The penny magazine of the Society for the Diffusion of Useful Knowledge, issue…

THE PENNY MAGAZINE

OF THE

Society for the Diffusion of Useful Knowledge.

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35.] PUBLISHED EVERY SATURDAY. [October 20, 1832

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CATCHING TURTLES.

[Illustration: Catching Turtles on the Coast of Cuba.]

It is not improbable that some of our readers, who reside near a great
commercial port, may have seen the landing of a cargo of strange-looking
animals, which, turned upon their backs, appear the most helpless of
creatures, and in this condition may have naturally led the spectator to
imagine that they are incapable of removing from place to place, and
have therefore little enjoyment of existence. These creatures, to use
the language of the epicure, are fine “lively turtles”--the term
“lively” being understood to mean that they have suffered little from a
long voyage--that they are in good health--and that the “green fat,” the
glory of aldermen, is in the most perfect state of excellence. Without
asking our readers to feel any very strong interest in the prospects of
high living which the arrival of a cargo of turtles offers to many
individuals who are somewhat too much inclined to set a high value upon
the gratifications of the palate, we may be able to satisfy a rational
curiosity as to the habits of these singular animals, which offer some
higher benefits to mankind than that of furnishing the most costly
luxury of a city feast.

The turtle and the tortoise belong to the same group of reptiles--in
fact the turtle is a tortoise which principally inhabits the water, and
is only found occasionally on the land. The two varieties represented in
the above plate are the Green Tortoise (_a_), and the Loggerhead
Tortoise (_b_). The former is the species chiefly used for food. It is
found, in great numbers, on the coasts of all the islands and continents
of the torrid zone. The shoals which surround these coasts are covered
with marine plants; and in these water pastures, which are near enough
to the surface to be readily seen by the naked eye in calm weather, a
prodigious abundance of animals, mostly amphibious, feed, and amongst
them multitudes of tortoises. Dampier, the old voyager, describing the
Gallapagos Islands, says, “There are good wide channels between these
islands fit for ships to pass; and in some places shoal water, where
there grows plenty of turtle grass; therefore these islands are
plentifully stored with sea turtle.” The tortoise, whether of the land
or water species, is, as most of our readers know, protected, both on
the back and belly, by a hollow shield, which is open at each end, for
the issuing of the head and fore-feet at one time, and the tail and
hind-feet at another.

The upper shield is termed the back-plate, or buckler; the lower shield
the breast-plate. The middle of the buckler, in most of the species, is
covered by numerous pieces or plates resembling horn in texture and
composition; and the beautiful substance known by the name of
tortoise-shell is obtained principally from a small species called the
Hawksbill. The feet of the marine tortoises are much longer than those
of the land, and their toes are united by a membrane so that they swim
with great facility. The head, feet, and tail are covered with small
scales. The jaws of the wide mouth are not provided with teeth, but the
jaw-bones are very hard and strong, and being at the same time very
rough, the animal is enabled to consume its vegetable food with ease,
and at the same time to crush the shell-fish on which the marine species
also feed. The green tortoise attains an enormous size and weight; some
individuals measuring six or seven feet in length from the tip of the
nose to the extremity of the tail, by three or four feet broad, and
weighing as much as eight hundred pounds. Dampier says, “I heard of a
monstrous green turtle once taken at Port Royal, in the bay of
Campeachy, that was four feet deep from the back to the belly, and the
belly six feet broad. Captain Rocky’s son, of about nine or ten years of
age, went in it (meaning in the shell) as in a boat, on board his
father’s ship about a quarter of a mile from the shore.” The green
tortoise commonly weighs from two to three hundred pounds.

The instinct which leads the female turtle to the shore to lay her eggs,
exposes her to the danger of becoming the prey of man. She deposits her
eggs on the loose sand, and abandons them at once to the chance, which
approaches almost to a certainty in the southern hemisphere, that they
will be hatched by the influence of the sun’s rays. She digs, by means
of her fore-feet, one or more holes about a foot wide and two feet deep,
in which she usually deposits more than a hundred eggs. These eggs are
round, and are two or three inches in diameter; they are covered with a
membrane something like wet parchment. The female generally lays three
times in each year, at intervals of about a fortnight or three weeks.
They almost always go ashore in the night time. A loose sand being
essential to the hatching of the eggs, the turtles frequent only
particular shores; but these are often several hundred miles from their
feeding places. The eggs are hatched in less than a month after they are
laid; and in about eight or ten days the young reptiles crawl to the
water. Few, however, reach their native element, in proportion to the
number produced. They become the prey of sea-fowl and various quadrupeds
of prey. The tiger is an especial enemy to the tortoise; but man is
still more actively engaged in their destruction. The collection of
tortoise eggs forms one of the most important of the occupations of the
Indians of the Orinoco. Humboldt has given a most interesting account of
this branch of commerce, of which we shall furnish an abstract in a
future number.

