We have seen in the foregoing pages how the phases of Nature, with their somewhat variable dates, are everywhere employed in the determination of time; how in the moon there lies ready to hand a clear, stable (at least within very narrow limits), and constant unit of time which could be turned to account in calculating; and how out of the fusion of natural phases and moons there arose a roughly empirical lunisolar year. For the more accurate fixing both of the seasons and of the months the phases of the stars are employed; these, being dependent on the sun, keep pace with the natural year, but, unlike the phases of Nature, are not subject to climatic variations but are astronomically fixed.

It is however possible astronomically to fix the solar year by a second method, viz. the observation of the annual course of the sun, especially of the solstices: the observation of the equinoxes is a much more difficult matter. The observation of the solstices can be performed in a way similar to that mentioned above, p. 21, in which noon is determined by the position of the sun, but is much more difficult to carry out and requires far more accurate and delicate methods. Two fixed points at least are necessary—a standing-ground and in the simplest case a mark on the horizon; other methods are still more complicated. An observation of the annual course of the sun, therefore, unlike that of the stars,—which everywhere, no matter where, can be performed immediately—demands a fixed place and special aids to determination. It follows that the observation of the solstices and equinoxes belongs to a much higher stage of civilisation than does that of the stars. It can only arise among a people with a fixed dwelling-place, since a race which leads a nomadic life and changes dwellings and camps is without the necessary fixed points of observation. After all it is only natural—and this actually is the case—that the observation of the course of the sun should be in use only among certain specially gifted peoples.

It is used by the Eskimos, who have a very highly developed sense of place, and know how to make good maps. Moreover where the sun in winter stands very low on the horizon, and for a time altogether disappears beneath it, the conditions are very favourable for the observation of its return. Older authors say that by the rays of the sun on the rocks the Eskimos can tell with tolerable accuracy when it is the shortest day[1039]; more recently we have been told of the Ammasalik that they can calculate beforehand the time of the shortest day—and that accurately to the day—not only from the solstitial point, but also from the position of Altair in the morning twilight[1040]. They begin their spring when the sun rises at the same spot as Altair[1041]. This is a quite isolated, but an accurate, determination of the course of the sun from the fixed stars. The Hudson Bay Eskimos of Labrador recognise the arrival of the solstices by the bearing of the sun with reference to certain fixed landmarks[1042]. The Central Eskimos must do the same, since they are acquainted with the winter solstice and when this and new moon coincide they omit their intercalary month[1043].

The tribes of Arizona observed the course of the sun, more particularly to determine the dates of their religious ceremonies, but also to decide the time of secular occupations. Among the Zuñi the winter solstice begins when the rising sun strikes a certain point at the south-west end of ‘Corn Mountain’, and a great feast is then celebrated. Then the sun moves to the north, passes the moon at ayonawa yälläne, and continues round to a point north-west of Zuñi, which is called ‘Great Mountain’, where it sets consecutively for four days at the same point. The last day is the summer solstice. On this occasion also a great festival is celebrated[1044]. The Hopi determine the time for their religious ceremonies, for planting, and for sowing by observing the points on the horizon where the sun rises or sets. The winter ceremonies are determined by the position of the sunset, the summer by the position of the sunrise. The two points of the solstices are called the ‘houses’ of the sun. There are 13 landmarks, by means of which the seasons are determined from the ecliptic. The number suggests that there is some connexion with the months. It would in that case be a quite isolated example of the regulation of the months by the observation of the sun’s position[1045].

The Incas erected artificial marks. There were in Cuzco sixteen towers, eight to the west and eight to the east, arranged in groups of four. The two middle ones were smaller than the others, and the distance between the towers was eight, ten, or twenty feet. The space between the little towers through which the sun passed at sunrise and sunset was the point of the solstices. In order to verify this the Inca chose a favourable spot from which he observed carefully whether the sun rose and set between the little towers to east and west. For the observation of the equinoxes richly ornamented pillars were set up in the open space before the temple of the sun. When the time approached, the shadow of the pillars was carefully observed. The open space was circular and a line was drawn through its centre from east to west. Long experience had taught them where to look for the equinoctial point, and by the distance of the shadow from this point they judged of the approach of the equinox. When from sunrise to sunset the shadow was to be seen on both sides of the pillar and not at all to the south of it, they took that day as the day of the equinox. This last account is for Quito, which lies just under the equator. At the spring equinox the maize was reaped and a feast was celebrated, at the autumn equinox the people celebrated one of their four principal feasts[1046]. The months were calculated from the winter solstice.

