Chapter 14 - Page 2

for hypothenuse; the second has for its sides the
perpendicular cliff, the height of which we wish to measure, the distance
which separates the little stick from the bottom of the cliff, and my
visual ray also forms its hypothenuse, which proves to be prolongation of
that of the first triangle."

"Ah, captain, I understand!" cried Herbert. "As the distance from the
stick to the pole is to the distance from the stick to the base of the
cliff, so is the height of the pole to the height of the cliff."

"Just so, Herbert," replied the engineer; "and when we have measured the
two first distances, knowing the height of the pole, we shall only have a
sum in proportion to do, which will give us the height of the cliff, and
will save us the trouble of measuring it directly."

The two horizontal distances were found out by means of the pole, whose
length above the sand was exactly ten feet.

The first distance was fifteen feet between the stick and the place where
the pole was thrust into the sand.

The second distance between the stick and the bottom of the cliff was
five hundred feet.

These measurements finished, Cyrus Harding and the lad returned to the
Chimneys.

The engineer then took a flat stone which he had brought back from one of
his previous excursions, a sort of slate, on which it was easy to trace
figures with a sharp shell. He then proved the following proportions:--

15:500::10:x

500 x 10= 5000

5000

15=333.3

From which it was proved that the granite cliff measured 333 feet in
height.

Cyrus Harding then took the instrument which he had made the evening
before, the space between its two legs giving the angular distance between
the star Alpha and the horizon. He measured, very exactly, the opening of
this angle on a circumference which he divided into 360 equal parts. Now,
this angle by adding to it the twenty-seven degrees which separated Alpha
from the antarctic pole, and by reducing to the level of the sea the height
of the cliff on which the observation had been made, was found to be fifty-
three degrees. These fifty-three degrees being subtracted from ninety
degrees--the distance from the pole to the equator--there remained thirty-
seven degrees. Cyrus Harding concluded, therefore, that Lincoln Island was
situated on the thirty-seventh degree of the southern latitude, or taking
into consideration through the imperfection of the performance, an error of
five degrees, that it must be situated between the thirty-fifth and the
fortieth parallel.

There was only the longitude to be obtained, and the position of the
island would be determined, The engineer hoped to attempt this the same
day, at twelve o'clock, at