dear friends; it is the Sun himself that you now see; these summits that you behold him gilding are the mountains that lie on the Moon's southern rim. We are rapidly nearing her south pole."
"After doubling her north pole!" cried Ardan; "why, we must be circumnavigating her!"
"Exactly; sailing all around her."
"Hurrah! Then we're all right at last! There's nothing more to fear from your hyperbolas or parabolas or any other of your open curves!"
"Nothing more, certainly, from an open curve, but every thing from a closed one."
"A closed curve! What is it called? And what is the trouble?"
"An eclipse it is called; and the trouble is that, instead of flying off into the boundless regions of space, our Projectile will probably describe an elliptical orbit around the Moon—"
—"What!" cried M'Nicholl, in amazement, "and be her satellite for ever!"
"All right and proper," said Ardan; "why shouldn't she have one of her own?"
"Only, my dear friend," said Barbican to Ardan, "this change of curve involves no change in the doom of the Projectile. We are as infallibly lost by an ellipse as by a parabola."
"Well, there was one thing I never could reconcile myself to in the whole arrangement," replied Ardan cheerfully; "and that was destruction by an open curve. Safe from that, I could say, 'Fate, do your worst!' Besides, I don't believe in the infallibility of your ellipsic. It may prove just as unreliable as the hyperbola. And it is no harm to hope that it may!"
From present appearances there was very little to justify Ardan's hope. Barbican's theory of the elliptic orbit was unfortunately too well grounded to allow a single reasonable doubt to be expressed regarding the Projectile's fate. It was to gravitate for ever around the Moon—a sub-satellite. It was a new born individual in the astral universe, a microcosm, a little world in itself, containing, however, only three inhabitants and even these destined to perish pretty soon for want of air. Our travellers, therefore, had no particular reason for rejoicing over the new destiny reserved for the Projectile in obedience to the inexorable laws of the centripetal and centrifugal forces. They were soon, it is true, to have the opportunity of beholding once more the illuminated face of the Moon. They might even live long enough to catch a last glimpse of the distant Earth bathed in the glory of the solar rays. They might even have strength enough left to be able to chant one solemn final eternal adieu to their dear old Mother World, upon whose features their mortal eyes should never again rest in love and longing! Then, what was their Projectile to become? An inert, lifeless, extinct mass, not a particle better than the most defunct asteroid that wanders blindly through the fields of ether. A gloomy fate to look forward to. Yet, instead of grieving over the inevitable, our bold travellers actually felt thrilled with delight at the prospect of even a momentary deliverance from those gloomy depths of darkness and of once more finding themselves, even if only for a few hours, in the cheerful precincts illuminated by the genial light of the blessed Sun!
The ring of light, in the meantime, becoming brighter and brighter, Barbican was not long in discovering and pointing out to his companions the different mountains that lay around the Moon's south pole.
"There is Leibnitz on your right," said he, "and on your left you can easily see the peaks of Doerfel. Belonging rather to the Moon's dark side than to her Earth side, they are visible to terrestrial astronomers only when she is in her highest northern latitudes. Those faint peaks beyond them that you can catch with such difficulty must be those of Newton and Curtius."
"How in the world can you tell?" asked Ardan.
"They are the highest mountains in the circumpolar regions," replied Barbican. "They have been measured with the greatest care; Newton is 23,000 feet high."
"More or less!" laughed Ardan. "What Delphic oracle says so?"
"Dear friend," replied Barbican quietly, "the visible mountains of the Moon have been measured so carefully and so accurately that I should hardly hesitate in affirming their altitude to be as well known as that of Mont Blanc, or, at least, as those of the chief peaks in the Himalayahs or the Rocky Mountain Range."
"I should like to know how people set about it," observed Ardan incredulously.
"There are several well known methods of approaching this problem," replied Barbican; "and as these methods, though founded on different principles, bring us constantly to the same result, we may pretty safely conclude that our calculations are right. We have no time, just now to draw diagrams, but, if I express myself clearly, you will no doubt easily catch the general principle."
"Go ahead!" answered Ardan. "Anything but Algebra."
"We want no Algebra now," said Barbican, "It can't enable us to find principles, though it certainly enables us to apply them. Well. The Sun at a certain altitude shines on one side of a mountain and flings a shadow on the other. The length of this shadow is easily found by means of a telescope, whose object glass is provided with a micrometer. This consists simply of two parallel spider threads, one of which is stationary and the other movable. The Moon's real diameter being known and occupying a certain space on the object glass, the exact space occupied by the shadow can be easily ascertained by means of the movable thread. This space, compared with the Moon's space, will give us the length of the shadow. Now, as under the same circumstances a certain height can cast only a certain shadow, of course a knowledge of the one must give you that of the other, and vice versa. This method, stated roughly, was that followed by Galileo, and, in our own day, by Beer and Maedler, with extraordinary success."
"I certainly see some sense in this method," said Ardan, "if they took extraordinary pains to observe correctly. The least carelessness would set them wrong, not only by feet but by miles. We have time enough, however, to listen to another method before we get into the full blaze of the glorious old Sol."
"The other method," interrupted M'Nicholl laying down his telescope to rest his eyes, and now joining in the conversation to give himself something to do, "is called that of the tangent rays. A solar ray, barely passing the edge of the Moon's surface, is caught on the peak of a mountain the rest of which lies in shadow. The distance between this starry peak and the line separating the light from the darkness, we measure carefully by means of our telescope. Then—"
"I see it at a glance!" interrupted Ardan with lighting eye; "the ray, being a tangent, of course makes right angles with the radius, which is known: consequently we have two sides and one angle—quite enough to find the other parts of the triangle. Very ingenious—but now, that I think of it—is not this method absolutely impracticable for every mountain except those in the immediate neighborhood of the light and shadow line?"
"That's a defect easily remedied by patience," explained Barbican—the Captain, who did not like being interrupted, having withdrawn to his telescope—"As this line is continually changing, in course of time all the mountains must come near it. A third method—to measure the mountain profile directly by means of the micrometer—is evidently applicable only to altitudes lying exactly on the lunar rim."
"That is clear enough," said Ardan, "and another point is also very clear. In Full Moon no measurement is possible. When no shadows are made, none can be measured. Measurements, right or wrong, are possible only when the solar rays strike the Moon's surface obliquely with regard to the observer. Am I right, Signor Barbicani, maestro illustrissimo?"
"Perfectly right," replied Barbican. "You are an apt pupil."
"Say that again," said Ardan. "I want Mac to hear it."
