Chapter 14 Chapter Fourteen

The next day, April 16, which was Easter Sunday, the inhabitants came out of their grottoes at dawn to wash their clothes.The engineer intended to start making soap as soon as he could find the necessary raw materials, baking soda or potash, fat or oil.As for new clothes, this is an important issue that should be discussed at an appropriate time and place.Their clothes are strong enough to last at least six months, even with the daily wear and tear of physical labor, but it all depends on whether the island is near inhabited land.This can be resolved if the day is sunny. The sun rises above the clear horizon, telling people that a sunny day has arrived.This is a beautiful autumn day, as if the warm season is about to say goodbye, and it seems to be a special souvenir for people.

The elevation of the cliff must now be measured in order to complete last night's observations. Don't you need an instrument like the compasses you used last night?Herbert said to the engineer. No, boy, replied the engineer, we will do it another way, but only as accurately as yesterday. Herbert wanted to learn everything he could afford, so he went with the engineer to the seashore.Pencroft, Neb, and the correspondent remained where they were, engaged in other duties. Cyrus.Smith prepared a straight wood, and knowing his length he would score well, he calculated exactly from his height that the length of the wood was twelve feet.Herbert held the plumb line that Smith had given him, made of flexible vegetable fibers, with a stone attached to one end.When they were twenty feet from the sea and nearly five hundred feet from the vertical cliff, Smith carefully inserted the pole into the sand to a depth of two feet, keeping it perpendicular to the ground by means of a vertical line.

After this step, he retreated a considerable distance, and then lay face down on the sand, where his eyes could see both the top of the pole and the upper edge of the cliff.He carefully marked the point of observation with a stick, and said to Herbert: Do you know the most basic principles of geometry? Know a little bit, Mr. Smith.Herbert said he had no desire to show himself at all. Do you remember the conditions that two similar triangles should have? Remember, replied Herbert, that their corresponding sides are proportional. Well, boy, I just made two similar right triangles, the first one is smaller, and its three sides are: the vertical wooden pole and the distance from this small stick to the bottom of the wooden pole, and my sight is The hypotenuse of the triangle, the three sides of the second triangle are: the vertical cliff. What we want to measure is its height. side, the hypotenuse is also the extension of the hypotenuse of the first triangle.

Ah, Mr. Smith, I see!Herbert exclaimed that the distance between the stick and the pole was to the distance between the stick and the bottom of the precipice, as the height of the post was to the height of the precipice. "That's right, Herbert," said the engineer, "we already know the length of the pole, and by measuring the two horizontal distances, and then working out the ratio, we can find the height of the cliff, without having to measure it directly." They measured two horizontal distances with a wooden pole, which was exactly ten feet high on the sand. The first distance was fifteen feet from the stick to the place where the pole was inserted.

The second distance was five hundred feet from the stick to the bottom of the cliff. When it was over, Cyrus.Smith and the boy went back to the grotto. The engineer produced a slab stone which he had brought back from one of his hunting trips.This stone is like a slate, and it is easy to scratch words on it with sharp shells.He found the following ratios: Fifteen: five hundred ∥ ten: X Five hundred × ten ∥ five thousand Five thousand ÷ fifteen ∥ three hundred and thirty-three.three From this it follows that the height of the granite cliff is 333 feet. Then Cyrus.Smith took out the instrument he had made the night before, and the distance between the two feet of the compass was the angular distance between the second cross and the horizontal line.He first divided a circle into three hundred and sixty equal parts, and then dropped the compass angles on the circle with great precision, and the result was ten degrees.Add to this angle the cross 2's distance from the South Pole of 27 degrees, and then subtract the value of the height from the sea surface on the cliff where the observation was made to obtain an angle of 37 degrees.The distance between the South Pole and the horizon is ninety degrees, and fifty-three degrees are subtracted from ninety degrees to leave thirty-seven degrees.Therefore, Cyrus.The conclusion of Smith's survey is that Lincoln Island is on the 37th parallel south latitude.Taking into account the degree of inaccuracy in the calculations, assuming an error of five degrees, the position of the island must lie between thirty-five and forty degrees south latitude.

