It had long been well known that as the moon describes her monthly path round the earth we see the same markings substantially in the same positions on the disc, so that substantially the same face of the moon is turned towards the earth. It occurred to Galilei to inquire whether this was accurately the case, or whether, on the contrary, some change in the moon’s disc could be observed. He saw that if, as seemed likely, the line joining the centres of the earth and moon always passed through the same point on the moon’s surface, nevertheless certain alterations in an observer’s position on the earth would enable him to see different portions of the moon’s surface from time to time. The simplest of these alterations is due to the daily motion of the earth. Let us suppose for simplicity that the observer is on the earth’s equator, and that the moon is at the time in the celestial equator. Let the larger circle in fig. 58 represent the earth’s equator, and the smaller circle the section of the moon by the plane of the equator. Then in about 12 hours the earth’s rotation carries the observer from A, where he sees the moon rising, to B, where he sees it setting. When he is at C, on the line joining the centres of the earth and moon, the point O appears to be in the centre of the moon’s disc, and the portion _c_ O _c′_ is visible, _c_ R _c′_ invisible. But when the observer is at A, the point P, on the right of O, appears in the centre, and the portion _a_ P _a′_ is visible, so that _c′ a′_ is now visible and _a c_ invisible. In the same way, when the observer is at B, he can see the portion _c b_, while _b′ c′_ is invisible and Q appears to be in the centre of the disc. Thus in the course of the day the portion _a_ O _b′_ (dotted in the figure) is constantly visible and _b_ R _a′_ (also dotted) constantly invisible, while _a c b_ and _a′ c′ b′_ alternately come into view and disappear. In other words, when the moon is rising we see a little more of the side which is the then uppermost, and when she is setting we see a little more of the other side which is uppermost in this position. A similar explanation applies when the observer is not on the earth’s equator, but the geometry is slightly more complicated. In the same way, as the moon passes from south to north of the equator and back as she revolves round the earth, we see alternately more and less of the northern and southern half of the moon. This set of changes—the simplest of several somewhat similar ones which are now known as =librations= of the moon—being thus thought of as likely to occur, Galilei set to work to test their existence by observing certain markings of the moon usually visible near the edge, and at once detected alterations in their distance from the edge, which were in general accordance with his theoretical anticipations. A more precise inquiry was however interrupted by failing sight, culminating (at the end of 1636) in total blindness.