab, namely rajab and sha’ban.” The first sentence, if authentic, doubtless refers to an intercalation, since the words are ‘move the months’, and not ‘the holy character of the months’; but we can hardly insist so far upon the expression. The last sentence is more conclusive. It shews, namely, that not only was safar I shifted to safar II, but at the same time rajab was moved to sha’ban. This is a system, not an incidental expedient to render possible a military expedition in a holy month. Later authorities add that the holy character of safar was moved to rabi I, and that the process went on from month to month until every month in the year had at one time or another been declared holy. How this is to be understood is shewn by the oldest report which has been handed down to us. It comes from Modjahid, who was born in the year 21 of the Hegira. “The heathen were accustomed in every month of the lunar year to go on pilgrimages for only two years.” It must be realised that in the course of a cycle of 33 years a month of the lunar year will coincide two to three times, according to the series, with one and the same month of the lunisolar year, and that the months of the Mohammedan lunar year and of the old Arabian lunisolar year, which must once have existed, have the same names. Modjahid’s statement can only be understood thus: that the heathen pilgrimage was re-arranged every third year in relation to the Mohammedan lunar months—two years is a rough approximation for ‘sometimes two, sometimes three years’—because it was to be kept in place in regard to the solar year. But the pilgrimage took place in a definite month, and therefore the months also belonged to a lunisolar year. If the months of the lunisolar year are compared with those of the lunar year confusion results, since both series have the same names. Let us take, for example, a sentence of the distinguished chronologist Albiruni, who represents the opinion that nasî means the intercalation of a month: “The first intercalation applied to muharram, in consequence safar was called muharram, rabi I was called safar, and so on; and in this way all the names of all the months were changed. The second intercalation applied to safar; in consequence the next following month (rabi I, the original rabi II)[915] was called safar, and this went on till the intercalation had passed through all twelve months and returned to muharram.” When other writers, not so well trained in chronology, say that the hallowing of the month was transferred from muharram to safar and from safar to rabi I, this means that, according to the year, the safar or rabi I of the lunar year corresponds to the muharram of the lunisolar year. When in the speech of the qalammas, safar I and rajab are simultaneously shifted to the month following in each case, this involves the shifting of the whole series of months. A genuine intercalation therefore takes place. The term nasî, ‘to push aside’, resembles the world-wide description of the intercalation of the month. Safar I is ‘forgotten’, but upon this it follows that not this month is holy, but the following one, which is now also called safar I but corresponds to safar II of the strictly lunar year. The sanctity or non-sanctity of the months was for the people the all-important point, and the qalammas, who was a religious authority, was obliged to refer to it. Hence he declared the month as free and the following month as holy without expressing himself, as we should have wished, in the technical terms of chronology. The people understood him: if the month after dhu-l-hijja was free, it followed that not this month but the next was holy, the month with which the new year began, safar I. The intercalation therefore involves a transference of the sanctity of the month following the feast of pilgrims to the next but one after the feast. Hence has arisen the misunderstanding that the nasî consisted only in a transference of the sanctity of the months.
The tribe of Kinana, to which the qalammas belonged, inhabited the district around Mecca, and the famous tribe of the Koraish, its most distinguished branch, was supreme in Mecca[916]. The calendar regulation therefore took place in the interests of Mecca and its trade, and it is quite ridiculous to say that the sanctity of a month was transferred to another merely in order to render possible a predatory excursion. Besides this would make matters no better, since all the tribes concerned would have to have peace or war in the same months. A shifting of this nature would only be really effectual if it offered a means of surprising an unsuspecting neighbour in time of peace. Probability therefore also points to the view that the nasî was a genuine intercalation carried out by a person appointed for the purpose, so that the dates of the markets and the pilgrimage might be fixed at the proper times of the year. For this no intercalary cycle was employed, any more than elsewhere: the empirical intercalation sufficed, and it was made known to the people at the feast of pilgrims, whence the knowledge spread all over. However the entrusting of such power over the calendar to one individual lends itself only too easily to abuses with a view to ends which have nothing to do with the calendar. The stock example is afforded by the Roman pontifices at the end of the Republic. It is therefore nothing to wonder at that the calendar should have been disorganised during Mohammed’s stay in Mecca. Hence also the attempts at determining the calendar from two or three certainly known dates are vain, for when a system is lacking or is broken up it is impossible to compute a calendar systematically from a couple of dates. Mohammed’s action is thus to be explained:—The misuse of the intercalation had destroyed the dependence of the pilgrimage upon the time of the year: Mohammed wished to create order, and did so in radical fashion by forbidding the intercalation, the misuse of which he saw, but the usefulness of which he failed to recognise.
