In any case it will be remarked that this measurement of shadows, intervals, or profiles can only be made when the solar rays strike the moon obliquely in relation to the observer.  When they strike her directly—­in a word, when she is full—­all shadow is imperiously banished from her disc, and observation is no longer possible.

Galileo, after recognising the existence of the lunar mountains, was the first to employ the method of calculating their heights by the shadows they throw.  He attributed to them, as it has already been shown, an average of 9,000 yards.  Hevelius singularly reduced these figures, which Riccioli, on the contrary, doubled.  All these measures were exaggerated.  Herschel, with his more perfect instruments, approached nearer the hypsometric truth.  But it must be finally sought in the accounts of modern observers.

Messrs. Boeer and Moedler, the most perfect selenographers in the whole world, have measured 1,095 lunar mountains.  It results from their calculations that 6 of these mountains rise above 5,800 metres, and 22 above 4,800.  The highest summit of the moon measures 7,603 metres; it is, therefore, inferior to those of the earth, of which some are 1,000 yards higher.  But one remark must be made.  If the respective volumes of the two orbs are compared the lunar mountains are relatively higher than the terrestrial.  The lunar ones form 1/70 of the diameter of the moon, and the terrestrial only form 1/140 of the diameter of the earth.  For a terrestrial mountain to attain the relative proportions of a lunar mountain, its perpendicular height ought to be 6-1/2 leagues.  Now the highest is not four miles.

Thus, then, to proceed by comparison, the chain of the Himalayas counts three peaks higher than the lunar ones, Mount Everest, Kunchinjuga, and Dwalagiri.  Mounts Doerfel and Leibnitz, on the moon, are as high as Jewahir in the same chain.  Newton, Casatus, Curtius, Short, Tycho, Clavius, Blancanus, Endymion, the principal summits of Caucasus and the Apennines, are higher than Mont Blanc.  The mountains equal to Mont Blanc are Moret, Theophylus, and Catharnia; to Mount Rosa, Piccolomini, Werner, and Harpalus; to Mount Cervin, Macrobus, Eratosthenes, Albateque, and Delambre; to the Peak of Teneriffe, Bacon, Cysatus, Philolaus, and the Alps; to Mount Perdu, in the Pyrenees, Roemer and Boguslawski; to Etna, Hercules, Atlas, and Furnerius.

Such are the points of comparison that allow the appreciation of the altitude of lunar mountains.  Now the trajectory followed by the projectile dragged it precisely towards that mountainous region of the southern hemisphere where rise the finest specimens of lunar orography.

CHAPTER XVII.

TYCHO.

At 6 p.m. the projectile passed the South Pole at less than thirty miles, a distance equal to that already reached at the North Pole.  The elliptical curve was, therefore, being rigorously described.