engineer.

"No, my boy," replied the latter, "we are going to proceed differently,
but in as precise a way."

Herbert, wishing to learn everything he could, followed the engineer to
the beach. Pencroft, Neb, and the reporter remained behind and occupied
themselves in different ways.

Cyrus Harding had provided himself with a straight stick, twelve feet
long, which he had measured as exactly as possible by comparing it with
his own height, which he knew to a hair. Herbert carried a plumb-line
which Harding had given him, that is to say, a simple stone fastened
to the end of a flexible fiber. Having reached a spot about twenty feet
from the edge of the beach, and nearly five hundred feet from the cliff,
which rose perpendicularly, Harding thrust the pole two feet into
the sand, and wedging it up carefully, he managed, by means of the
plumb-line, to erect it perpendicularly with the plane of the horizon.

That done, he retired the necessary distance, when, lying on the sand,
his eye glanced at the same time at the top of the pole and the crest of
the cliff. He carefully marked the place with a little stick.

Then addressing Herbert--"Do you know the first principles of geometry?"
he asked.

"Slightly, captain," replied Herbert, who did not wish to put himself
forward.

"You remember what are the properties of two similar triangles?"

"Yes," replied Herbert; "their homologous sides are proportional."

"Well, my boy, I have just constructed two similar right-angled
triangles; the first, the smallest, has for its sides the perpendicular
pole, the distance which separates the little stick from the foot of the
pole and my visual ray 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 horizont