THE MEASURE OF THE GRANITE WALL—AN APPLICATION OF THE THEOREM OF
SIMILAR TRIANGLES—THE LATITUDE OF THE ISLAND—AN EXCURSION TO THE
NORTH—AN OYSTER-BED—PLANS FOR THE FUTURE—THE SUN’S PASSAGE OF THE
MERIDIAN—THE CO-ORDINATES OF LINCOLN ISLAND.
At daybreak the next day, Easter Sunday, the colonists left the
Chimneys and went to wash their linen and clean their clothing. The
engineer intended to make some soap as soon as he could obtain some
soda or potash and grease or oil. The important question of renewing
their wardrobes would be considered in due time. At present they were
strong, and able to stand hard wear for at least six months longer. But
everything depended on the situation of the island as regarded
inhabited countries, and that would be determined this day, providing
the weather permitted.
The sun rising above the horizon, ushered in one of those glorious days
which seem like the farewell of summer. The first thing to be done was
to measure the height of Prospect Plateau above the sea.
“Do you not need another pair of compasses?” asked Herbert, of the
engineer.
“No, my boy,” responded the latter, “this time we will try another and
nearly as precise a method.”
Pencroff, Neb, and the reporter were busy at other things; but Herbert,
who desired to learn, followed the engineer, who proceeded along the
beach to the base of the granite wall.
Smith was provided with a pole twelve feet long, carefully measured off
from his own height, which he knew to a hair. Herbert carried a
plumb-line made from a flexible fibre tied to a stone. Having reached a
point 20 feet from the shore and 500 feet from the perpendicular
granite wall, Smith sunk the pole two feet in the sand, and, steadying
it carefully, proceeded to make it plumb with the horizon. Then, moving
back to a spot where, stretched upon the sand, he could sight over the
top of the pole to the edge of the cliff, bringing the two points in
line, he carefully marked this place with a stone. Then addressing
Herbert,
“Do you know the first principles of geometry?” said he.
“Slightly, sir,” answered Herbert, not wishing to seem forward.
“Then you remember the relation of similar triangles?”
“Yes, sir,” answered Herbert. “Their like sides are proportional.”
“Right, my boy. And I have just constructed two similar right angled
triangles:—the smaller has for its sides the perpendicular pole and the
distances from its base and top to the stake; the second has the wall
which we are about to measure, and the distances from its base and
summit to the stake, which are only the prolongation of the base and
hypothenuse of the first triangle.
“I understand,” cried Herbert. “As the distance from the stake to the
pole is proportional to the distance from the stake to the base of the
wall, so the height of the wall is proportional to the height of the
rod.”
“Exactly,” replied the engineer, “and after measuring the first two
distances, as we know the height of the pole, we have only to calculate
the proportion in order to find the height of the wall.”
The measurements were made with the pole and resulted in determining
the distances from the stake to the foot of the pole and the base of
the wall to be 15 and 500 feet respectively. The engineer and Herbert
then returned to the Chimneys, where the former, using a flat stone and
a bit of shell to figure with, determined the height of the wall to be
333.33 feet.
Then taking the compasses, and carefully measuring the angle which he
had obtained the night before, upon a circle which he had divided into
360 parts, the engineer found that this angle, allowing for the
differences already explained, was 53°. Which, subtracted from 90°—the
distance of the pole from the equator—gave 37° as the latitude of
Lincoln Island. And making an allowance of 5° for the imperfections of
the observations, Smith, concluded it to be situated between the 35th
and the 40th parallel of south latitude.
But, in order to establish the co-ordinates of the island, the
longitude also must be taken. And this the engineer determined to do
when the sun passed the meridian at noon.
They therefore resolved to spend the morning in a walk, or rather an
exploration of that part of the island situated to the north of Shark
Gulf and the lake; and, if they should have time, to push on as far as
the western side of South Mandible Cape. They would dine on the downs
and not return until evening.