The wood-cut at the head of this article represents the manner in which
the marine tortoises are caught on the coast of Cuba, and on parts of
the South American continent. The Count de Lacepede, in his History of
Oviparous Quadrupeds, has described the various modes in which the
business of tortoise-catching is carried on; and we shall conclude this
notice with an abstract of his account. It must be remarked that the
turtle is a most important addition to the ordinary mode of victualling
a ship; and that, therefore, the war in which the human race engages
against them is rendered absolutely necessary by the wants of
navigators. The turtles which are demanded in England for the
gratification of a luxurious appetite, constitute a very small number,
when compared with those which offer an agreeable and salutary food to
the hardy crews who are engaged in the commerce of the tropical seas.

“In spite of the darkness which is chosen by the female tortoises for
concealment when employed in laying their eggs, they cannot effectually
escape from the pursuit of their enemies: the fishers wait for them on
the shore, at the beginning of the night, especially when it is
moonlight, and, either as they come from the sea, or as they return
after laying their eggs, they either dispatch them with blows of a club,
or turn them quickly over on their backs, not giving them time either to
defend themselves, or to blind their assailants, by throwing up the sand
with their fins. When very large, it requires the efforts of several men
to turn them over, and they must often employ the assistance of
handspikes or levers for that purpose. The buckler of this species is so
flat as to render it impossible for the animal to recover the recumbent
posture, when it is once turned on its back.

“A small number of fishers may turn over forty or fifty tortoises, full
of eggs, in less than three hours. During the day, they are employed in
securing those which they had caught in the preceding night. They cut
them up, and salt the flesh and the eggs. Sometimes they may extract
above thirty pints of a yellow or greenish oil from one large
individual; this is employed for burning, or, when fresh, is used with
different kinds of food. Sometimes they drag the tortoises they have
caught, on their backs, to enclosures, in which they are reserved for
occasional use.

“The tortoise fishers from the West Indies and the Bahamas, who catch
these animals on the coasts of Cuba and its adjoining islands,
particularly the Caymanas, usually complete their cargoes in six weeks
or two months; they afterwards return to their own islands, with the
salted turtle, which is used for food both by the whites and the
negroes. This salt turtle is in as great request in the American
colonies, as the salted cod of Newfoundland is in many parts of Europe;
and the fishing is followed by all these colonists, particularly by the
British, in small vessels, on various parts of the coast of Spanish
America, and the neighbouring desert islands.

“The green tortoise is likewise often caught at sea in calm weather, and
in moon-light nights. For this purpose two men go together in a small
boat, which is rowed by one of them, while the other is provided with a
harpoon, similar to that used for killing whales. Whenever they discover
a large tortoise, by the froth which it occasions on the water in rising
to the surface, they hasten to the spot as quickly as possible, to
prevent it from escaping. The harpooner immediately throws his harpoon
with sufficient force to penetrate through the buckler to the flesh; the
tortoise instantly dives, and the fisher gives out a line, which is
fixed to the harpoon, and, when the tortoise is spent with loss of
blood, it is hauled into the boat or on shore.”


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THE FLEMISH LANGUAGE.--No. 2.

Perhaps our readers may not be unwilling to see a few more specimens of
the Flemish language. It should be stated that this book of dialogues,
from which our last specimens were taken, contains at the end a kind of
manual of good manners, it being the opinion of the writer--“that youth
have long been in want of a treatise on manners, which should be based
upon our usages, and adapted to the state of our knowledge.”

We give a few of the maxims of this Dutch Chesterfield for the use of
those whom they may concern.

Directions for behaviour at table:--

Het _zoud_ neémt men met You must take the _salt_
het _punt_ van het mes, with the _point_ of
het welk men aen zyn your knife, after
_brood_ moet afvaegen. having wiped it on your
_bread_.

Instead of a literal translation we have given the meaning, marking with
Italics a few words which are the most striking in the two languages.
But besides those which we have marked, other similarities, such as
_welk_, “whilk or which,” will be detected in this and the following
specimen:--

_Daer is niets zoo _There is nought so
ongemanierd_ dan _iet_ unmannered_ as to take
van de schotel te _aught_ from the dish
neémen met het _forket with the _fork_
waer_ men _mede eét_. wherewith you eat, or,
literally, “_where man_
with _eats_.”

We think so; and we also say with the Dutch Chesterfield--

_Opent_ den mond _niet te _Open not_ your mouth
wyt_ als _gy eét_. _too wide_ when _ye
eat_.

The reason for this precept is obvious; the Dutch Chesterfield has,
however, thought it necessary to tell his countrymen the _why_ and
_wherefore_ of it.

Vraegt _niet te drinken Ask _not_ (for something)
terwyl gy zup eét; wagt _to drink_ the _while
tot dat gy iet_ anders ye eat soup; wait_ till
_geëéten hebt_. _that ye somewhat
(aught)_ else _have
eaten_.

And, above all,--

Gaept _niet rond ter wyl Look not (gape) _round_
gy drinkt_. the _while ye drink_.

Perhaps these maxims may be enough for one lesson. The original goes on
for some length, and, finally, admonishes young folks not to carry off
cakes, apples, &c. in their pockets from the table. We cordially concur
in this advice.

