THE MYSTERIOUS ISLAND. Jules Verne
this very evening, to obtain our latitude by calculating the height of the Southern Cross, that is, from the southern pole above the horizon. You understand, my friends, that before undertaking the work of installation in earnest it is not enough to have found out that this land is an island; we must, as nearly as possible, know at what distance it is situated, either from the American continent or Australia, or from the principal archipelagoes of the Pacific.”
“In fact,” said the reporter, “instead of building a house it would be more important to build a boat, if by chance we are not more than a hundred miles from an inhabited coast.”
“That is why,” returned Harding, “I am going to try this evening to calculate the latitude of Lincoln Island, and to-morrow, at midday, I will try to calculate the longitude.”
If the engineer had possessed a sextant, an apparatus with which the angular distance of objects can be measured with great precision, there would have been no difficulty in the operation. This evening by the height of the pole, the next day by the passing of the sun at the meridian, he would obtain the position of the island. But as they had not one he would have to supply the deficiency.
Harding then entered the Chimneys. By the light of the fire he cut two little flat rulers, which he joined together at one end so as to form a pair of compasses, whose legs could separate or come together. The fastening was fixed with a strong acacia thorn which was found in the wood pile. This instrument finished, the engineer returned to the beach, but as it was necessary to take the height of the pole from above a clear horizon, that is, a sea horizon, and as Claw Cape hid the southern horizon, he was obliged to look for a more suitable station. The best would evidently have been the shore exposed directly to the south; but the Mercy would have to be crossed, and that was a difficulty. Harding resolved, in consequence, to make his observation from Prospect Heights, taking into consideration its height above the level of the sea—a height which he intended to calculate next day by a simple process of elementary geometry.
The settlers, therefore, went to the plateau, ascending the left bank of the Mercy, and placed themselves on the edge which looked northwest and southeast, that is, above the curiously-shaped rocks which bordered the river.
This part of the plateau commanded the heights of the left bank, which sloped away to the extremity of Claw Cape, and to the southern side of the island. No obstacle intercepted their gaze, which swept the horizon in a semi-circle from the cape to Reptile End. To the south the horizon, lighted by the first rays of the moon, was very clearly defined against the sky.
At this moment the Southern Cross presented itself to the observer in an inverted position, the star Alpha marking its base, which is nearer to the southern pole.
This constellation is not situated as near to the antarctic pole as the Polar Star is to the arctic pole. The star Alpha is about twenty-seven degrees from it, but Cyrus Harding knew this and made allowance for it in his calculation. He took care also to observe the moment when it passed the meridian below the pole, which would simplify the operation.
Cyrus Harding pointed one leg of the compasses to the horizon, the other to Alpha, and the space between the two legs gave him the angular distance which separated Alpha from the horizon. In order to fix the angle obtained, he fastened with thorns the two pieces of wood on a third placed transversely, so that their separation should be properly maintained.
That done, there was only the angle to calculate by bringing back the observation to the level of the sea, taking into consideration the depression of the horizon, which would necessitate measuring the height of the cliff. The value of this angle would give the height of Alpha, and consequently that of the pole above the horizon, that is to say, the latitude of the island, since the latitude of a point of the globe is always equal to the height of the pole above the horizon of this point.
The calculations were left for the next day, and at ten o’clock every one was sleeping soundly.
Chapter 14
The next day, the 16th of April, and Easter Sunday, the settlers issued from the Chimneys at daybreak, and proceeded to wash their linen. The engineer intended to manufacture soap as soon as he could procure the necessary materials—soda or potash, fat or oil. The important question of renewing their wardrobe would be treated of in the proper time and place. At any rate their clothes would last at least six months longer, for they were strong, and could resist the wear of manual labor. But all would depend on the situation of the island with regard to inhabited land. This would be settled to-day if the weather permitted.
The sun rising above a clear horizon, announced a magnificent day, one of those beautiful autumn days which are like the last farewells of the warm season.
It was now necessary to complete the observations of the evening before by measuring the height of the cliff above the level of the sea.
“Shall you not need an instrument similar to the one which you used yesterday?” said Herbert to the 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 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.
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