At half-past 8 the little party set out, following the edge of the
channel. Opposite, upon Safety Islet, a number of birds of the
sphemiscus family strutted gravely about. There were divers, easily
recognizable, by their disagreeable cry, which resembled the braying of
an ass. Pencroff, regarding them with gastronomic intent, was pleased
to learn that their flesh, though dark colored, was good to eat. They
could also see amphibious animals, which probably were seals, crawling
over the sand. It was not possible to think of these as food, as their
oily flesh is detestable; nevertheless Smith observed them carefully,
and without disclosing his plans to the others, he announced that they
would very soon, make a visit to the island. The shore followed by the
colonists was strewn with mollusks, which would have delighted a
malacologist. But, what was more important, Neb discovered, about four
miles from the Chimneys, among the rocks, a bed of oysters, left bare
by the tide.
“Neb hasn’t lost his day,” said Pencroff, who saw that the bed extended
some distance.
“It is, indeed, a happy discovery,” remarked the reporter. “And when we
remember that each oyster produces fifty or sixty thousand eggs a year,
the supply is evidently inexhaustable.”
“But I don’t think the oyster is very nourishing,” said Herbert.
“No,” answered Smith. “Oysters contain very little azote, and it would
be necessary for a man living on them alone to eat at least fifteen or
sixteen dozen every day.”
“Well,” said Pencroff, “we could swallow dozens and dozens of these and
not exhaust the bed. Shall we have some for breakfast?”
And, without waiting for an answer, which he well knew would be
affirmative, the sailor and Neb detached a quantity of these mollusks
from the rocks, and placed them with the other provisions for
breakfast, in a basket which Neb had made from the hibiscus fibres.
Then they continued along the shore between the downs and the sea.
From time to time Smith looked at his watch, so as to be ready for the
noon observation.
All this portion of the island, as far as South Mandible Cape, was
desert, composed of nothing but sand and shells, mixed with the debris
of lava. A few sea birds, such as the sea-gulls and albatross,
frequented the shore, and some wild ducks excited the covetousness of
Pencroff. He tried to shoot some, but unsuccessfully, as they seldom
lit, and he could not hit them flying.
This made the sailor say to the engineer:—
“You see, Mr. Smith, how much we need guns!”
“Doubtless, Pencroff,” answered the reporter, “but it rests with you.
You find iron for the barrels, steel for the locks, saltpetre, charcoal
and sulphur for the powder, mercury and nitric acid for the fulminate,
and last of all, lead for the balls, and Mr. Smith will make us guns of
the best quality.
“Oh, we could probably find all these substances on the island,” said
the engineer. “But it requires fine tools to make such a delicate
instrument as a firearm. However, we will see after awhile.”
“Why, why did we throw the arms and everything else, even our
penknives, out of the balloon?” cried Pencroff.
“If we hadn’t, the balloon would have thrown us into the sea,” answered
Herbert.
“So it would, my boy,” answered the sailor; and then another idea
occurring to him:—
“I wonder what Mr. Forster and his friend thought,” he said, “the next
day, when they found they balloon had escaped?”
“I don’t care what they thought,” said the reporter.
“It was my plan,” cried Pencroff, with a satisfied air.
“And a good plan it was, Pencroff,” interrupted the reporter, laughing,
“to drop us here!”
“I had rather be here than in the hands of the Southerners!” exclaimed
the sailor, “especially since Mr. Smith has been kind enough to rejoin
us!”
“And I, too,” cried the reporter. “After all, what do we lack here?
Nothing.”
“That means—everything,” answered the sailor, laughing and shrugging
his shoulders. “But some day we will get away from this place.”
“Sooner, perhaps, than you think, my friends,” said the engineer, “if
Lincoln Island is not very far from an inhabited archipelego or a
continent. And we will find that out within an hour. I have no map of
the Pacific, but I have a distinct recollection of its southern
portion. Yesterday’s observation places the island in the latitude of
New Zealand and Chili. But the distance between these two countries is
at least 6,000 miles. We must therefore determine what point in this
space the island occupies, and that I hope to get pretty soon from the
longitude.