Among the Amazulu, we are told, the path of the sun in winter is different from its summer path: for it travels northward till it reaches a certain place,—a mountain or a forest (where it rises and sets)—and it does not pass beyond these two places; it comes out of its winter house; when it comes out it goes southward to its summer place. We say that when it quits its winter place it is fetching the summer, until it reaches a certain mountain or tree; and then it turns northward again, fetching the winter, in constant succession. These are its houses; we say so, for it stays in its winter house a few days: and when it quits that place we know that it has ended the winter and is now fetching the summer; and indeed it travels southward until, when the summer has grown, it enters the summer house a few days, and then quits it again, in constant succession[1047]. The Basuto also call the summer solstice the house of the sun, and intelligent chiefs adjust the reckoning of the months by it[1048].

For the Bismarck Archipelago the following details are given. On the island of Vuatam there is celebrated some time after the solstice and usually at the beginning of January—the exact date depends on the weather—a festival the object of which is to regulate the course of the sun and to secure good weather. In the whole of the north-eastern part of the Gazelle Peninsula the fact of the solstice is known, although no festival is celebrated. When the sun had its greatest southern amplitude it rose over Birar on St. George’s Channel. A native magistrate, To Kakao, explained how the sun would turn again and would finally attain its greatest northern amplitude on the horizon when it sank between the volcanic mountains ‘South Daughter’ and ‘Mother’. In Valaur the view is completely cut off to the east, and so the sun is observed at its setting, the turning-point in the south being formed by two mountain peaks situated close together. Another southern turning-point is furnished by still another mountain. The spot denoting the turning-point in the Baining mountain is chosen rather far off, and the observation is therefore not very accurate. The solstices are brought into connexion with the variation of the monsoons. To Kakao said that the north-east trade-wind blew all the time the sun was in the south (November to February), but during the time when it was situated in a northerly direction (May to August) the south-east monsoon prevailed. In Valaur the south-east monsoon blows as long as the sun sets WNW (May to August): but from November to February, when the sun sets WSW, the north-west trade blows[1049]. The Moanu of the Admiralty Islands name the divisions of the year according to the position of the sun. If it stands north of the equator the division in question is called morai im paün (‘war sun’), since it is during this time more particularly that wars are carried on. When the sun stands above the equator this division is named morai in kauas (‘sun of friendship’): this is the time of peace and of mutual visits. When the sun turns southward the colder season, morai unonou, begins[1050].

One would suspect that this Melanesian science, like the knowledge of the stars, is borrowed from the Polynesians: for the latter understood the annual course of the sun. In Tahiti the place of the sunrise was called tataheita, that of the sunset topa-t-era. The annual movement of the sun from the south towards the north was recognised, and so was the fact that all these points of the daily approach to the zenith lay in a line. This meridian was called t’era-hwattea, the northern point of it tu-errau, and the opposite point above the horizon, or the south, toa[1051]. According to other sources the December solstice was called rua-maoro or rua-roa, the June solstice rua-poto. The Hawaiians called the northern limit of the sun in the ecliptic ‘the black, shining road of Kane’, and the southern limit ‘the black, shining road of Kanaloa’. The equator was named ‘the bright road of the spider’ or ‘the road to the navel of Wakea’, equivalent to ‘the centre of the world’[1052]. How the Polynesians came to recognise the tropics and the equator is unfortunately unknown, but certainly they did it like other peoples by observing the solstices and equinoxes at certain landmarks.

