sir,” answered the lad.
“Then, if I am not mistaken, to-morrow will be one of the four days in the year when the mean and real time are the same; that is to say, my boy, that to-morrow, within some seconds of noon by the clocks, the sun will pass the meridian. If, therefore, the weather is clear, I think I will be able to obtain the longitude of the island within a few degrees.”
“Without a sextant or instruments?” asked Spilett.
“Yes,” replied the engineer. And since it is so clear, I will try to-night to find our latitude by calculating the height of the Cross, that is, of the Southern Pole, above the horizon. You see, my friends, before settling down, it will not do to be content with determining this land to be an island; we must find out its locality.”
“Indeed, instead of building a house, it will be better to build a ship, if we are within a hundred miles of an inhabited land.”
“That is why I am now going to try to get the latitude of the place, and to-morrow noon to calculate the longitude.”
If the engineer had possessed a sextant, the work would have been easy, as this evening, by taking the height of the pole, and to-morrow by the sun’s passage of the meridian, he would have the co-ordinates of the island. But, having no instruments he must devise something. So returning to the Chimneys, he made, by the light of the fire, two little flat sticks which he fastened together with a thorn, in 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 10 o’clock everybody slept profoundly.
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