“Is not the Low Archipelago nearest us in latitude,” asked Herbert.
“Yes,” replied the engineer, “but it is more than 1,200 miles distant.”
“And that way?” inquired Neb, who followed the conversation with great
interest, pointing towards the south.
“Nothing!” answered Pencroff.
“Nothing, indeed,” added the engineer.
“Well, Cyrus,” demanded the reporter, “if we find Lincoln Island to be
only 200 or 300 miles from New Zealand or Chili?”
“We will build a ship instead of a house, and Pencroff shall command
it.”
“All right, Mr. Smith,” cried the sailor; “I am all ready to be
captain, provided you build something seaworthy.”
“We will, if it is necessary,” answered Smith.
While these men, whom nothing could discourage, were talking, the hour
for taking the observation approached. Herbert could not imagine how
Mr. Smith would be able to ascertain the time of the sun’s passage of
the meridian of the island without a single instrument. It was 11
o’clock, and the party, halting about six miles from the Chimneys, not
far from the place where they had found the engineer after his
inexplicable escape, set about preparing breakfast. Herbert found fresh
water in a neighboring brook, and brought some back in a vessel which
Neb had with him.
Meantime, the engineer made ready for his astronomical observation. He
chose a smooth dry place upon the sand, which the sea had left
perfectly level. It was no more necessary, however, for it to be
horizontal, than for the rod which he stuck in the sand to be
perpendicular. Indeed, the engineer inclined the rod towards the south
or away from the sun, as it must not be forgotten that the colonists of
Lincoln Island, being in the Southern Hemisphere, saw the orb of day
describe his diurnal arc above the northern horizon.
Then Herbert understood how by means of the shadow of the rod on the
sand, the engineer would be able to ascertain the culmination of the
sun, that is to say, its passage of the meridian of the island, or, in
other words, the _time_ of the place. For the moment that the shadow
obtained its minimum length it would be noon, and all they had to do
was to watch carefully the end of the shadow. By inclining the rod from
the sun Smith had made the shadow longer, and therefore its changes
could be the more readily noted.
When he thought it was time, the engineer knelt down upon the sand and
began marking the decrease in the length of the shadow by means of
little wooden pegs. His companions, bending over him, watched the
operation with the utmost interest.
The reporter, chronometer in hand, stood ready to mark the minute when
the shadow would be shortest. Now, as this 16th of April was a day when
the true and mean time are the same, Spilett’s watch would give the
true time of Washington, and greatly simplify the calculation.
Meantime the shadow diminished little by little, and as soon as Smith
perceived it begin to lengthen he exclaimed:—
“Now!”
“One minute past 5,” answered the reporter.
Nothing then remained but the easy work of summing up the result. There
was, as we have seen, five hours difference between the meridian of
Washington and that of the island. Now, the sun passes around the earth
at the rate of 15° an hour. Fifteen multiplied by five gives
seventy-five. And as Washington is in 77° 3’ 11” from the meridian of
Greenwich, it follows that the island was in the neighborhood of
longitude 152° west.
Smith announced this result to his companions, and, making the same
allowance as before, he was able to affirm that the bearing of the
island was between the 35° and 37° of south latitude, and between the
150° and 155° of west longitude.
The difference in this calculation, attributable to errors in
observation, was placed, as we have seen, at 5° or 300 miles in each
direction. But this error did not influence the conclusion that Lincoln
Island was so far from any continent or archipelago that they could not
attempt to accomplish the distance in a small boat.
In fact, according to the engineer, they were at least 1,200 miles from
Tahiti and from the Low Archipelago, fully 1,800 miles from New
Zealand, and more than 4,500 miles from the coast of America.
And when Cyrus Smith searched his memory, he could not remember any
island in the Pacific occupying the position of Lincoln Island.