spot upon the equator of our satellite, and the interval between successive reappearances of the same phase to observers on the earth. The physical cause of the coincidence of times of rotation and revolution was touched upon in a previous chapter. We have said that the moon continuously presents to us the same hemisphere. This is generally true, but not entirely so. Galileo, by long scrutiny, familiarised himself with every detail of the lunar-disc that came within the limited grasp of his telescopes, and he recognised the fact that according as the position of the moon varied in the sky, so the aspect of her face altered to a slight degree; that certain regions at the edge of her disc, alternately came in sight and receded from his view. He perceived, in fact, an _apparent_ rocking to and fro of the globe of the moon; a sort of balancing or _libratory_ motion. When the moon was near the horizon he could see spots upon her uppermost edge, which disappeared as she approached the zenith, or highest point of her nightly path; and as she neared this point, other spots, before invisible, came into view, near to what had been her lower edge. Galileo was not long in referring this phenomenon to its true cause. The centre of motion of the moon being the centre of the earth, it is clear that an observer on the surface of the latter, looks down upon the rising moon as from an eminence, and thus he is enabled to see more or less over or around her. As the moon increases in altitude, the line of sight gradually becomes parallel to the line joining the observer and the centre of the earth, and at length he looks her full in the face: he loses the full view and catches another side face view as she nears the horizon in setting. This phenomenon, occurring as it does, with a daily period, is known as the _diurnal libration_. But a kindred phenomenon presents itself in another period, and from another cause. The moon rotates upon her axis at a speed that is rigorously uniform. But her orbital motion is not uniform, sometimes it is faster, and at other times slower than its average rate. Hence, the angle through which she moves along her orbit in a given time, now exceeds, and now falls short of the angle through which she turns upon her axis. Her visible hemisphere thus changes to an extent depending upon the difference between these orbital and axial angles, and the apparent balancing thus produced is called the _libration in longitude_. Then there is a _libration in latitude_ due to the circumstance that the axis of the moon is not exactly perpendicular to the plane of her orbit; the effect of this inclination being, that we sometimes see a little more of the north than of the south polar regions of our satellite, and _vice versâ_.[6]