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?”