It has been pointed out above that the Sumerian months completely correspond in character to those of the primitive peoples[917]. The establishing of the months in their definite places followed originally from the reference to the seasons, not from the position in the series of months. The seasons on their part were, as always, brought into relation to the phases of the stars. There is indeed little information as to this point, but what little there is is sufficient to establish it. It is however much to be desired that specialists should pay more attention to the matter and if possible procure more information. The Pleiades are brought into connexion with the annual inundations, which took place about the time of the invisibility of these stars, i. e. between their evening setting and morning rising[918]. The name of the constellation Virgo means ‘root of the sprouting wheat-stalk, or corn’, that of the star Spica ‘proclaimer of the sprouting wheat-stalk’. These names agree with the evening rising of this constellation, which at the date 2,000 B. C. took place about the 28th of February of our modern calendar, and with the morning setting, which took place some 16 days later. Circumstances exclude the ripening, which took place in the second half of April.[919] Consequently the months were also determined by the phases of the stars: among the names of months there is one which points to this fact, ‘the month in which the white star (bar-zag) sinks down from the culmination-point’[920]. The naming of the months from the stars has not been carried through consistently, but each month, just as e. g. among the Maoris, was fixed by one or more risings of stars. There are several lists in which now one, now two, or even three of the fixed stars are assigned to each of the twelve months[921]. In the Creation epic, Tablet V, 4 ff., we read:—“For twelve months he set down three constellations, according to the times of the year fashioned he the groups of stars.” Among the Maoris all the stars suitable to the time in question are used in the fixing of the month: in Babylonia there was probably a gradual limitation to the stars of the ecliptic, i. e. the 12 signs of the zodiac, the number of which points to the fact that they owe their origin to the endeavour to fix the twelve months astronomically[922]. This is an important advance of Babylonian stellar science, that the constellations of the ecliptic should be separated from the others. Weidner, p. 21, inverts matters when he says, with reference to a list in which, instead of the fainter constellations of the zodiac, neighbouring bright stars are given (e. g. Sirius instead of Cancer):—“The system of the paranatellonta is also found already, i. e. the system which allows neighbouring bright stars or constellations to step in instead of less bright constellations of the zodiac. But this is no longer primitive astronomy, it marks rather, as Weissbach has already pointed out with reference to Newcomb-Engelmann, the beginnings of a scientific astronomy.” On the contrary, as the examples from the primitive peoples shew, in the utilising of stars to fix a point of time or a month no notice is originally taken of the position of the star within or without the ecliptic, but the most easily recognisable stars and constellations are naturally preferred, wherever they may be situated. A list of fixed stars which determine months, including also stars situated outside the ecliptic, is primitive; it is out of the question that a constellation outside the ecliptic is referred to instead of a sign of the zodiac in the proper sense—that in which the constellations of the zodiac are to be regarded as the prius. After the signs of the zodiac have been fixed, so that a systematic duodecimal division of the year has been obtained, the stars situated outside the ecliptic are compared with the signs of the zodiac in order to indicate with accuracy to which month they belong, or in other words the system of the paranatellonta is found.
It is indispensable to enter into the all-important question of the intercalation, but here opinions are so directly opposed to one another that Weidner establishes a very accurate 38-year intercalary cycle as early as the time of the dynasty of Ur, while Kugler denies the existence of any intercalary cycle before the year 528 B. C.; Kugler again publishes a document in which an intercalary rule is recognised as dating from a time after 504 B. C.[923], while Weidner regards this as a copy of a much older original. An impartial opinion can only be arrived at by working through the material, and this is impossible for anyone who is not an Assyriologist: I am all the more compelled, therefore, to limit myself to suggestions and to the comparison with primitive conditions[924].