We shall conclude with directions for sitting at table:--

Als _gy zult gezeten_ When _ye_ shall be
zyn, _struht u niet uyt _seated_, _stretch ’o
op_ uwen _stoel; zet not out_ upon your seat
uwe beenen niet (_stool_); _set o’_
overeen;_ wiegt _niet_ legs (_bones_) _not_
met _uwen stoel;_ maer over (across) one
_houd u regt, de voeten another; rock not with
op_ den _grond _’o stool;_ but _hold
geplaetst_. ’o right_ (straight)
the _feet placed_ on
the _ground_.

Directions how to hold hats and reticules in company:--

Eenen _jongeling houd_ A _younker holds_ his
zynon _hoed_ op zyne _hat_ (_hood_) _upon_
_knieën_, zonder het his _knees_, but
binnenste te _laeten without _letting_ you
zien_, Eene _jonge _see_ the inside (het
dogter_ houd insgelyks binnenste.) A _young
_haere_ tassche _op girl_ (daughter)
haere knieen_. _holds_ in like manner
_her_ bag on her
_knees_.


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COMETS.--No. 1.

Most of our readers must have heard of the comet of Biela, which appears
in the present year, and has caused no small alarm among those who are
entirely ignorant of the nature of comets in general, and of the track
of this particular one. We have met with an amusing little book on this
comet of 1832, by Littrow, professor of astronomy at Vienna, from which
we shall give the substance of a few extracts, that may not be
uninteresting.

There are only four comets whose orbits are yet accurately known. That
which appears in the present year is called Biela’s comet, from its
having been discovered by an Austrian officer of that name in Bohemia in
1826. Its period of revolution round the sun is six years and two
hundred and seventy days. Though it had been seen before in 1772 and
1805, it was not known to be a comet of so short a period. In the
present year, 1832, we shall have its fourth visit. On the 27th of next
November the comet will be nearest to the sun, but even then about
seventy-two millions of geographical miles distant from that body: and
on the 22d of this month (October) it will be nearest to the earth, and
at the distance of about forty-four millions of miles from us.

The number of comets must be very great, for the appearance of near five
hundred has been recorded; and if we consider how many must have passed
unnoticed in the early history of the world for want of persons to
observe them, we may form some idea of the prodigious quantity of these
bodies. From 1769 to 1807 no comet appeared that attracted any attention
from people in general, though astronomers during this period observed
no fewer than thirty-six. There being then so many of these wanderers
whose course is unknown, it may be supposed a possible thing that one of
them should run foul of the earth; and supposing it to be a body of any
considerable magnitude and density, such a shock would entirely put an
end to the present order of existence. Setting aside however, the
question as to the magnitude and real nature of comets, let us consider
what chance there is of our knocking against the comet of the present
year, which, from the position of its orbit, looks much more threatening
than any other that is known.

On the 29th of the present month this comet of Biela will be distant
from a certain point in the earth’s _orbit_ only about 2⅓ of the earth’s
diameters, or about twenty thousand miles in round numbers. If the earth
were at this very point of its annual track on the same 29th of October,
it _might_ happen that we should feel such effects from the comet, or
from the enormous mass of vapour composing it (computed to be more than
one hundred and fifty times greater than the mass of our earth,) as to
destroy all animal and vegetable life. But as the earth will not be at
this dangerous point till the 30th of November, or thirty-two days
_later_ than the comet, we shall have nothing to fear from it this time.
For the earth moving in its orbit at the rate of about 67,680
geographical miles in one hour, it will be 51,978,240 miles distant from
the comet on the 29th of this month, and in no danger at all of being
affected by it in any way that we can estimate.

Perhaps few people will trouble themselves about this comet any more,
when they learn that they are quite safe for the present. But how, it
may be asked, are we sure that on some future occasion we may not
approach too near? If the comet should be in its nearest point to the
sun on the 28th of December, instead of the 27th of November, then we
should really approach it within the short distance above-mentioned. But
this near approach cannot take place, unless the comet should be in its
nearest point to the sun in the latter part of December; and this again
will not take place till the year 1933, when the comet will be in its
perihelion (i. e. nearest point to the sun) on the 31st of December, and
again in the year 2115, on the 26th of the same month. But, should the
comet’s period of six years and two hundred and seventy days be somewhat
changed in the course of the next century, from the action of Jupiter
and other planets, (which is far from improbable,) this would diminish
still further the chance of any unpleasant proximity in the years 1933
or 2115. This we hope will console those who regard this visitor with
more feelings of fear than curiosity.

It may be added that this comet is a very small one, and, though its
vapour occupies so enormous a space, the real kernel or bright part of
the comet is not more than sixty or eighty miles in diameter; and hence
it is conjectured that if it really is a _body_ properly so called, it
must be very small indeed, and that, even in a near approach to the
earth, any injury that it might do by its attraction would be hardly
felt. Again, says Littrow--“as to the tail and its deadly vapours,
which, as they say, threaten us with such dreadful consequences, we
really have nothing at all to fear from _them_: and for the following
plain, but quite satisfactory reason--the comet has no tail.”