That the Greeks also recognised the solstices by means of the observation of certain landmarks may be gathered from a passage in Homer. In the Odyssey Eumaeus says of his native land: “A certain island Syrie ... above Ortygia, where the sun turns”[1053]. Wherever Syrie lay, even though in the realm of fable, the idea is that it lies in the direction of the spot at which the sun at its turning rises or sets. It therefore serves as a landmark, it is ‘the house of the sun’. Hesiod is so familiar with the winter and summer solstices that he reckons time from them in days[1054].

A much discussed question is whether the ancient Germans were acquainted with the solstices and equinoxes, an assumption which must be adopted by anyone who regards the Yule festival as a solstitial festival. Their acquaintance with these points has been denied and with this view I myself have concurred[1055]. After my researches in primitive time-reckoning, however, I can no longer maintain this opinion for the later heathen times of the north. For it has been shewn that primitive peoples—and especially those living far north, e. g. the Eskimos—observed the solstices well from certain points on the horizon. Now it has already been seen that the northern peoples observed the times of day in the same manner[1056], and this observation was also extended to the annual course of the sun. It is said, for example, that autumn lasts from the equinox until the sun sets in eyktarstað, i. e. the position in which it stands in the eykt[1057]; and that south of Iceland and Greenland the sun at the time of the shortest days inhabits eyktarstað and dagmálastað (that is to say at 9 a. m.)[1058]. The evidence, it is true, comes down from Christian days: but the method of determining time is of native origin and certainly goes back into heathen times. Hence it should not be denied that, although nothing of the kind has transpired, the solstices and equinoxes might have been approximately determined in the same way, and it may be that the regulation of the calendar profited by this.

Any other day of the year can be fixed by observation in the same way, though the observation of the solstices is probably the oldest. As late as the beginning of the 19th century this method was adopted in Norway as a check to the prime-staff. On certain farms there was a definite stone, buried in the earth, to which the people repaired for these observations. They noticed when the sun rose and shone out above certain mountain peaks, or when its last rays touched this or that summit. They also observed the length of the shadow on the face of a cliff, or noted when it touched the brow of a mountain or a certain stone. Thence they were able to give the important days of the year, e. g. the festival of St. Paul or Candlemas. Our authority says that the observation was very inaccurate, so that the Christmas Day of the people might fall on January 2. But it was not so bad as that, since they still followed the old style. The sun-mark for the first summer day (April 14) agreed with the 23rd of April[1059].

Agricultural peoples in particular have developed various methods of this kind. The rice-cultivating peoples of the East Indies use various methods in order to determine the important time of sowing. Of the observation of the stars we have already spoken[1060]. Among the Kayan of Sarawak an old priest determines the official time of sowing from the position of the sun by erecting at the side of the house two oblong stones, one larger and one smaller, and then observing the moment when the sun, in the lengthening of the line of connexion between these two stones, sets behind the opposite hill. The sowing-day is the only one determined by astronomical methods. In other respects the time-reckoning is a more or less arbitrary one and is dependent on the agriculture[1061]. Of the hollows in a block of stone at Batu Sala, in the river-bed of the upper Mahakam, it is said that they originated in the fact that the priestesses of the neighbouring tribes used formerly to sit on the stone every year in order to observe when the sun would set behind a certain peak of the opposite mountain. This date then decided the time for the beginning of the sowing[1062].

In the first example we have artificially erected marks instead of the usual natural landmarks: compare also the towers at Cuzco. The pillars of Quito were a kind of gnomon, an instrument of immense importance for the scientific astronomy and accurate time-determination of antiquity. In this case the observation was much simplified on account of the situation just below the equator. The method is used again in Borneo, where it is very important to determine the right time for sowing the seed, and the approach of the short dry season before it in which the timber from the clearings must be dried and burnt. The Kenyah observe the position of the sun. Their instrument is a straight cylindrical pole of hardwood, fixed vertically in the ground and carefully adjusted with the aid of plumb-lines; the possibility of its sinking deeper into the earth is prevented. The pole is a little longer than the outstretched arms of its maker and stands on a cleared space by the house, surrounded by a strong fence. The observer has further a flat stick on which lengths measured from his body are marked off by notches. The other side has a larger number of notches, of which one marks the greatest length of the midday shadow, the next one its length three days after it has begun to shorten, and so on. The shadow is measured every midday. As it grows shorter after reaching its maximal length the man observes it with special care, and announces to the village that the time for preparing the land is near at hand[1063]. In Bali and Java the seasons are determined by the aid of a gnomon of rude construction, having a dial divided into twelve parts[1064].