Where surplus months exist, there is no intercalation in the proper sense, although the same name, e. g. the ‘harvest month’, will recur sometimes after 12, sometimes after 13 months, since owing to the fluctuating and unstable nature of the naming of the months the latter are distributed according to circumstances[925]. This covers the difficulty. Such seems to have been the state of affairs in the pre-Sargonic period at Lagash. Certainly Kugler (II, 216) has tried to demonstrate intercalary years: this is possible in the sense given above, but actually very uncertain, since the starting-points for the arrangement of the months are anything but certain[926]. Only the arising of a fixed series of months makes a genuine intercalation possible, since as a rule the general custom is to intercalate a definite month (in Babylonia, at least later, there were two such months, adarru and ululu). The process is either an omission of one month in the series of thirteen, or an intercalation of one month in the series of twelve. The former appears in Lagash in the time of Sargon, the latter in the time of Dungi. We have found that the intercalation among the primitive peoples takes place as need arises. If the series of months is fixed, but the intercalation is neglected, the months must get out of place in relation to the seasons: this can be demonstrated in a couple of cases. So if the translation of the name of the fourth month in the list from Lagash is correct—šu-kul-na, ‘sowing month’—the harvest month, še-kin-kud, is the twelfth, and is therefore at a distance of eight months instead of the five which the natural conditions shew[927]. Further the list at the time of Dungi shews a disarrangement of the months as compared with the Sargonic list, the tenth month having dropped out and the following months being now pushed one place forwards. This difference can be explained either by a neglect of the intercalation, or by the fluctuating nature of the nomenclature: in the latter case there is really no genuine intercalation.
At the time of Dungi and his successors we have documentary evidence for a number of years with intercalation.[928] At this date Kugler stoutly denies and Weidner supports the existence of an intercalary cycle. Weidner says:—“If we denote Dungi 39 (the 39th year of his reign) by I, the following years are proved by documents to contain intercalary months:—II, V, XI, XIV, XVI, XVIII, XX, XXIII, XXVI, XXIX, XXXII, XXXV, XXXVIII. But between Dungi 43 and 49 there is at least one more leap-year to be added, most probably Dungi 46, i. e. VIII. For the period of 38 years we should then have 14 intercalary months attested. This is therefore an intercalary system that works quite well. A 19-year intercalary cycle however it cannot be, since in that case, corresponding to the former part, the years XXI, XXIV, etc. in the latter would have to be leap-years. We have therefore to assume a 38-year intercalary cycle, which in perfection far surpasses that of 19 years. It is the half of the well-known 76-year cycle of Callippus.” The conclusion is unwarrantable from the premises. For the intercalation which takes place just as need arises keeps the months firmly in their place in the solar year, and attains the same result as an intercalary cycle. A period of 76 Indian years will contain just as many months as a Callippean cycle. The only conclusive factor therefore is the periodicity, and this is not proved. Through an accident of tradition the leap-years are known for a period of 38 years, and it is obvious that during these 38 years an empirical intercalation, regularly carried out, kept the lunisolar year in order. The evidence that even under the Hammurabi dynasty no intercalary cycle existed is given by Kugler[929].
But there is also direct evidence that the intercalation took place empirically, i. e. as need arose. Ungnad has shewn this from a comparison of the known leap-years. Best known of all is the letter of Hammurabi to Siniddinam:—“Since the year has a deficiency, let the previous month be entered as Elul II. And instead of bringing the taxes on the 25th Tishritu to Babylon, let them be brought to Babylon on the 25th Elul II”[930]. For the empirical correcting of the position of months the stars are used among the primitive peoples, and so also in Babylonia. A tablet in the British Museum[931] gives the following injunction:—“The constellation dilgan rises heliacally in the month nisan. As often as this constellation remains invisible, its month shall be forgotten”. The same injunction is given in regard to other constellations from which months are named. The expression that the month Nisan is to be ‘forgotten’ reminds one of the description of the intercalary month as the ‘lost’ or ‘forgotten’ month among certain tribes of N. American Indians, and of the expression of the Masai. The forgotten month is not the intercalary month in our sense, i. e. not the second of two months that have arisen by doubling; it is the first. This month must be passed over, not counted, forgotten, its name must be transferred to the following month, so that the year may run properly. The establishing of the months by means of phases of the stars is so abundantly demonstrated for primitive peoples in the preceding pages that no words need be wasted in describing the method of its carrying out. It is a method that works perfectly well but is entirely empirical, and where recourse is had to this method we know that the regulation by a definite intercalary cycle does not exist. With a more extended development of the method a still better result can be obtained, and this is the direction that the Babylonians have taken. The regulation runs:—“If on the first day of the month nisannu the constellation of the Pleiades and the moon are together, the year shall be an ordinary one. If on the third day of the month nisannu the constellation of the Pleiades and the moon stand together, the year shall be a full one (i. e. a leap-year)”[932]. The meaning and effect of this rule are explained by Schiaparelli. But this too is an empirical rule, aimed at an empirical, not a cyclical, intercalation. Where an intercalary cycle exists, no such rule is needed.
