are probably due to the same cause.  Among the most noteworthy valleys of the largest class must, of course, be placed the great valley of the Alps, one of the most striking objects in the northern hemisphere, which also includes the great valley south-east of Ukert.  The Rheita valley, the very similar chasm west of Reichenbach, and the gorge west of Herschel, are also notable examples in the southern hemisphere.  The borders of some of the Maria (especially that of the Mare Crisium) and of many of the depressed rimless formations, furnish instances of winding valleys intersecting their borders:  the hilly regions likewise often abound in long branching defiles.

BRIGHT RAY-SYSTEMS.—­Reference has already been made to the faint light streaks and markings often found on the floors of the ring-mountains and in other situations, and to the brilliant nimbi surrounding some of the smaller craters; but, in addition to these, many objects on the moon’s visible surface are associated with a much more remarkable and conspicuous phenomenon—­the bright rays which, under a high sun, are seen either to radiate from them as apparent centres to great distances, or, in the form of irregular light areas, to environ them, and to throw out wide-spreading lucid beams, extending occasionally many hundreds of miles from their origin.  The more striking of these systems were recognised and drawn at a very early stage of telescopic observation, as may be seen if we consult the quaint old charts of Hevel, Riccioli, Fontana, and other observers of the seventeenth century, where they are always prominently, though very inaccurately, portrayed.  The principal ray-systems are those of Tycho, Copernicus, Kepler, Anaxagoras, Aristarchus, Olbers, Byrgius A, and Zuchius; while Autolycus, Aristillus, Proclus, Timocharis, Furnerius A, and Menelaus are grouped as constituting minor systems.  Many additional centres exist, a list of which will be found in the appendix.

The rays emanating from Tycho surpass in extent and interest any of the others.  Hundreds of distinct light streaks originate round the grey margin of this magnificent object, some of them extending over a greater part of the moon’s visible superficies, and “radiating,” in the words of Professor Phillips, “like false meridians, or like meridians true to an earlier pole of rotation.”  No systematic attempt has yet been made to map them accurately as a whole on a large scale, for their extreme intricacy and delicacy would render the task a very difficult one, and, moreover, would demand a long course of observation with a powerful telescope in an ideal situation; but Professor W.H.  Pickering, observing under these conditions at Arequipa, has recently devoted considerable attention both to the Tycho and other rays, with especially suggestive and important results, which may be briefly summarised as follows:—­