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?"
"Yes," replied Herbert; "their homologous sides are proportional."
"Well, my boy, I have just constructed two similar right-angled
triangles; the first, the smallest, has for its sides the perpendicular
pole, the distance which separates the little stick from the foot of the
pole and my visual ray for hypothenuse; the second has for its sides the
perpendicular cliff, the height of which we wish to measure, the distance
which separates the little stick from the bottom of the cliff, and my
visual ray also forms its hypothenuse, which proves to be prolongation of
that of the first triangle."
"Ah, captain, I understand!" cried Herbert. "As the distance from the
stick to the pole is to the distance from the stick to the base of the
cliff, so is the height of the pole to the height of the cliff."
"Just so, Herbert," replied the engineer; "and when we have measured the
two first distances, knowing the height of the pole, we shall only have a
sum in proportion to do, which will give us the height of the cliff, and
will save us the trouble of measuring it directly."
The two horizontal distances were found out by means of the pole, whose
length above the sand was exactly ten feet.
The first distance was fifteen feet between the stick and the place where
the pole was thrust into the sand.
The second distance between the stick and the bottom of the cliff was
five hundred feet.
These measurements finished, Cyrus Harding and the lad returned to the
Chimneys.
The engineer then took a flat stone which he had brought back from one of
his previous excursions, a sort of slate, on which it was easy to trace
figures with a sharp shell. He then proved the following proportions:--