The following conclusion will, we hope, remove whatever apprehension may
still lurk in the minds of the most timid, as to the danger which they
have to fear from this comet in the years 1933, 2115, and in subsequent
years--should their lives be so far prolonged.

“We have already stated that Biela’s comet can only come near the earth
when it is at its least distance from the sun, in the latter part of
December. But since this proximity of the comet to the sun may just as
well happen on _every other_ day of the year as in December, and since
its period is six years two hundred and seventy days, or about two
thousand five hundred days, in round numbers,--after a lapse of two
thousand five hundred years, a near _approach_ (not an actual collision)
to the comet is _probable_. I say merely _probable_, from which it must
not be concluded that such an event actually will take place in two
thousand five hundred years. This result merely means that a man might
bet two thousand five hundred to ten, or to one hundred, that the comet
will not come _near_ the earth for the next ten or one hundred years. At
the end of two thousand five hundred years there will be an equal chance
that the comet will make this near approach, or that it will not. And
after two thousand five hundred years the chance of its approaching the
earth will go on increasing, but at so slow a rate that many thousands
of years must elapse before the event can be _really_ expected.”


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THE PARTHENON.

[Illustration: Remains of the Parthenon.]

We shall proceed with our description of the Athenian antiquities in the
British Museum, as soon as the collection is numbered according to its
present arrangement. We understand from the Officers of the Institution
that this essential assistance to the visitor will be immediately given;
for the old order of the several pieces of sculpture being considerably
altered, a reference to the former numbers only would prove
embarrassing. In the mean time we give that view of the Parthenon, for
which the representation of the temple of Apollo Epicurius, near
Phigalia, was substituted by mistake.


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NAPLES.

In a preceding number we endeavoured to give our readers a notion of the
situation and main features of Naples. We shall now devote a page to a
few of the interesting objects contained within that city.

The first in importance is the _Studj_ or _Museo Borbonico_, or, what we
may better call, the National Museum. In many respects this magnificent
establishment is unrivalled in the world. Besides a rich statue gallery
which boasts the Farnesian Hercules, the all perfect Aristides, the
Farnesian Toro, a Venus perhaps superior in loveliness to the Medicean,
and other masterpieces of ancient Greek art, the Museum contains a
gallery of pictures with two of Raphael’s best works, and splendid
specimens of Titian, Correggio, Claude, Salvator Rosa, and other great
masters; and, moreover, a library, a collection of Etruscan vases, a
cabinet of ancient coins and medals, and rooms filled with the ancient
relics of Herculaneum and Pompeii.

The collection of vases, which have nearly all been discovered and dug
up in the kingdom, is the richest in existence; but it is more
especially the collection of the objects rescued from the two interred
cities, that gives the Museum of Naples its superiority to others.

In this collection are found some of the most perfect works of ancient
art in bronze, domestic implements of nearly every sort, mechanical
tools, surgical and mathematical instruments, rings, necklaces, and
other specimens of jewellery, and even the entire apparatus of a woman’s
toilet. The attentive visitor, by studying these objects, may in a few
hours obtain a better insight into the domestic manners of the ancients,
than whole years devoted to books can give him. One of the most
interesting departments of this unique collection, is that of the
papyri, or manuscripts, discovered in the excavations of Herculaneum.
The ancients did not bind their books (which, of course, were all
manuscripts) like us, but rolled them up in scrolls. When these of
Herculaneum were discovered, they presented, as they still do, the
appearance of burnt sticks, or cylindrical pieces of charcoal, which
they had acquired from the action of the heat contained in the lava that
buried the whole city. They seem quite solid both to the eye and touch,
yet an ingenious monk discovered a process of detaching leaf from leaf
and unrolling them, by which they could be read without much difficulty.
When these manuscripts were first exposed to the air a considerable
number of them crumbled to dust. Our countryman, the late Sir Humphry
Davy, destroyed the integrity of a few by making unsuccessful
experiments, which he fancied might produce a result that would
supersede the slow and laborious process now adopted; but about eighteen
hundred still remain. Four of them have been unrolled, and fac-similies
of them, with translations, published by the Neapolitan government.

To pass to a very different object. One of the singularities of Naples
is its Campo Santo, or cemetery for the poor. This is situated on the
skirts of the town, looking towards Mount Vesuvius. A wall of
inconsiderable elevation encloses a quadrangular space, whose surface is
cut into three hundred and sixty-five holes, like the mouths of wells or
cisterns. One of these holes is opened every day; the dead bodies of the
poor of that day--without coffins--without so much as a rag about
them--are thrown one upon another, as they arrive, through the mouth
into a deep cave below cut in the tufa rock, and at night a stone is
laid over the horrid sepulchre and secured by cement. The next day the
cave next in order of date is opened, and so on through the year. At the
end of the year, the first cave is again opened, by which time its
contents, the decomposition of which is assisted by quick-lime, are
reduced to little more than bones.

