The next day, the 16th of April, Easter Sunday, the colonists left the Chimneys at daybreak and proceeded to wash their linen and to clean their clothes. The engineer counted on making soap as soon as he could procure the basic materials necessary for the saponificaiton, soda or potash, fat or oil. The important question of the renewal of the wardrobe would also be treated in its proper time and place. In any case, their clothes would easily last six more months because they were well made and could resist the stress of manual labors. But all would depend on the position of the island with respect to inhabited lands. This they would determine on this very day if the weather permitted it.
They proceeded to wash their linen.
Now the sun rose on a clear horizon announcing a magnificent day, one of those beautiful days of autumn which are the final farewells to the warm season.
They therefore proceeded to complete the observations of the previous day by measuring the height of Grand View Plateau above sea level.
“Will you need an instrument like the one that you used yesterday?” Herbert asked the engineer.
“No, my child,” he answered, “we will proceed differently but in a manner almost as precise.”
Herbert, loving instruction in all things, followed the engineer, who turned away from the foot of the granite wall and went down to the edge of the beach. During this time Pencroff, Neb and the reporter were occupied with various activities.
Cyrus Smith had provided himself with a sort of straight pole, twelve feet long, which he had measured as accurately as possible by comparing it with his own height which he knew to the nearest inch. Herbert carried a plumb line that Cyrus Smith had given him, that is to say a simple stone fixed to the end of a flexible fiber.
Arriving about twenty feet from the edge of the shore and about five hundred from the granite wall which rose perpendicularly, Cyrus Smith drove the pole two feet into the sand and, wedging it in with care, he succeeded, by means of the plumb line, in placing it perpendicular to the plane of the horizon.
That done he backed up a distance such that when he lay down on the sand, the visual ray from his eye simultaneously skimmed the top of the pole and the top of the wall. Then he carefully marked this point with a thorn.
When he lay down on the sand...
Then, addressing Herbert:
“Do you know the elementary principles of geometry?” he asked him.
“A little, Mister Cyrus,” replied Herbert, who did not wish to stick his neck out.
“Do you recall what are the properties of two similar triangles?”
“Yes,” replied Herbert. “Their homologous sides are proportional.”
“Well, my child, I have constructed two similar right triangles. The first, the smaller one, has for its sides the perpendicular pole, the distance which separates the thorn from the base of the pole, and my visual ray for a hypotenuse; the second has for sides the perpendicular wall, whose height we are measuring, the distance that separates the thorn from the base of this wall, and my visual ray also forming its hypotenuse which is the prolongation of the hypotenuse of the first triangle.”
“Ah, Mister Cyrus, I understand” cried Herbert. “The distance from the thorn to the pole divided by the distance from the thorn to the base of the wall is equal to the height of the pole divided by the height of this wall.”
“They are equal, Herbert,” replied the engineer, “and when we have measured the first two distances, and since we know the height of the pole, we will only have a calculation to make of the ratio, which will give us the height of the wall and will save us the trouble of measuring it directly.”
The two horizontal distances were determined by means of the pole, whose length above the sand was exactly ten feet.
The first distance was fifteen feet between the thorn and the point where the pole had been driven into the sand. The second distance, between the thorn and the base of the wall, was five hundred feet.
These measurements completed, Cyrus Smith and the lad returned to the Chimneys.
There the engineer took a stone plate which he had brought back from his previous excursions, a sort of shale slate, on which it was easy to trace some numbers by means of a sharp quill. He therefore established the following proportion:
15 : 500 : : 10 : x 500 × 10 = 5000 5000 ---- = 333.33. 15
From this it was established that the height of the granite wall measured three hundred thirty three feet.1
Cyrus Smith then took the instrument which he had made the previous evening and whose two slats, by their separation, gave him the angular distance of the star Alpha above the horizon. He very accurately measured this angle against a circumference that he had divided into three hundred sixty equal parts. Now this angle was 10°. Consequently the total angular distance between the pole and the horizon, adding the 27° between Alpha and the antarctic pole and reducing it by the height above sea level of the plateau on which the observation was made, gave 37°. Cyrus Smith therefore concluded that Lincoln Island was situated on the 37th degree south latitude, or, taking an error of 5° into account in view of the imperfection of these operations, that it was situated between the 35th and the 40th parallel.
It remained to obtain the longitude in order to completely determine the coordinates of the island. This the engineer would attempt to determine this very day at noon, that is to say at the moment when the sun passed the meridian.
It was decided that they would take a walk this Sunday or rather an exploration of that part of the island situated between the north of the lake and Shark’s Gulf, and if the weather permitted, they would continue this reconnaissance up to the northern side of South Mandible Cape. They would eat on the dunes and only return by evening.
