certained 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Captain, who did not like being interrupted, having withdrawn to his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."