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 versá; and also their apparent risings and settings when they cease to be visible after sun-set, or begin to be visible after sun-rise 5. Several of the propositions contained in the former of these treatises are still necessary to be understood, as fundamental parts of astronomy.

45

The work of Euclid, just mentioned, is of the same kind.

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.

43 Cosmical setting and rising.
45 Heliacal.

44 Acronical.

46 A. A.

p.

53.

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 supported 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. Anaximander" 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 this opinion, we cannot judge of its value; 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 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.

We find this doctrine so distinctly insisted on by Aristotle, that we may almost look on him as the establisher of it 48. "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 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 differences; for 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, having a spherical form, must be the cause

48 Arist. de Cœlo. Lib. ii. cap. xiv. Casaub. p. 290 F.

of this. And again, by the appearances of the stars, it is clear, not only that it is spherical, 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 vertically over us undergo a great change, and are not the same to those that travel to the north and to the south. For some stars are seen in Egypt or at Cyprus, but are not seen in the countries to the north of these; and the stars that in the north are visible while they make a complete circuit, there undergo a setting. So that from this it is manifest, not only that the form of the earth is round, but also that it is a part of not a very large sphere: for otherwise the difference would not be so obvious to persons making so small a change of place. Wherefore we may judge that those persons who connect the region in the neighbourhood of the pillars of Hercules with that towards India, and who assert that in this way the sea is ONE, do not assert things very improbable. They confirm this conjecture by the elephants, which are said to be of the same species (yevos) towards each extreme; as if this circumstance was a consequence of the conjunction of the extremes. mathematicians, who try to gather from reasoning the measure of the circumference, make it amount to 400,000 stadia; whence we collect that the earth is not only spherical, but is not large compared with the magnitude of the other stars."

The

When this notion was once suggested, it was de

fended and confirmed by such arguments as we find in later writers: for instance, that the tendency of all things was to fall to the place of heavy bodies, and that this place being the centre of the earth, the whole earth had no such tendency; that the inequalities on the surface were so small as not materially to affect the shape of so vast a mass; that drops of water naturally form themselves into figures with a convex surface; that the end of the ocean would fall if it were not rounded off; that we see ships, when they go out to sea, disappearing downwards, which shows the surface to be convex. These are the arguments still employed in impressing the doctrines of astronomy upon the student of our own days; and thus we find that, even at the early period of which we are now speaking, truths had begun to accumulate which form a part of our present treasures.

Sect. 10.-The Phases of the Moon.

WHEN men had formed a steady notion of the moon as a solid body, revolving about the earth, they had only further to conceive it spherical, and to suppose the sun to be beyond the orbit of the moon, and they would find that they had obtained an explanation of the varying forms which the bright part of the moon assumes in the course of a month. For the convex

50 Pliny, Nat. Hist. ii. LXV.