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 is the 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