The Kayan use a somewhat different method. The weather-prophet lets in a beam of light through a hole in the roof of his chamber in the long-house, and measures the distance of the patch of light from the point vertically below the hole. Thus they obtain a measurement similar to that given by the shadow on a sun-dial[1065]. Still more elaborate is the method used by some of the Klementan by which time is determined from the position of a star. A tall bamboo vessel is filled with water and then inclined until it points directly towards a certain star. It is set upright again, and the level of the water left in the vessel is measured. In order to determine the seed-time the vessel is provided with an empirically given mark at a certain height, and when the level of the water coincides with the mark after the inclining of the vessel towards the star, it is the time for sowing[1066]. The writers omit to say that the observation must take place at a certain time of day, e. g. morning or evening twilight. Then it becomes possible to determine the season by the height of the star above the horizon.

All this is neither primitive nor native. In Bali and Java the Brahmin and Islamite priests observed the sun-dial, and from there the practice came to Borneo. Where the idea of using a vessel of water for measurement originated I am unable to determine, but it is much too refined to be a primitive invention. The only genuinely primitive method is the observation of the annual course of the sun and the solstices by the aid of certain landmarks on the horizon. This method is found in all parts of the world, but only among certain peoples. It has never attained real importance for the regulation of the calendar: the development of the calendar to greater accuracy proceeds by the indirect way of the lunisolar time-reckoning.

By way of appendix a few notices of the aids used in calculating may be collected. They are almost always quite simple—knots in a string, the tally, or the joints of the body.

The use of the tally in counting the years has already been dealt with above[1067]; this use is certainly later, each stick attaining so to speak an individual life. It is otherwise with the counting of the days, where the question usually is to determine the number of days which will elapse before an assembly or some other undertaking previously agreed upon, so that all may arrive together. The same reckoning may also occasionally serve a second purpose.

The Peruvian quipos mark the culminating-point of the method of counting by knots in a cord. Something similar existed among the Nahyssan of Carolina. Time was measured and a rude chronology was arranged by means of knots of various colours. This system proved so convenient in dealing with the Indians that it was adopted for that purpose by a governor of South Carolina[1068]. When a chief of the Miwok of California decides to hold a dance in his village, he dispatches messengers to the neighbouring rancherias, each bearing a string wherein is tied a number of knots. Every morning thereafter the invited chief unties one of the knots, and when the last one is reached, they joyfully set forth for the dance—men, women, and children[1069]. Sticks serve the same purpose. Once when the Natchez and the Chocktaw wished to attack the French in Louisiana, each tribe received a bundle of sticks, one of which was to be withdrawn and destroyed each day, so that they might strike their blows at the same time[1070]. The Pawnee used the tally for counting nights, months, and years, but had advanced so far as to employ picture-writing in doing so. * means day or sun, × star or night, ☾ moon, month[1071]. This is the forerunner of the Indian picture-calendar already mentioned[1072].

According to Barrow the Caffres assist their memories by means of a tally, although this authority did not himself find this custom among them; but the Hottentot servants of the colonists, among whom were several Caffres, used this method in counting the number of the cattle earned[1073]. Among the Wagogo if it was desired to count the days, e. g. in connexion with the sitting of a court of justice, as many knots were tied in a string as there were nights to elapse before this date. In Nigeria palm-nuts are used in counting[1074], just as in southern Brazil the years are counted by means of acajou nuts[1075], and as the tribes of Bolivia count with grains of maize[1076]. The Baganda, in order to keep in mind the days of the month, tie knots in a piece of plant-fibre and afterwards count the knots[1077]. In New Guinea the months were counted by means of notches cut in trees: the New Zealanders are said to have added every month a little piece of wood or a small stone to a heap[1078].