Since by the letter of Hammurabi it is indisputably established that the intercalation took place not in years previously determined but at the command of the king, those who in spite of this would maintain the existence of an intercalary cycle hold to the assertion that the 27-year intercalary period was not a strictly fixed but a free cycle. In other words the intercalation rule only runs:—“Within a period of 27 years 10 intercalary months are to be inserted, but the choice of the leap-years is left open to the astronomer”[933]. But this is nothing less than an abandonment of the intercalary cycle. The purpose of such a cycle is to render it possible to compute the calendar beforehand for any number of years to come, and this purpose is frustrated by a regulation of this kind. It only says that in x years y intercalary months occur: this is not a rule for intercalation but an empirical observation, which readily results from a proper treatment of the empirical intercalation. Such observations must have been made by the Babylonians. In a tablet published by Kugler it is said of Saturn and of the fixed star kak-si-di, respectively, “ ... the period of the visibility of Sirius amounts to 27 years. Turn back and consider day after day,” according to Weidner, p. 73; according to Kugler I, 47 the inscription runs, “Day by day ... shalt thou see (the same phenomena as 59, or 27, years before).” Both Kugler and Weidner find here a 27-year intercalary cycle regulated by the star; the former places it before 533 B. C., the latter at a considerably earlier period. But in accordance with what has here been said about the empirical regulation of the intercalation by phases of the stars it follows that there is no intercalation at all, but only the empirical verification of the fact that the new moon and Sirius come back after 27 years into the same mutual relationship: this will actually be the result with an accurate treatment of the intercalation based on the observation of this constellation.
Under these circumstances it would have been an easy matter to establish an intercalary cycle, but the demand for this is an affair of practical life: astronomy is concerned only with the calculation. The failure to observe this fact has led the discussion astray. The calendar is of course the most conservative of all human things; centuries after the establishment of very accurate calculations of the course of the moon and the introduction of a good intercalary cycle, the Jews adhered to the empirical observation of the new moon, and we know how difficult it is in modern times to introduce any improvement into the calendar. Because in Babylon there was a central government which could arrange the intercalation in proper fashion, the lunisolar year was kept in order, and in practical life there was no necessity to be able to calculate months and days for several years in advance. The empirical intercalation worked well, and there was no need to replace it by an intercalary cycle. The latter is indeed a simplification undertaken on practical grounds, an intercalating rule being substituted for the immediate astronomical observation: astronomy is concerned only with the calculation and with the further refinement of the rule. In so far as I am able to pronounce upon the material Kugler is right: no cyclically regulated intercalation existed before the Persian period; but from this it is in no way possible to arrive at any decision as to the position of the Babylonian astronomy. The regulation of the months by the phases of the stars was a suggestive problem for the astronomers, and it led to the recognition of the periodicity of the phenomena. This is the prius, not the desired establishment of an intercalary cycle.
A second means of fixing the months in their position in the solar year is afforded by the regulation by the solstices and equinoxes; but since, as will be shown in the following chapter, the observation of these is difficult and is seldom undertaken, a regulation of this nature is correspondingly rare. It can be demonstrated for the Eskimos[934], the Kwakiutl[935], and the Hopi, whose 13 ‘sun-points’ doubtless correspond to the 13 months[936]. Of the Basuto it is said that an attempt is made to determine the time of sowing from the moon, but that the people commonly go wrong in their reckoning, and after much dispute are obliged to fall back upon the climatic conditions and the state of the vegetation as more certain marks for the time of sowing. Intelligent chiefs, however, rectify the calendar (i. e. the moon-months) by the summer solstice, which they call the summer house of the sun[937].