At eight thirty in the morning the small troop followed the border of the channel. On the opposite shore, on Safety Island, numerous birds promenaded gravely. They were the diving birds of the penguin species, very recognizable by their disagreeable cry which brings to mind the braying of the donkey. Pencroff could only consider them from the eating point of view and learned with a certain satisfaction that their flesh, though blackish, was very edible.
They could also see large amphibians crawling on the sand, seals no doubt, who seemed to have chosen the islet for refuge. It was hardly possible to consider these animals from the alimentary point of view because their oily flesh is detestable; however, Cyrus Smith observed them carefully and, without making his plans known, announced to his companions that they would soon pay a visit to the islet.
The shoreline followed by the colonists was scattered with innumerable shellfish some of which would have given joy to an amateur of malacology. There were among others phasianella, terebratula, trigonia, etc. But what would be very useful was this vast oyster bed discovered by Neb among the rocks at low tide, located about four miles from the Chimneys.
“Neb will not have wasted his day,” shouted Pencroff, observing the bank of ostracodes which spread out to the open sea.
“In fact it is a fortunate discovery,” said the reporter, “and if, as is claimed, each oyster produces fifty to sixty thousand eggs per annum, we will have an inexhaustible reserve.”
“Only I believe the oyster is not very nourishing,” said Herbert.
“No,” replied Cyrus Smith. “The oyster contains very little protein and if a man ate them exclusively he would need no less than fifteen to sixteen dozen each day.”
“Good,” said Pencroff. “We could devour dozens upon dozens before exhausting the bank. Shall we take some for our lunch?”
And without waiting for a reply to his proposition, knowing full well that it would be approved in advance, the sailor and Neb detached a certain quantity of these mollusks. They placed them in a sort of hibiscus fiber net that Neb had made and which already contained the meal’s menu; then they continued to ascend the shore between the dunes and the sea.
From time to time Cyrus Smith consulted his watch in order to prepare for the moment when the solar observation would take place, which had to be at noon precisely.
All of this portion of the island was very arid up to the point which closed Union Bay and which had received the name of South Mandible Cape. They saw there only sand and shells mixed with the debris of lava. Several sea birds frequented this desolated coast, sea gulls, large albatrosses as well as wild duck who with good reason excited Pencroff’s covetousness. He tried to attack them with arrows but without result because they hardly remained still and he could not reach them in flight.
This led the sailor to repeat to the engineer:
“You can see, Mister Cyrus, that unless we have one or two fowling pieces, our equipment will leave much to be desired.”
“Doubtless, Pencroff,” replied the reporter, “but it depends only on you. Get us iron for the barrel, steel for the firing pins, saltpeter, carbon and sulphur for the powder, mercury and nitric acid for the detonater, and finally lead for the balls and Cyrus will make us guns of the highest quality.”
“Oh!” replied the engineer, “without doubt we could find all these substances on the island, but a gun is a delicate instrument which requires tools of high precision. However we will see later on.”
“Why,” cried Pencroff, “did we throw overboard all the weapons that the basket carried, and our utensils, even our pocket knives?”
“But if we hadn’t thrown them out, Pencroff, it would be us that the balloon would have thrown to the bottom of the sea,” said Herbert.
“What you say is true, my boy,” replied the sailor.
Then passing to another thought:
“But think,” he added, “what must have been the bewilderment of Jonathan Forster and his companions when the next morning they found the square empty and the machine flown away.”
“My last care is to know what they thought,” said the reporter.
“Nevertheless, it was I who thought of the idea,” said Pencroff, with a pleased look.
“A good idea, Pencroff,” replied Gideon Spilett laughing, “and one which has placed us where we are.”
“I would rather be here than in the hands of the Southerners,” cried the sailor, “especially since Mister Smith has been kind enough to come and join us.”
“And I also, truly.” replied the reporter. “Besides, what do we lack? Nothing!”
“If that is not... everything.” answered Pencroff, who roared with laughter, shaking his large shoulders, “but one day or another we will find the means to leave.”
“And perhaps sooner than you imagine, my friends,” the engineer then said, “if Lincoln Island is only a moderate distance from an inhabited archipelago or a continent. In an hour we will know. I do not have a map of the Pacific but I have a very clear memory of its southern portion. The latitude which I obtained yesterday placed Lincoln Island between New Zealand on the west and the coast of Chile on the east. But between these two lands the distance is at least six thousand miles. It thus remains to determine which point the island occupies on this large space of ocean and it is that which the longitude will give us within the hour with a sufficient approximation, I hope.”
“Isn’t the archipelago of Tuamotu the nearest to us in latitude?” asked Herbert.
“Yes,” replied the engineer, “but the distance which separates us from it is more than twelve hundred miles.”