Now just wait for the longitude to be calculated to determine the location of the island.The engineer intends to carry out the experiment at twelve o'clock in the noon of this day, when the sun passes the meridian. They decided to go on a trip on Sunday, that is, to explore the area between the north side of the lake and Shark Bay.If there was time, they would continue north of the Cape of the South Jaw.Booked breakfast on the dunes and didn't come back until early evening. At half-past eight the party moved along the edge of the channel.On the safety island opposite, many birds were swaggering.They bray like donkeys, and you can tell they are diving birds.Pencroft saw them only from the point of view of eating.He was very satisfied, because although the meat of this bird was darker, it tasted good.

They also saw some huge amphibians crawling on the sand, undoubtedly seals.They probably intend to make their home on the small island. This kind of animal is impossible to look at from the point of view of eating, because the meat of seals is very greasy and unpalatable.But Cyrus.Smith still looked at them very carefully. He didn't say what he thought, but told everyone that they would go to the island soon.There are countless shells scattered on the beach, some of which a conchologist would be delighted to see; among them are physalis mussels, triangular clams and more.But it was even more affordable: at low tide, Neb discovered a large clam farm among the rocks nearly five miles from the cave.

Neb's day was not in vain.said Pencroft, looking at the great clam-field. It was a lucky discovery, said the correspondent, since each clam was said to produce fifty to sixty thousand eggs a year, so that we could never run out of them. All I know is that clams are not very nutritious.Herbert said. Yes, Smith said, clams contain very little protein, and if a person eats only clams all day, he needs to eat at least fifteen to sixteen dozen a day. great!We could eat as much as we could, said Pencroft, but there would never be enough clams here.Shall we bring some for breakfast? The sailor and Neb knew that everyone was in favor, and without waiting for an answer, they picked up a large pile of clams.They put the clams in a mesh bag of hibiscus fiber that Neb had made, with the rest of the food they had already contained, and they continued up the shore between the dunes and the sea.

Smith looked at his watch from time to time in order to observe the sun on time, which had to be done at noon. This part of the island, as far as the South Jaw at the end of Union Bay, is deserted.There is nothing to see here, only sand and shells, mixed with some fragments of lava.Only a few sea-birds frequented this deserted shore, such as gulls, giant albatrosses, and mallards, for which Pencroft was very fond.He tried to shoot some of them down with his arrows, but failed, the ducks seldom stopped, and he was not yet able to shoot them while they were flying. Then the sailor said to the engineer:

You see, Mr. Smith, we can't shoot anything in our lives without a shotgun or two! Of course there is no doubt, Pencroft, said the correspondent, but that depends on you.Find us some iron for the barrel, steel for the firing-pin, saltpetre, charcoal, and brimstone for the gunpowder, mercury and nitric acid for thormer, and lead for bullets; We make it. oh!The engineer replied that it is certain that these things can be found on the island.However, the construction of the gun is very delicate and requires special tools to manufacture.Let's talk about it later! Why then, exclaimed Pencroft, did we throw out all the weapons in the basket, all the utensils, even our knives?

