was supposed to turn about the visible pole and another pole opposite to this, and these poles were connected by an imaginary Axis. The circle which divided the sphere exactly midway between these poles was called the Equator (ionμépivos). The two circles parallel to this which bounded the sun's path among the stars were called Tropics (TроTIKαi), because the sun turns back again towards the equator when he reaches them. The stars which never set are bounded by a circle called the Arctic Circle (aρKTIKоs, and άρктоs, the Bear, the constellation to which some of the principal stars within that circle belong). A circle about the opposite pole is called Antarctic, and the stars which are within it can never rise to us11. The sun's path or circle of the signs is called the Zodiac, or circle of animals; the points where this circle meets the equator are the Equinoctial Points, the days and nights being equal when the sun is in them; the Solstitial Points are those where the sun's path touches the tropics; his motion to the south or to the north ceases when he is there, and he appears in that respect to stand still. The Colures (kóλovpoi, mutilated) are circles which pass through the poles and through the equinoctial and solstitial points; they have their name because they are only visible in part, a portion of them being below the horizon. 41 The Arctic and Antarctic Circles of modern astronomers are different from these. The Horizon (opiwv) is commonly understood as the boundary of the visible earth and heaven. In the doctrine of the sphere, this boundary is a great circle, that is, a circle of which the plane passes through the centre of the sphere; and, therefore, an entire hemisphere is always above the horizon. The term occurs for the first time in the work of Euclid, called Phænomena (Þaurópeva). We possess two treatises written by Autolycus (who lived about 300 B. C.) which trace deductively the results of the doctrine of the sphere. Supposing its diurnal motion to be uniform, in a work entitled Περὶ Κινουμένης Σφαίρας, “On the Moving Sphere,” he demonstrates various properties of the diurnal risings, settings, and motions of the stars. In another work, Περὶ Επιτολῶν καὶ Δύσεων, “On Risings and Settings," tacitly assuming the sun's motion in his circle to be uniform, he proves certain propositions, with regard to the risings and settings of the stars, at the same time when the sun rises and sets", or vice versá15; and also their apparent risings and settings when they cease to be visible after sun-set, or begin to be visible after sun-rise". Several of the propositions contained in the former of these treatises are still necessary to be understood, as fundamental parts of astronomy. The work of Euclid, just mentioned, is of the 42 Delambre, Astron. Ancienne, p. 19. "Cosmical setting and rising. 46 Heliacal. 43 Ib. p. 25. 45 Acronical. same kind. 47 Delambre finds in it evidence that Euclid was merely a book-astronomer, who had never observed the heavens. We may here remark the first instance of that which we shall find abundantly illustrated in every part of the history of science; that man is prone to become a deductive reasoner;-that as soon as he obtains principles which can be traced to details by logical consequence, he sets about forming a body of science, by making a system of such reasonings. Geometry has always been a favourite mode of exercising this propensity: and that science, along with Trigonometry, Plane and Spherical, to which the early problems of astronomy gave rise, have, up to the present day, been a constant field for the exercise of mathematical ingenuity; a few simple astronomical truths being assumed as the basis of the reasoning. Sect. 9.-The Globular Form of the Earth. THE establishment of the globular form of the earth is an important step in astronomy, for it is the first of those convictions, directly opposed to the apparent evidence of the senses, which astronomy irresistibly proves. To make men believe that up and down are different directions in different places; that the sea, which seems so level, is, in fact, convex; that the earth, which appears to rest on a solid foundation, is, in fact, not sup47 A. A. p. 53. ported at all; are great triumphs both of the power of discovering and the power of convincing. We may readily allow this, when we recollect how recently the doctrine of the antipodes, or the existence of inhabitants of the earth, who stand on the opposite side of it, with their feet turned towards ours, was considered both monstrous and heretical. Yet the different positions of the horizon at different places, necessarily led the student of spherical astronomy toward this notion of the earth as a round body. Anaximander48 is said by some to have held the earth to be globular, and to be detached or suspended; he is also stated to have constructed a sphere, on which were shown the extent of land and water. As, however, we do not know the arguments upon which he maintained the earth's globular form, we cannot judge of the value of his opinion; it may have been no better founded than a different opinion ascribed to him by Laertius, that the earth had the shape of a pillar. Probably, the authors of the doctrine of the globular form of the earth were led to it, as we have said, by observing the different height of the pole at different places. They would find that the space which they passed over from north to south on the earth, was proportional to the change of place of the horizon in the celestial sphere; and as the horizon is, at every place, in the direction 48 See Brucker, Hist. Phil. vol. i. p. 486. of the earth's apparently level surface, this observation would naturally suggest to them the opinion that the earth is placed within the celestial sphere, as a small globe in the middle of a much larger one. 66 We find this doctrine so distinctly insisted on by Aristotle, that we may almost look on him as the establisher of it49. "As to the figure of the earth, it must necessarily be spherical." This he proves, first by the tendency of things, in all places, downwards. He then adds, " And, moreover, from the phenomena according to the sense: for if it were not so, the eclipses of the moon would not have such sections as they have. For in the configurations in the course of a month, the deficient part takes all different shapes; it is straight, and concave, and convex; but in eclipses it always has the line of division convex; wherefore, since the moon is eclipsed in consequence of the interposition of the earth, the periphery of the earth must be the cause of this by having a spherical form. And again, from the appearances of the stars, it is clear, not only that the earth is round, but that its size is not very large: for when we make a small removal to the south or the north, the circle of the horizon becomes palpably different, so that the stars overhead undergo a great change, and are not the same to those that travel to the north 49 50 Arist. de Cœlo. Lib. ii. cap. xiv. ed. Casaub. p. 290. VOL. I. M |