The catacombs of Naples, whose entrance is under the hill of
Capo-di-Monte, and the grotto of Posilippo, at the extremity of the
western suburb of the city, are also remarkable objects. The first are
of great extent, and contain many curious specimens of painting and
subterranean architecture by the early Christians, and an appalling mass
of human skulls and bones, the relics of the victims of a plague that
depopulated Naples some two centuries back. The second is a subterranean
passage cut through the hill of Posilippo in remote antiquity, but
enlarged and improved as a road in modern times. It is considerably more
than half a mile long by twenty-four feet broad; its height is unequal,
varying from twenty-five to sixty feet: it is well paved with large
flags of lava. By night, it is _now_ tolerably well illuminated by lamps
suspended from its rugged roof, but by day the “darkness visible” that
reigns through the passage renders it always solemn and sometimes
embarrassing. Being the only frequented road to and from the town of
Pozzuoli, Baia, Cuma, and other places, there is seldom a lack of
passengers; and their voices, as they cry to each other in the dark, and
the noise of their horses’ tread and of the wheels of their waggons,
carriages, and gigs, echoing through the grotto and the deep vaults
which in many places branch off from it laterally, produce to the ear of
the stranger an effect that is almost terrific. Immediately above the
entrance to the grotto, coming from the city, stands on a romantic
cliff, which has been in part cut away to widen the approach to the
subterranean road, an ancient Roman tomb in almost perfect preservation.
This tomb is supposed to have been that of the great poet Virgil, and is
visited as such by every traveller. Its claim has been questioned in
vain; mankind are attached to such pleasant illusions, (if this be one,
which we by no means decide,) and continue from age to age to crowd to
the spot. A laurel once flourished by the side of the venerable
sepulchre and covered its roof; but the successive thousands and
thousands of visitors, each anxious for a memorial gathered in such a
spot, have not left leaf, branch, stem, or root of the sacred tree.

In the old part of the city, among some Roman ruins called the
“_Anticaglia_,” are supposed to exist part of the walls of the theatre
where the Emperor Nero sang and played on the lyre like a common actor.
The Neapolitans care little about this; but their great boast, that
which they fancy renders them the envy of the world, is their
Opera-house of San Carlo, which in truth, must be acknowledged as the
most spacious and most splendid theatre in Europe.

[Illustration: The Grotto of Posilippo and Tomb of Virgil.]


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FRACTIONS.

It is not our intention to write a treatise on the part of arithmetic
which stands at the head of this article, or to enter into the reasons
why so many persons, who can solve a simple question in which there are
nothing but whole numbers, are puzzled by anything which contains
fractions. Our object is, to give some slight notions on this part of
the subject to those who are already able to work the four rules in
whole numbers.

When we add any two numbers together, it is understood that both of them
have the same unit, or that both are some number of times the same
thing. Thus, that two and three make five, means that two _yards_ and
three _yards_ make five _yards_, or that two _pounds_ and three _pounds_
make five _pounds_, and so on. We do not in that case say anything of
two _yards_ and three _feet_, or of two _pounds_ and three _shillings_.
The following questions might arise:--If we have a distance which is
neither six yards nor seven yards, but something between the two, how
are we to represent this in numbers, and form rules for adding and
subtracting this length to or from others of the same kind, without
introducing a new measure, or talking of any other length except a yard?
The answer to this will bring us, as we shall see, to the common meaning
of the word _fraction_, and the way of representing a fraction. As we
cannot measure anything exactly, we must first decide what degree of
accuracy is necessary. This will vary in different operations, but we
will suppose, for example’s sake, that a line may be rejected as
insignificant, of which it would take more than a hundred to make a
yard. If then we divide a yard into one hundred equal parts, and first
remove the six whole yards which the above-mentioned distance contains,
we have a remainder which does not contain all the hundred parts just
mentioned, since it is less than one yard. Suppose that, on measuring
the remainder, we find it to contain more than 53 and less than 54 of
the hundred parts: if then we call it 53 parts out of a hundred of a
yard, the error committed will be less than one part out of a hundred;
that is, by what was supposed above, it will be sufficient to say that
the length of the whole is 6 yards and 53 of the hundred equal parts
which would compose another yard, or 53 hundredths of a yard. If we were
inventing a system of arithmetic, we might choose among many different
ways of representing this. For example, 6 yards 53_{100} of a yard; 6
yards and 53÷100 of a yard; and so on. The common method is the
following, 6-53/100 yards, it being always understood that when we write
two numbers under one another with a line between, the unit of which we
speak, be it a yard, pound, acre, or any other, is cut into as many
equal parts as are shown by the lower number, and as many of them are
taken as is shown by the higher number. Thus, ⅞ of a mile is the length
obtained by cutting a mile into 8 equal parts, and taking 7 of them,
being of course less than the whole mile by one of these parts.

Such a fraction as we have described is less than the unit of which it
is a part; but a whole number of units and a fraction may be represented
together by the same method. If, in the preceding example, we had
divided each of the six yards into 100 parts, there would have been 600
such parts, which, with the 53 parts furnished by the fraction, would
have made 653, not of yards, but of the hundredth parts of yards. This
we should represent by 653/100, denoting that each of a succession of
yards has been divided into 100 parts, out of which collection of parts
653 have been taken. The term fraction is applied equally to all cases;
and with this extension of meaning, the unit itself maybe represented as
a fraction, for one yard is 2/2 yards, or 3/3 yards, or 4/4 yards, and
so on.

