"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?"