The phenomena of the rising and setting of stars

One of the earliest problems in the practical geometry of a calendar priesthood arose in watching for the return of the equinoxes. One way in which the priests of antiquity fixed. With a sufficiently long piece of cord fairly high accuracy can be secured. Laying off the east and west points of the horizon to record the equinoxes was probably done in a similar way, two poles or stones being erected in line with the rising or setting sun of the summer solstice, and a third equidistant from one of them in line with it and the rising or setting sun of the winter solstice. The sun of the equinoxes would rise and set along the line bisecting the angle between the sun's positions on the solstices. The Egyptians already recognized that this could also be done by making a line at right angles to the meridian. The division of the daily shadow path into hour angles was a later device probably of Babylonian origin, and betrays the early connexion between the art of space measurement and the social necessity of recording the passage of time. The division of the equinoctial half-circle into twelve divisions is not surprising. Of all integral sub-multiples of 360° the angle 15° is the smallest whole number which we can easily make by elementary methods of construction. By knotting cords at equal lengths we can peg out an equilateral triangle. Successive bisection of the angles of the equilateral triangle then gives 30° and 15°.

The phenomena of the rising and setting of stars show that the sun changes its position relative to the fixed stars, as if retreating eastwards through a complete circle in the celestial sphere. To account for the changing height of the noonday sun and tile duration of the days and nights throughout the year, a second conception took shape. The sun appears to slip back through a track, the ecliptic, which is placed obliquely with reference to the polar axis. By about three thousand B.C. we have ample evidence that the priests of Egypt had constructed simple instruments for measuring tile angular direction of tile stars, and were accustomed to watch for tile moment when a star crosses the meridian, i.e. the great semicircle which cuts the north horizon, the Pole Star, the zenith vertically above the observer, and tile south horizon. By noting the direction of the sun from the south horizon when it crosses the meridian at noon, they were able to identify the sun's annual track through a belt of twelve star clusters, called the Zodiac, corresponding to the twelve 30-day months of the Babylonian year. The star clusters of the Zodiac are not systems of bodies with any known relation among themselves. They are simply signposts of the seasons. The times of rising and setting of a zodiacal constellation and its height above the southern horizon when it crosses the meridian correspond fairly closely with the times of sunrise and of sunset and with the height of the noon sun six months earlier or later. The names of the Zodiac star clusters are: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces.

That two of these names are familiar to all of us draws attention to the farreaching importance of the hypothesis which gradually developed from this foundation. It is true that all the facts are equally intelligible on another view, if we bear in mind what we now know about the immense distance of the fixed stars. The sun's apparent track through the ecliptic is also explicable if we assume that our train is moving and the sun's engine is at rest. All that we can see is compatible with the more sophisticated, and for the present purpose less straightforward, hypothesis that the earth pursues a slanting annual track around the sun with its polar axis always at the same angle to the ecliptic plane. On either view we have made a very big advance in our knowledge of the earth through widening our knowledge of the heavens. We shall see this better when we have taken into account another class of events which clarified the recognition that our earth itself is a spherical body.