         15:500::10:x

        500 x 10= 5000

       5000

         15=333.3

From which it was proved that the granite cliff measured 333 feet in
height.
Cyrus Harding then took the instrument which he had made the evening
before, the space between its two legs giving the angular distance between
the star Alpha and the horizon. He measured, very exactly, the opening of
this angle on a circumference which he divided into 360 equal parts. Now,
this angle by adding to it the twenty-seven degrees which separated Alpha
from the antarctic pole, and by reducing to the level of the sea the height
of the cliff on which the observation had been made, was found to be fifty-
three degrees. These fifty-three degrees being subtracted from ninety
degrees--the distance from the pole to the equator--there remained thirty-
seven degrees. Cyrus Harding concluded, therefore, that Lincoln Island was
situated on the thirty-seventh degree of the southern latitude, or taking
into consideration through the imperfection of the performance, an error of
five degrees, that it must be situated between the thirty-fifth and the
fortieth parallel.
There was only the longitude to be obtained, and the position of the
island would be determined, The engineer hoped to attempt this the same
day, at twelve o'clock, at which moment the sun would pass the meridian.
It was decided that Sunday should be spent in a walk, or rather an
exploring expedition, to that side of the island between the north of the
lake and Shark Gulf, and if there was time they would push their
discoveries to the northern side of Cape South Mandible. They would
breakfast on the downs, and not return till evening.
At half-past eight the little band was following the edge of the channel.
On the other side, on Safety Islet, numerous birds were gravely strutting.
They were divers, easily recognized by their cry, which much resembles the
braying of a donkey. Pencroft only considered them in an eatable point of
view, and learnt with some satisfaction that their flesh, though blackish,
is not bad food.
Great amphibious creatures could also be seen crawling on the sand;
seals, doubtless, who appeared to have chosen the islet for a place of
refuge. It was impossible to think of those animals in an alimentary point
of view, for their oily flesh is detestable; however, Cyrus Harding
observed them attentively, and without making known his idea, he announced
to his companions that very soon they would pay a visit to the islet. The
beach was strewn with innumerable shells, some of which would have rejoiced
the heart of a conchologist; there were, among others, the phasianella, the
terebratual, etc. But what would be of more use, was the discovery, by Neb,
at low tide, of a large oysterbed among the rocks, nearly five miles from
the Chimneys.
"Neb will not have lost his day," cried Pencroft, looking at the spacious
oyster-bed.
"It is really a fortunate discovery," said the reporter, "and as it is
said that each oyster produces yearly from fifty to sixty thousand eggs, we
shall have an inexhaustible supply there."
"Only I believe that the oyster is not very nourishing," said Herbert.
"No," replied Harding. "The oyster contains very little nitrogen, and if
a man lived exclusively on them, he would have to eat not less than fifteen
to sixteen dozen a day."
"Capital!" replied Pencroft. "We might swallow dozens and dozens without
exhausting the bed. Shall we take some for breakfast?"
And without waiting for a reply to this proposal, knowing that it would
be approved of, the sailor and Neb detached a quantity of the molluscs.
They put them in a sort of net of hibiscus fiber, which Neb had
manufactured, and which already contained food; they then continued to
climb the coast between the downs and the sea.
From time to time Harding consulted his watch, so as to be prepared in
time for the solar observation, which had to be made exactly at midday.
All that part of the island was very barren as far as the point which
closed Union Bay, and which had received the name of Cape South Mandible.
Nothing could be seen there but sand and shells, mingled with debris of
lava. A few sea-birds frequented this desolate coast, gulls, great
albatrosses, as well as wild duck, for which Pencroft had a great fancy. He
tried to knock some over with an arrow, but without result, for they seldom
perched, and he could not hit them on the wing.
This led the sailor to repeat to the engineer,--
"You see, captain, so long as we have not one or two fowling-pieces, we
shall never get anything!"
"Doubtless, Pencroft," replied the reporter, "but it depends on you.
Procure us some iron for the barrels, steel for the hammers, saltpeter.
coal and sulphur for powder, mercury and nitric acid for the fulminate, and
lead for the shot, and the captain will make us first-rate guns."
"Oh!" replied the engineer, "we might, no doubt, find all these
substances on the island, but a gun is a delicate instrument, and needs
very particular tools. However, we shall see later!"
"Why," cried Pencroft, "were we obliged to throw overboard all the
weapons we had with us in the car, all our implements, even our pocket-
knives?"
"But if we had not thrown them away, Pencroft, the balloon would have
thrown us to the bottom of the sea!" said Herbert.
"What you say is true, my boy," replied the sailor.
Then passing to another idea,--"Think," said he, "how astounded Jonathan
Forster and his companions must have been when, next morning, they found
the place empty, and the machine flown away!"
"I am utterly indifferent about knowing what they may have thought," said
the reporter.
"It was all my idea, that!" said Pencroft, with a satisfied air.
"A splendid idea, Pencroft!" replied Gideon Spilett, laughing, "and which
has placed us where we are."
"I would rather be here than in the hands of the Southerners," cried the
sailor, "especially since the captain has been kind enough to come and join
us again."
"So would I, truly!" replied the reporter. "Besides, what do we want?
Nothing."
"If that is not--everything!" replied Pencroft, laughing and shrugging
his shoulders. "But, some day or other, we shall find means of going away!"
"Sooner, perhaps, than you imagine, my friends," remarked the engineer,
"if Lincoln Island is but a medium distance from an inhabited island, or
from a continent. We shall know in an hour. I have not a map of the
Pacific, but my memory has preserved a very clear recollection of its
southern part. The latitude which I obtained yesterday placed New Zealand