Had they not been thrown out then, Pencroft, the balloons would have sunk us to the bottom of the sea!Herbert said. Well, you're telling the truth, kid.said the sailor. Then the sailor thought of other problems. You think, he said, Jonathan.The next morning, Foster and his partner found that the man had run away and the balloon had flown. They must have died of panic! I don't care about them.said the correspondent. This is all my idea!said Pencroft triumphantly. That is a good idea, Pencroft!Ji Ding.It brought us here, laughed Spilett. I'd rather be here than in the hands of the Southerners, cried the sailor, especially since Mr. Smith is back with us. I thought so too, really!And, said the correspondent, what more do we want?Nothing is missing. If not this place has everything!Pencroft shrugged his shoulders and said with a smile, besides, one day we will try to get out of here! If Lincoln Island is only an average distance from the inhabited islands or the mainland, said the engineer, then, my friends, this day may come sooner than you think.We shall know the position of Lincoln Island in an hour.I don't have a map of the Pacific, but the geography of the southern Pacific is pretty clear in my head.According to the latitude I found yesterday, Lincoln Island is bounded by New Zealand to the west and the coast of Chile to the east.But the distance between these two countries is at least six thousand miles.It is necessary, therefore, to ascertain at what point in this great ocean the island lies, which we shall soon know from the longitude, which I believe may be quite accurate. Are the Pamotu Islands the nearest place to us on the same latitude?asked Herbert. Yes, replied the engineer, but we are still more than twelve hundred miles away from it. where?Neb pointed south, interested in what the others had said. There is nothing there.replied Pencroft. Yes, nothing.the engineer added. Cyrus, asked the correspondent, what if Lincoln Island was within two or three thousand miles of New Zealand or Chile? Then, replied the engineer, we will not build a house, but build a ship first, and Pencroft will command it. Well, said the sailor loudly, I am always ready to be the captain, just waiting for you to make a ship that can sail! We'll build one if necessary.Cyrus.Smith replied. Indeed, these people never panic when encountering problems. They talked and talked, and the observation time gradually approached.Herbert could never guess Cyrus.How could Smith determine the course of the sun through the meridian of the island without any instruments. The observers were at this time about six miles from the grotto, not far from the part of the dune where they found the engineer after his mysterious rescue.They stopped here to prepare to eat, and it was already half past eleven.Herbert ran to a nearby stream, and returned with some fresh water in a bottle which Neb had brought. While preparing to eat, Smith arranged everything and planned to make astronomical observations.He chose an open place on the seashore, where the ground is very flat after low tide.The fine sand was as smooth as ice, not a grain of sand seemed misplaced.It did not matter much whether the ground was level, nor did it matter much whether the six-foot-high post was perpendicular to the ground.On the contrary, the engineer also tilted it to the south, that is, the direction where the seashore faces away from the sun, because one thing must be remembered: since the island is in the southern hemisphere, the arc of the sun seen by the residents of Lincoln Island is not on the south horizontal line, but to the north. Now Herbert understood how the engineer intended to fix the culmination of the sun, that is, the position passing through the island's meridian.The so-called orientation passing the meridian of the island, in other words, is the due south of the local area.His method was to measure the projection of a pole on the sand, which, in the absence of instruments, allowed him to obtain quite the exact results he sought. It stands to reason that when the length of the shadow shrinks to the shortest, it should be twelve o'clock at noon. If you look carefully at the end of the shadow, you can find the moment when the shadow begins to lengthen after gradually shortening.Cyrus.By tilting the pole toward the sun, Smith made the shadow longer, so its change was easier to see.The longer the hour hand of a sundial, the easier it is to distinguish the movement of the needle point.The shadow of the pole is equivalent to the pointer on the sundial. Cyrus.Smith estimated that the time was up, so he knelt on the sand, and the shadow of the pole gradually shortened, so he inserted small wooden stakes into the ground one by one following the shadow as a mark.His companions stooped to watch the work in progress with great interest.The correspondent, watch in hand, was ready to report the moment when the shadow was at its shortest.One more point needs to be made, Cyrus.The day Smith made the observation was April 16, and the official time of this day was exactly the same as the average time, so Gideon.The time on Spilett's watch was the real time in Washington at that time, so the calculation was simple.At this time, with the movement of the sun, the shadow gradually shortened, waiting for Cyrus.When Smith noticed that the shadows started to grow back, he asked, when? Five past one.Ji Ding.Spilett replied immediately. They now just need to calculate the results.It doesn't get any easier than this.It can be seen that the longitude difference between Washington and Lincoln Island is about five hours, that is to say, at noon on Lincoln Island, it is already five o'clock in the evening in Washington.The apparent motion of the sun around the earth takes four minutes for each degree, that is, it moves fifteen degrees in one hour.Fifteen degrees times five (hours) equals seventy-five degrees. Since the longitude of Washington is 77 degrees, 3 minutes and 11 seconds, it is the 77th degree from the Greenwich meridian, which is the starting point of the Greenwich meridian in both the United States and the United Kingdom. From this, it can be calculated: It must be seventy-seven and seventy-five degrees west of the Greenwich meridian, or one hundred and fifty-two degrees west. Cyrus.Smith announced this result to his partners, and at the same time, as in calculating latitude, estimated the possible errors in observation.He believed he could ascertain the position of Lincoln Island to lie between thirty-five and forty degrees in latitude and between one hundred and fifty and one hundred and fifty-five degrees west of the Greenwich meridian in longitude. It can be seen that in the observation, he estimated that the possible error is five degrees up and down, which is 60 miles at a time. In the actual position, the possible error caused by five degrees of latitude and longitude is 300 miles. But this error does not affect the inference that needs to be known.Obviously Lincoln Island is so far from any country or island that it would be too risky to go there in a small boat. According to calculations, this island is actually at least 1,200 miles away from Teddy Island and the Pamotu Islands, more than 1,800 miles away from New Zealand, and more than 4,500 miles away from the west coast of the United States. ! Cyrus.Smith recalled that he could not recall any island in this part of the Pacific near Lincoln Island.