The Mysterious Island Jules Verne (red white royal blue txt) 📖

a way that they could be opened and shut like compasses, and returned with them to the beach. But as the sea horizon was hidden from this point by Claw Cape, the engineer determined to make his observation from Prospect Plateau, leaving, until the next day, the computation of the height of the latter, which could easily be done by elementary geometry.

The colonists, therefore, went to the edge of the plateau which faced the southeast, overlooking the fantastic rocks bordering the shore. The place rose some fifty feet above the right bank of the Mercy, which descended, by a double slope, to the end of Claw Cape and to the southern boundary of the island. Nothing obstructed the vision, which extended over half the horizon from the Cape to Reptile Promontory. To the south, this horizon, lit by the first rays of the moon, was sharply defined against the sky. The Cross was at this time reversed, the star Alpha being nearest the pole. This constellation is not situated as near to the southern as the polar star is to the northern pole; Alpha is about 27° from it, but Smith knew this and could calculate accordingly. He took care also to observe it at the instant when it passed the meridian under the pole, thus simplifying the operation.

The engineer opened the arms of his compass so that one pointed to the horizon and the other to the star, and thus obtained the angle of distance which separated them. And in order to fix this distance immovably, he fastened these arms, respectively, by means of thorns, to a cross piece of wood. This done, it was only necessary to calculate the angle obtained, bringing the observation to the level of the sea so as to allow for the depression of the horizon caused by the height of the plateau. The measurement of this angle would thus give the height of Alpha, or the pole, above the horizon; or, since the latitude of a point on the globe is always equal to the height of the pole above the horizon at that point, the latitude of the island.

This calculation was postponed until the next day, and by ten o’clock everybody slept profoundly.

XIV

The measure of the granite wall⁠—An application of the theorem of similar triangles⁠—The latitude of the island⁠—An excursion to the north⁠—An oyster-bed⁠—Plans for the future⁠—The sun’s passage of the meridian⁠—The coordinates of Lincoln Island.

At daybreak the next day, Easter Sunday, the colonists left the Chimneys and went to wash their linen and clean their clothing. The engineer intended to make some soap as soon as he could obtain some soda or potash and grease or oil. The important question of renewing their wardrobes would be considered in due time. At present they were strong, and able to stand hard wear for at least six months longer. But everything depended on the situation of the island as regarded inhabited countries, and that would be determined this day, providing the weather permitted.

The sun rising above the horizon, ushered in one of those glorious days which seem like the farewell of summer. The first thing to be done was to measure the height of Prospect Plateau above the sea.

“Do you not need another pair of compasses?” asked Herbert, of the engineer.

“No, my boy,” responded the latter, “this time we will try another and nearly as precise a method.”

Pencroff, Neb, and the reporter were busy at other things; but Herbert, who desired to learn, followed the engineer, who proceeded along the beach to the base of the granite wall.

Smith was provided with a pole twelve feet long, carefully measured off from his own height, which he knew to a hair. Herbert carried a plumb-line made from a flexible fibre tied to a stone. Having reached a point twenty feet from the shore and five hundred feet from the perpendicular granite wall, Smith sunk the pole two feet in the sand, and, steadying it carefully, proceeded to make it plumb with the horizon. Then, moving back to a spot where, stretched upon the sand, he could sight over the top of the pole to the edge of the cliff, bringing the two points in line, he carefully marked this place with a stone. Then addressing Herbert,

“Do you know the first principles of geometry?” said he.

“Slightly, sir,” answered Herbert, not wishing to seem forward.

“Then you remember the relation of similar triangles?”

“Yes, sir,” answered Herbert. “Their like sides are proportional.”

“Right, my boy. And I have just constructed two similar right angled triangles:⁠—the smaller has for its sides the perpendicular pole and the distances from its base and top to the stake; the second has the wall which we are about to measure, and the distances from its base and summit to the stake, which are only the prolongation of the base and hypotenuse of the first triangle.”

“I understand,” cried Herbert. “As the distance from the stake to the pole is proportional to the distance from the stake to the base of the wall, so the height of the wall is proportional to the height of the rod.”

“Exactly,” replied the engineer, “and after measuring the first two distances, as we know the height of the pole, we have only to calculate the proportion in order to find the height of the wall.”

The measurements were made with the pole and resulted in determining the distances from the stake to the foot of the pole and the base of the wall to be fifteen and five hundred feet respectively. The engineer and Herbert then returned to the Chimneys, where the former, using a flat stone and a bit of shell to figure with, determined the height of the wall to be 333.33 feet.

Then taking the compasses, and carefully measuring the angle which he had obtained the night before, upon a circle which he had divided into three hundred and sixty parts, the engineer found that this angle, allowing for the differences already explained, was 53°.