to the west of Lincoln Island, and the coast of Chile to the east. But
between these two countries, there is a distance of at least six thousand
miles. It has, therefore, to be determined what point in this great space
the island occupies, and this the longitude will give us presently, with a
sufficient approximation, I hope."
"Is not the archipelago of the Pomoutous the nearest point 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?" asked Neb, who followed the conversation with extreme
interest, pointing to the south.
"That way, nothing," replied Pencroft.
"Nothing, indeed," added the engineer.
"Well, Cyrus," asked the reporter, "if Lincoln Island is not more than
two or three thousand miles from New Zealand or Chile?"
"Well," replied the engineer, "instead of building a house we will build
a boat, and Master Pencroft shall be put in command--"
"Well then," cried the sailor, "I am quite ready to be captain--as soon
as you can make a craft that's able to keep at sea!"
"We shall do it, if it is necessary," replied Cyrus Harding.
But while these men, who really hesitated at nothing, were talking, the
hour approached at which the observation was to be made. What Cyrus Harding
was to do to ascertain the passage of the sun at the meridian of the
island, without an instrument of any sort, Herbert could not guess.
The observers were then about six miles from the Chimneys, not far from
that part of the downs in which the engineer had been found after his
enigmatical preservation. They halted at this place and prepared for
breakfast, for it was half-past eleven. Herbert went for some fresh water
from a stream which ran near, and brought it back in a jug, which Neb had
provided.
During these preparations Harding arranged everything for his
astronomical observation. He chose a clear place on the shore, which the
ebbing tide had left perfectly level. This bed of fine sand was as smooth
as ice, not a grain out of place. It was of little importance whether it
was horizontal or not, and it did not matter much whether the stick six
feet high, which was planted there, rose perpendicularly. On the contrary,
the engineer inclined it towards the south, that is to say, in the
direction of the coast opposite to the sun, for it must not be forgotten
that the settlers in Lincoln Island, as the island was situated in the
Southern Hemisphere, saw the radiant planet describe its diurnal arc above
the northern, and not above the southern horizon.
Herbert now understood how the engineer was going to proceed to ascertain
the culmination of the sun, that is to say its passing the meridian of the
island or, in other words, determine due south. It was by means of the
shadow cast on the sand by the stick, a way which, for want of an
instrument, would give him a suitable approach to the result which he
wished to obtain.
In fact, the moment when this shadow would reach its minimum of length
would be exactly twelve o'clock, and it would be enough to watch the
extremity of the shadow, so as to ascertain the instant when, alter having
successively diminished, it began to lengthen. By inclining his stick to
the side opposite to the sun, Cyrus Harding made the shadow longer, and
consequently its modifications would be more easily ascertained. In fact,
the longer the needle of a dial is, the more easily can the movement of its
point be followed. The shadow of the stick was nothing but the needle of a
dial. The moment had come, and Cyrus Harding knelt on the sand, and with
little wooden pegs, which he stuck into the sand, he began to mark the
successive diminutions of the stick's shadow. His companions, bending over
him, watched the operation with extreme interest. The reporter held his
chronometer in his hand, ready to tell the hour which it marked when the
shadow would be at its shortest. Moreover, as Cyrus Harding was working on
the 16th of April, the day on which the true and the average time are
identical, the hour given by Gideon Spilett would be the true hour then at
Washington, which would simplify the calculation. Meanwhile as the sun
slowly advanced, the shadow slowly diminished, and when it appeared to
Cyrus Harding that it was beginning to increase, he asked, "What o'clock is
it?"
"One minute past five," replied Gideon Spilett directly. They had now
only to calculate the operation. Nothing could be easier. It could be seen
that there existed, in round numbers, a difference of five hours between
the meridian of Washington and that of Lincoln Island, that is to say, it
was midday in Lincoln Island when it was already five o'clock in the
evening in Washington. Now the sun, in its apparent movement round the
earth, traverses one degree in four minutes, or fifteen degrees an hour.
Fifteen degrees multiplied by five hours give seventy-five degrees.
Then, since Washington is 770ø 3' 11" as much as to say seventy-seven
degrees counted from the meridian of Greenwich which the Americans take for
their starting-point for longitudes concurrently with the English--it
followed that the island must be situated seventy-seven and seventy-five
degrees west of the meridian of Greenwich, that is to say, on the hundred
and fifty-second degree of west longitude.
Cyrus Harding announced this result to his companions, and taking into
consideration errors of observation, as he had done for the latitude, he
believed he could positively affirm that the position of Lincoln Island was
between the thirty-fifth and the thirty-seventh parallel, and between the
hundred and fiftieth and the hundred and fifty-fifth meridian to the west
of the meridian of Greenwich.
The possible fault which he attributed to errors in the observation was,
it may be seen, of five degrees on both sides, which, at sixty miles to a
degree, would give an error of three hundred miles in latitude and
longitude for the exact position.
But this error would not influence the determination which it was
necessary to take. It was very evident that Lincoln Island was at such a
distance from every country or island that it would be too hazardous to
attempt to reach one in a frail boat.
In fact, this calculation placed it at least twelve hundred miles from
Tahiti and the islands of the archipelago of the Pomoutous, more than
eighteen hundred miles from New Zealand, and more than four thousand five
hundred miles from the American coast!
And when Cyrus Harding consulted his memory, he could not remember in any
way that such an island occupied, in that part of the Pacific, the
situation assigned to Lincoln Island.