33. Among the important contributions of the Greeks to astronomy must be placed the development, chiefly from the mathematical point of view, of the consequences of the rotation of the celestial sphere and of some of the simpler motions of the celestial bodies, a development the individual steps of which it is difficult to trace. We have, however, a series of minor treatises or textbooks, written for the most part during the Alexandrine period, dealing with this branch of the subject (known generally as Spherics, or the Doctrine of the Sphere), of which the Phenomena of the famous geometer Euclid (about 300 B.C.) is a good example. In addition to the points and circles of the sphere already mentioned (chapter I., [§§ 8-11]), we now find explicitly recognised the horizon, or the great circle in which a horizontal plane through the observer meets the celestial sphere, and its pole,[17] the zenith,[18] or point on the celestial sphere vertically above the observer; the verticals, or great circles through the zenith, meeting the horizon at right angles; and the declination circles, which pass through the north and south poles and cut the equator at right angles. Another important great circle was the meridian, passing through the zenith and the poles. The well-known Milky Way had been noticed, and was regarded as forming another great circle. There are also traces of the two chief methods in common use at the present day of indicating the position of a star on the celestial sphere, namely, by reference either to the equator or to the ecliptic. If through a star S we draw on the sphere a portion of a great circle S N, cutting the ecliptic ♈ N at right angles in N, and another great circle (a declination circle) cutting the equator at M, and if ♈ be the first point of Aries ([§ 13]), where the ecliptic crosses the equator, then the position of the star is completely defined either by the lengths of the arcs ♈ N, N S, which are called the celestial longitude and latitude respectively, or by the arcs ♈ M, M S, called respectively the right ascension and declination.[19] For some purposes it is more convenient to find the position of the star by the first method, i.e. by reference to the ecliptic; for other purposes in the second way, by making use of the equator.
34. One of the applications of Spherics was to the construction of sun-dials, which were supposed to have been originally introduced into Greece from Babylon, but which were much improved by the Greeks, and extensively used both in Greek and in mediaeval times. The proper graduation of sun-dials placed in various positions, horizontal, vertical, and oblique, required considerable mathematical skill. Much attention was also given to the time of the rising and setting of the various constellations, and to similar questions.
35. The discovery of the spherical form of the earth led to a scientific treatment of the differences between the seasons in different parts of the earth, and to a corresponding division of the earth into zones. We have already seen that the height of the pole above the horizon varies in different places, and that it was recognised that, if a traveller were to go far enough north, he would find the pole to coincide with the zenith, whereas by going south he would reach a region (not very far beyond the limits of actual Greek travel) where the pole would be on the horizon and the equator consequently pass through the zenith; in regions still farther south the north pole would be permanently invisible, and the south pole would appear above the horizon.
Fig. 15.—The equator, the horizon, and the meridian.
Further, if in the figure H E K W represents the horizon, meeting the equator Q E R W in the east and west points E W, and the meridian H Q Z P K in the south and north points H and K, Z being the zenith and P the pole, then it is easily seen that Q Z is equal to P K, the height of the pole above the horizon. Any celestial body, therefore, the distance of which from the equator towards the north (declination) is less than P K, will cross the meridian to the south of the zenith, whereas if its declination be greater than P K, it will cross to the north of the zenith. Now the greatest distance of the sun from the equator is equal to the angle between the ecliptic and the equator, or about 23-1∕2°, Consequently at places at which the height of the pole is less than 23-1∕2° the sun will, during part of the year, cast shadows at midday towards the south. This was known actually to be the case not very far south of Alexandria. It was similarly recognised that on the other side of the equator there must be a region in which the sun ordinarily cast shadows towards the south, but occasionally towards the north. These two regions are the torrid zones of modern geographers.
Again, if the distance of the sun from the equator is 23-1∕2°, its distance from the pole is 66-1∕2°; therefore in regions so far north that the height P K of the north pole is more than 66-1∕2°, the sun passes in summer into the region of the circumpolar stars which never set (chapter I., [§ 9]), and therefore during a portion of the summer the sun remains continuously above the horizon. Similarly in the same regions the sun is in winter so near the south pole that for a time it remains continuously below the horizon. Regions in which this occurs (our Arctic regions) were unknown to Greek travellers, but their existence was clearly indicated by the astronomers.