In the Nicobars notched sticks in the form of a scimitar-blade are in use. They have notches on the edge and on the flat, the former denote months, the latter the days of the waning and waxing moon. They are used e. g. in finding out when a child of the owner learned to walk. The Shompen take a piece of bamboo and make as many bends in it as they mean to reckon days[1079]. The Negritos of Zambales in order to count the days make knots in a cord of bejuco and cut off one of these knots every day[1080]. On the Solomon Islands also knotted cords are used for the same purpose[1081]. The counting is particularly necessary for the celebrating of the great feast of the dead at the proper time. The eating the death, gana matea, begins with the burial; they eat first, as they say, ‘his graves’, after that they eat ‘his days’—the 5th, 10th, and after that every ten up to the hundredth, and it may be, in the case of a father, wife, or mother, even so far as the thousandth. For counting the days, so that the guests from distant villages may arrive on the proper days, they use cycas fronds, one in the hands of each party, on which the appointed days are marked by the pinching off or turning down of a leaflet as each day passes[1082]. According to another authority the moons are counted. At the coming of the young moon after the death of a man either a knot is made in a thread or a notch is cut in a piece of wood. Up to thirty moons are then counted. The object is to calculate the time up to the great funeral wake of dead chiefs. For young people it takes place from 20 to 30 months afterwards, for old people after 10 months, for an unimportant person as soon as 3 or 4 months afterwards[1083]. In Nauru, west of the Gilbert Islands, knots were tied in a string when days were to be counted, e. g. the 15 days of the confinement of a woman[1084].

Only seldom is it mentioned that the months are counted on the fingers, although obviously this must often happen; the Klamath and the Modok used to do so formerly[1085]. Certain very primitive peoples use not only fingers and toes but also other parts of the body in counting. The day of an assembly is determined in this fashion by an Australian tribe which in words can seldom count more than four. The people touch various parts of each other’s bodies—the wrist, the arm, the head—each of which stands for a special day, until the intended day is reached. Thus two or more groups can accurately determine the lapse of time and can meet on the day agreed upon[1086]. The curious names of months of the Tunguses of the Sea of Okhotsk[1087] are similarly to be explained, as is shewn by the method of counting the year used by the Yukaghir. They call the year n-e’ -malgil, which means ‘all the joints’. The reckoning of the months by the joints is done in the following manner. They bend the third row of phalanges of the fingers on both hands, and put them together. The line of the joining they call July. Then the knuckles of the second row of phalanges on the right hand will be August. The joints between the phalanges and metacarpals represent September; the wrist-joint is October; the elbow-joint is November; the shoulder-joint, December; between the head and the backbone will be January; the shoulder-joint on the left arm will be February; the elbow-joint, March; the wrist-joint, April; the joint between the fingers and the palm, May; and the knuckles of the second row of phalanges on the left hand, June[1088].

These examples may suffice. The subject is monotonous and is of little importance for the calendar, since the days are counted independently of the latter, beginning at an arbitrary starting-point. The counting that is important for the calendar is that according to the days of the lunar month, but in this the primitive peoples hold to the concrete phenomenon of the moon. The habit of reckoning in this fashion may however be partly responsible for the fact that among certain peoples every day of the month has not been given a name, but the days are counted from certain points of departure, such as new moon, full moon, etc. Very rarely do we meet with a genuinely calendrical use of the tally. The Wa-Sania of East Africa, who as subjects of the Galla and later since the invasion of the Somali have been exposed to all kinds of civilising influences, make a notch for each day, and at the end of the month the stick is laid aside and a new one comes into use[1089]. Similarly at the southern end of Lake Nyassa pieces of wood strung on a cord are used in counting the days of the month that have passed[1090].

The Kiwai Papuans count the months by means of little sticks, which are tied into two bundles corresponding to the two seasons of the year. One end is pointed, the other oblique, and when a month has passed, the stick corresponding to it is turned round. The stick belonging to the month keke is provided with a top-knot and feather, that of karongo has a mark cut in it and a top-knot like that of keke, but no feather[1091].