In the brief space available it is only possible to refer to two or three of the men whose commanding intellects did so much to help on the development of the science. EUDOXUS of Knidus, in Asia Minor (408-355 B.C.), was, so far as we know, the first to attempt to represent the movements of the heavenly bodies by a simple mathematical process. His root idea was something like this. The Earth was in the centre of the universe, and it was surrounded, at a great distance from us, by a number of invisible transparent shells, or spheres. Each of these spheres rotated with perfect uniformity, though the speed of rotation differed for different spheres. One sphere carried the stars, and rotated from east to west in about 23 h. 56 m. The Sun was carried by another sphere, which rotated from west to east in a year, but the pivots, or poles, of this sphere were carried by a second, rotating exactly like the sphere of the stars. This explained how it is that the ecliptic--that is to say, the apparent path of the Sun amongst the stars--is inclined 23-½° to the equator of the sky, so that the Sun is 23-½° north of the equator at midsummer and 23-½° south of the equator at midwinter, for the poles of the sphere peculiar to the Sun were supposed to be 23-½° from the poles of the sphere peculiar to the stars. Then the Moon had three spheres; that which actually carried the Moon having its poles 5° from the poles of the sphere peculiar to the {22} Sun. These poles were carried by a sphere placed like the sphere of the Sun, but rotating in 27 days; and this, again, had its poles in the sphere of the stars. The sphere carrying the Moon afforded the explanation of the wavy motion of the Moon to and fro across the ecliptic in the course of a month, for at one time in the month the Moon is 5° north of the ecliptic, at another time 5° south. The motions of the planets were more difficult to represent, because they not only have a general daily motion from east to west, like the stars, and a general motion from west to east along the ecliptic, like the Sun and Moon, but from time to time they turn back on their course in the ecliptic, and "retrograde." But the introduction of a third and fourth sphere enabled the motions of most of the planets to be fairly represented. There were thus twenty-seven spheres in all--four for each of the five planets, three for the Moon, three for the Sun (including one not mentioned in the foregoing summary), and one for the stars. These spheres were not, however, supposed to be solid structures really existing; the theory was simply a means for representing the observed motions of the heavenly bodies by computations based upon a series of uniform movements in concentric circles.