The lower line of a fraction is called the _denominator_, and the upper
the _numerator_: these are Latin words, which may be literally
translated by the _namer_ and the _numberer_; the first tells _what
sort_ of parts is taken, and the second _how many_ of them are taken.
The following propositions will serve for consideration, and also to
familiarize the reader with the use of these terms. When the numerator
is less than the denominator, the fraction is less than a unit. When the
numerator is greater than the denominator, the fraction is greater than
the unit. Of two fractions which have the same denominator, that is the
greater which has the greater numerator. Of two fractions which have the
same numerator, that is the greater which has the less denominator. It
is usual to distinguish fractions which are less than the unit from
those which are greater by calling the former _proper_, and the latter
_improper_, fractions.

As yet we have only considered fractions of the unit; and it is always
understood that a simple fraction, such as ⅞, is a fraction of the unit,
or it is _one_ yard or _one_ pound which is divided into 8 parts.
Fractions of other numbers are written by placing the number to be
divided after the fraction of it which is to be taken, thus--¾ of 7,
which means that 7 is to be divided into 4 parts, of which parts, 3 are
taken. We now ask, what fraction of the unit is ¾ of 7, or into how many
parts must _one_ yard be cut, and how many times must one of those parts
be repeated, so as to give the same length which arises from cutting
_seven_ yards into 4 parts, and taking 3 of them? It is obvious that ¾
of 7 yards is 7 times as much as ¾ of 1 yard, or simply ¾ and 3 quarters
of a yard repeated 7 times is 21 quarters or 21/4. Similarly ⅖ of 8 is
16/5 of 1, or 16/5. Hence it follows that ¼ of 3 is ¾, ⅑ of 13 is 13/9,
and so on. If therefore we take the eighth part of nine, we get the same
as if we had repeated the eighth part of the unit nine times. We may
therefore consider a fraction, such as ⅚, in two ways, either as the
sixth part of five, or as the sixth part of unity repeated 5 times. It
may sometimes be necessary to take a fraction of a fraction, such as ⅖
of ⅞, or having found ⅞ of 1, to divide it into five parts, and take two
of them. We ask, what fraction of the unit would the result of this
double operation give? The answer is multiply the two numerators
together, and also the two denominators, which gives 14/40, or
two-fifths of seven-eighths of a yard is fourteen parts out of forty. To
see the reason, let us first take the more simple case ⅕ of ⅛. It is
plain that if we divide one yard into eight equal parts, and afterwards
divide each of these parts into 5 equal parts, we have divided the whole
yard into 8 times 5, or 40 equal parts. Consequently the fifth part of
an eighth part is one fortieth of the whole, or ⅕ of ⅛ is 1/40. But one
fifth of _seven_ eighths will be 7 times as much as ⅕ of _one_ eighth,
and will therefore be 7/40; again, _two_ fifths of ⅞ will be twice as
much as _one_ fifth of ⅞, and will therefore be 14/40, or ⅖ of ⅞ is
14/40, according to the rule. In the same way 3/7 of 11/10 is 33/70.
This rule corresponds to the multiplication of whole numbers, and is
therefore called multiplication of fractions. The connexion is not
obvious at first, owing to a little difference in our manner of speaking
about whole numbers and fractions. But if we were in the habit of saying
that 2 multiplied by 6 is six _of_ 2, in the same way as we say “six of
them,” “six of his men,” it would appear natural to call those rules
which tell us how many units there are in six _of_ two, and what
fraction of unit there is in ⅖ _of_ ⅞, by the same name. By this rule
all questions of fractions are solved, which would have required
multiplication if they had been in whole numbers. For example, if 1
pound cost 2 shillings, 6 pounds will cost 6 times 2 shillings;
similarly, if 1 pound costs ⅞ of a shilling, ⅖ of a pound will cost ⅖ of
⅞ of a shilling.

The most important proposition relating to fractions, being the one on
which the rules most materially depend, is the following: If the
numerator and denominator be either both multiplied or both divided by
the same number, the value of the fraction is not altered. For example,
take ⅗ and multiply its numerator and denominator by 4, which gives
12/20. In the second fraction we cut the unit into four times as many
parts as in the first, consequently each part of the unit signified in
the second fraction is the fourth of that signified in the first. But in
the second fraction, four times as many parts are taken as in the first,
by which the balance is restored. Let us suppose that two yards of cloth
are to be measured by a foot measure. The foot being ⅓ of the unit, and
6 of these being necessary, 6/3 will be the fraction in yards,
representing not only the number of yards measured, but in what parts of
yards they were measured. No one would object to an inch measure, which
is 1/12 of a foot, provided 12 times as many inches were given as there
were feet in the first case. But one inch is 1/36 of a yard, and 12
times 6 is 72; and in this way of measuring 72/36 would represent the
number of yards given, which is derived from 6/3 by multiplying the
numerator and denominator by 12. Similarly, one shilling, the unit being
a pound, is 1/20; and 12 pence, the unit being also a pound, is 12/240;
and 1/20 and 12/240 only differ in that the numerator and denominator of
the first must be multiplied by 12 in order to make the second.

