obvious motions of the heavenly bodies. But in the course of ages the Greek and Arabian astronomical observers discovered small divergences due to the various degrees of excentricity of the orbits of the moon and planets and their consequent varying rates of motion; and to explain these other spheres were added, together with smaller circles sometimes revolving excentrically, so that at length about sixty of these spheres, epicycles and excentrics were required to account for the various motions observed with the rude instruments, and the rates of motion determined by the very imperfect time-measurers of those early ages. And although a few great philosophers had at different times rejected this cumbrous system and had endeavoured to promulgate more correct ideas, their views had no influence on public opinion even among astronomers and mathematicians, and the Ptolemaic system held full sway down to the time of Copernicus, and was not finally given up till Kepler's _Laws_ and Galileo's _Dialogues_ compelled the adoption of simpler and more intelligible theories. We are now so accustomed to look upon the main facts of astronomy as mere elementary knowledge that it is difficult for us to picture to ourselves the state of almost complete ignorance which prevailed even among the most civilised nations throughout antiquity and the Middle Ages. The rotundity of the earth was held by a few at a very early period, and was fairly well established in later classical times. The rough determination of the size of our globe followed soon after; and when instrumental observations became more perfect, the distance and size of the moon were measured with sufficient accuracy to show that it was very much smaller than the earth. But this was the farthest limit of the determination of astronomical sizes and distances before the discovery of the telescope. Of the sun's real distance and size nothing was known except that it was much farther from us and much larger than the moon; but even in the century before the commencement of the Christian era Posidonius determined the circumference of the earth to be 240,000 stadia, equal to about 28,600 miles, a wonderfully close approximation considering the very imperfect data at his command. He is also said to have calculated the sun's distance, making it only one-third less than the true amount, but this must have been a chance coincidence, since he had no means of measuring angles more accurately than to one degree, whereas in the determination of the sun's distance instruments are required which measure to a second of arc.