“And that way?” said Neb, who followed the conversation with extreme interest, his hand pointing south.
“There, nothing,” replied Pencroff.
“Nothing, in fact,” added the engineer.
“Well, Cyrus,” asked the reporter, “if Lincoln Island is only two or three hunderd miles from New Zealand or from Chile?...”
“Well,” replied the engineer, “instead of making a house we will make a boat and Master Pencroff will be in charge of maneuvering it...”
“To be sure, Mister Cyrus,” cried the sailor, “I am all ready to be captain... as soon as you will find the means to construct a vessel large enough to take to sea.”
“We will make it, if that is necessary,” replied Cyrus Smith.
But while these men, who truly doubted nothing, were chatting, the hour approached during which the observation would take place. How would Cyrus Smith verify the passage of the sun on the meridian of the island without any instrument? Herbert could not guess.
The observers then found themselves at a distance of six miles from the Chimneys, not far from that part of the dunes in which the engineer had been found after his puzzling rescue. They halted in this locality and everyone got ready to eat since it was eleven thirty. Herbert went to get some sweet water from a stream which flowed nearby and he carried it in a jug provided by Neb.
During these preparations Cyrus Smith arranged everything for his astronomical observation. He chose a very flat place on the beach that the receding sea had perfectly leveled. This very fine bed of sand was made as smooth as glass without any grain of sand higher than another. However it was of little importance whether this bed was horizontal or not and of no importance that the six foot rod be placed perpendicularly. To the contrary, the engineer even inclined it to the south that is to say to the side opposite the sun, because it should not be forgotten that since Lincoln Island was situated in the southern hemisphere, the colonists saw the radiant orb describe its diurnal arc above the northern horizon and not the southern horizon.
Herbert then understood how the engineer was going to proceed to determine the sun’s highest point, that is to say its passage on the meridian of the island or in other terms, the local noontime. It was by means of the shadow projected on the sand by the rod, the means which, in the absence of an instrument, would give him an approximation sufficient for the result he wished to obtain.
In fact the moment when this shadow would attain its minimum length would be precisely noon and it would suffice to follow the end of this shadow in order to recognize the instant when, after having successively diminished it would begin to lengthen. By inclining the rod to the side opposite to the sun, Cyrus Smith produced a longer shadow and consequently his modification would make his determination easier. In fact, the larger the pointer of a dial is, the easier it is to follow the displacement of its point. The shadow of the rod was nothing more than the pointer of a dial.
When he thought that the moment had arrived, Cyrus Smith knelt on the sand and by means of small wooden pegs that he stuck into the sand, he began to check off the successive decreases in the shadow of the rod. His companions, leaning over him, followed the operation with extreme interest.
The reporter held his chronometer in his hand ready to note the time when the shadow would be its shortest. Inasmuch as Cyrus Smith was operating on the 16th of April, a day in which the true time and the average time coincide, the time given by Gideon Spilett would be the true time then at Washington, which would simplify the calculation.
The sun advanced slowly; the shadow of the rod diminished little by little and when it seemed to Cyrus Smith that it began to lengthen:
The sun advanced slowly.
“What time is it?” he said.
“Five o’clock and one minute," Gideon Spilett replied at once.
It remained only to make the calculation. Nothing was easier. There was, as they saw, in round figures, a difference of five hours between the meridian of Washington and that of Lincoln Island, that is to say, it was noontime on Lincoln Island when it was already five o’clock in the evening in Washington. Now the sun, in its apparent movement around the earth, covers one degree in four minutes making 15° per hour. 15° multiplied by five hours gives 75°.
Therefore since Washington is at 77° 3′ 11″ say 77° counting from the meridian of Greenwich—which the Americans take as the longitude reference concurrently with the English—it follows that the island was situated at 77° plus 75° to the west of the meridian of Greenwich, that is to say at the 152nd degree west longitude.
Cyrus Smith announced this result to his companions and taking account of the errors of observation, as he had done for the latitude, he could affirm that the coordinates of Lincoln Island were between the 35th and 40th parallel and between the 150th and the 155th meridians to the west of the meridian of Greenwich.
The possible variations that he attributed to observational errors were, as we saw, 5° both ways which, at sixty miles per degree, gave an error of three hundred miles in latitude or in longitude for the exact location.
But this error would have no influence on the decision they would have to make. It was very evident that Lincoln Island was at such a distance from all land or archipelagos that they could not hazard to cross this distance in a simple and fragile boat.
In fact this determination placed it at least twelve hundred miles from Tahiti and the islands of the archipelago of Tuamotu, more than eighteen hundred miles from New Zealand and more than four thousand five hundred miles from the American coast.
And when Cyrus Smith consulted his memory he could not recall in any fashion that an island occupied that part of the Pacific assigned to Lincoln Island.