Ancient astronomers, long before the invention of telescopes, and before the discovery of the Copernican system, devised an ingenious method of getting some light on the distance of the sun. It is attributed to Aristarchus of Samos. They reflected that, when the moon appeared precisely half full, this arose from the fact that the sun and the earth were at right angles to her; the sun illumining the half turned to him, and the plane of division between the illumined and unillumined portions extended stretching directly to the earth. They conceived the three bodies to stand at the angles of a right‐angled triangle, of which the distance of the moon from the earth was the base, and the distance of the sun was the hypothenuse. Hence they had only to measure the angle at the earth, which they could do, and then take into account their estimate of the moon’s distance, to arrive at the result sought. The plan is ingenious, and taught them that the sun was at least twenty times further off than the moon. But their estimate of the moon’s distance was altogether wide of the mark. They had no means of correctly estimating it. Moreover, even keen eyesight is a bad judge of whether the moon is precisely half full or not. The error of half a dozen hours would give a large mistake. Even with instruments such as we have, it cannot be precisely determined by direct observations; for the surface of the moon, as developed in a powerful telescope, is so uneven, jagged, and volcanic that the division between light and shade is a line too uneven and broken to be determined except by guessing at its mean course.