"Well, if I am not mistaken, to-morrow will be one of the four days in the year in which the real time is identical with average time; that is to say, my boy, that to-morrow, to within some seconds, the sun will pass the meridian just at midday by the clocks.If the weather is fine I think that I shall obtain the longitude of the island with an approximation of some degrees.""Without instruments, without sextant?" asked Gideon Spilett.
"Yes," replied the engineer.'Also, since the night is clear, I will try, 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.
