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].