Hence it is allowable to multiply the numerator and denominator of a
fraction by any number which is convenient, and which is called
multiplicand, since that operation does not alter its value. Thus, ⅔,
4/6, 6/9, 8/12, &c. are all of the same value, when the unit is the same
in all: in common language, we should say, that two out of three is the
same as four out of six, six out of nine, and so on. We are now able to
remove two fractions which have different denominators, and substitute
others of the same value with the same denominator. Take the fractions ⅔
and ⅘. If we ask which is the greater, no answer can at first be given,
for though the second, is 4 and the first 2, yet the second is four of
the _fifth_ parts only of unity, while the first is 2 of the _third_
parts. But if we multiply the numerator and denominator of each fraction
by the denominator of the other, the results will be 10/15 and 12/15,
which have the same value ⅔ and ⅘, and also have the same denominator as
each other. Hence we see that, 12/15 being greater than 10/15, ⅘ is
greater than ⅔. The sum of the two is the fifteenth part of unity
repeated 22 times or 22/15; the difference is two parts out of fifteen
or 2/15. Hence follow the common rules for addition and subtraction of
fractions.

We now come to the reverse of multiplication. We have shown how to find
the value of one fraction of another, such as ⅗ of 6/11; we now ask,
what fraction of ⅞ must be taken, to give ⅔ of 1 or simply ⅔? Into how
many parts must we cut ⅞, and how many times must we repeat one of those
parts, in order that the result may be the same as if we had cut unity
into three parts, and taken 2 of them? Reduce the fractions ⅞ and ⅔ to
other equivalent fractions having the same denominator, which are 21/24
and 16/24. If we cut 21/24, which is ⅞, into _twenty-one_ equal parts,
each of these parts is 1/24; if we repeat 1/24 _sixteen_ times, the
result is 16/24, which is ⅔: hence, if ⅞ be cut into 21 equal parts and
16 of these parts be taken, the resulting fraction is ⅔, or if we ask,
what fraction of ⅞ is ⅔? the answer is 16/21 of ⅞. By our former rule
16/21 of ⅞ is 112/168, which does not appear at first sight to be the
same as ⅔, but if we examine its terms, we shall find that on dividing
the numerator and denominator by 56 (which does not alter its value) it
is reduced to ⅔. This rule being the reverse of multiplication is called
division; the fraction which is to be cut into parts is called the
_divisor_, that which is to be produced from it the _dividend_, and the
fraction of the first, which it is necessary to take, in order to
produce the second, is called the _quotient_. Thus, 16/21 is the
quotient of ⅔ divided by ⅞. The rule deduced from this reasoning is:
Reverse the divisor, that is, for ⅞ write 8/7, and proceed as in
multiplication with the reversed divisor and the dividend. Thus, 8/7 of
⅔ is 16/21. This rule is used in every question where division would
have been used, if whole numbers only had been given. Thus if 4 pounds
cost 20 shillings, the price of one pound is found by dividing 20 by 4,
and is 5 shillings. If ⅞ of a pound cost ⅔ of a shilling, the price of
one pound is found by dividing ⅔ by ⅞ and is 16/21 of a shilling. This
might be established by independent reasoning as follows: As ⅞ of a
pound costs ⅔ of a shilling, and 7 pounds cost 8 times as much as ⅞ of a
pound, 7 pounds will cost 16/3 of a shilling. But as the price of one
pound is one-seventh of that of 7 pounds, for every third of a shilling
which 7 pounds cost, one pound will cost the twenty-first part of a
shilling. Hence the price of one pound is 16/21 as before.

We shall proceed in a future number to the explanation of Decimal
Fractions.


---------------------


THE WEEK.

October 27.--The birth-day of Captain Cook. James Cook was born in 1728
at the village of Marton in the North Riding of Yorkshire. His parents
were of the class of labourers. All the education he received amounted
only to English reading, writing and the elements of arithmetic. He was
then, at the age of thirteen, bound apprentice to a small shopkeeper in
the neighbouring town of Snaith, which is on the sea-coast. Here he
became so smitten with the love of a sea-life that he could not rest
till his wish was gratified; and his master was at last induced to let
him off, when he entered himself as one of the crew of a vessel engaged
in the coal trade. In this humble and laborious line of life he
continued till the breaking out of the war of 1755. He then entered the
navy, as a common seaman, of course. But now the native superiority of
the man began to assert itself; and in four years he rose to be Master
of the Mercury, one of the ships belonging to an expedition sent against
Quebec. Thus by far the most formidable of the difficulties were
overcome which he had to encounter in emerging from obscurity; he was
now on the direct road to preferment, and in a position in which his
good conduct and perseverance were sure to meet with their reward. While
stationed in this command on the coast of North America, he greatly
distinguished himself both by his skill and intrepidity as a seaman; and
he also made use of his leisure to rectify the defects of his original
education by studying mathematics and astronomy. He eventually made
himself in this way one of the most scientific naval officers of that
time. His reputation rose accordingly; and in 1768, when Government
resolved to send out the Endeavour to the South Sea to obtain an
observation of the approaching transit of Venus, Cook was selected to
command the ship. He conducted this expedition with admirable ability,
and so entirely to the public satisfaction, that, having returned home
in 1771, he was the following year appointed to proceed again to the
same regions with two ships, the Resolution and the Adventure, with the
object of endeavouring to settle the long-disputed question as to the
existence of a southern polar continent. On this voyage, in which he
circumnavigated the world, he was absent nearly three years; and
notwithstanding all the vicissitudes of climate and weather, and the
other dangers which he had encountered, he brought home, with the
exception of one, every man of the crew he had taken out with him. He
communicated to the Royal Society an account of the methods he had
adopted on this occasion for preserving the health of his men; and that
body in return elected him into their number, and voted him the Copley
gold medal as a testimony of their sense of his merits. To crown his
achievement, Captain Cook wrote the history of this expedition himself,
and wrote it admirably. In little more than a year after his return, he
sailed on his third and last voyage of discovery; the principal object
of which was to ascertain the practicability of a passage between the
Atlantic and Pacific Oceans along the northern coast of America. After
having been out on this expedition nearly three years, and having
explored a vast extent of sea and coast, the great circumnavigator put
in at the island of Owhyhee on his return home; and he was there killed
in a sudden and accidental rencontre with some of the natives on the
14th of February, 1779. The late Admiral Burney, who was present on this
occasion, mentions, in a note to his History of Discoveries in the South
Sea, an anecdote which deserves to be remembered. Of the party of
marines, by whom Captain Cook was accompanied when he met his death,
four were killed along with him; “and in the hasty retreat made,” says
Burney, “after the boats had put off, one man still remained on shore,
who could not swim. His officer, Lieutenant (now Colonel) Molesworth
Phillips, of the Marines, though himself wounded at the time, seeing his
situation, jumped out of the boat, swam back to the shore, and brought
him off safe.” The author proceeds to compare this conduct of Lieutenant
Phillips with a similar act performed in 1624 by a Dutch Captain,
Cornelys de Witte, who, when a boat’s crew which he commanded was
surprised in a port on the coast of America by an ambuscade of
Spaniards, and driven to sea after four of them had been killed, seeing
one of his men left behind on the beach, boldly returned to the shore in
the face of the enemy, and took him into his boat. “This was an act of
generosity,” observes the French translator of the account of the Dutch
voyage, “worth a wound which he received in his side, and of which he
was afterwards cured.” The news of the death of Cook was received by his
countrymen, and it may be said by the world, with the feeling that one
of the great men of the age was lost; and both in his own and in foreign
nations public honours were liberally paid to his memory. In the half
century of busy and enterprising exertion in every field of activity
which has elapsed since his death, no newer name in the same department
has yet eclipsed the lustre of his, and with reference to the peculiar
character of his fame, as contrasted with that of our other renowned
seamen, it has been well and justly remarked that, “while numberless
have been our naval heroes who have sought and gained reputation at the
cannon’s mouth, and amidst the din of war, it has been the lot of Cook
to derive celebrity from less imposing, but not less important exploits,
as they tended to promote the intercourse of distant nations, and
increase the stock of useful science.”[1]

-----

Footnote 1:

Gorton’s Biographical Dictionary.

[Illustration: Portrait of Captain Cook.]


---------------------


DOMESTIC PEACE.

Tell me on what holy ground
May domestic peace be found?
Halcyon-daughter of the skies!
Far on fearful wings she flies
From the tyrant’s scepter’d state,
From the rebel’s noisy hate.
In a cottag’d vale she dwells,
List’ning to the sabbath bells,
While all around her steps are seen
Spotless Honour’s meeker mien.
Love, the sire of pleasing fears,
Sorrow smiling through her tears;
And, mindful of the past employ,
Memory, bosom spring of joy!--COLERIDGE.


---------------------


_Ants of Brazil._--So numerous were the ants, and so great was the
mischief which they committed, that the Portugueze called this insect
the _King of Brazil_; but it is said by Piso, that an active husbandman
easily drove them away, either by means of fire or of water; and the
evil which they did was more than counterbalanced by the incessant war
which they waged against all other vermin. In some parts of South
America they march periodically in armies, such myriads together, that
the sound of their coming over the fallen leaves may be heard at some
distance. The inhabitants, knowing the season, are on the watch, and
quit their houses, which these tremendous, but welcome visitors clear of
centipedes, forty-legs, scorpion, snake, every living thing; and having
done their work, proceed upon their way.--_Southey’s Brazil._


---------------------


_Singular Customs._--There is a custom, proper to Sicily, which I must
not forget to mention. This is a right of purchase of a singular kind.
If any man buy an estate, be it house, land, or vineyard, the neighbour
of the purchaser, for the space of an entire year afterward, may eject
him by an advance of price. In vain would the first purchaser give more
to the original owner. This singular law is generally evaded by a
falsehood. The purchase-money is stated, in the articles of agreement,
at a higher sum than has been agreed upon in the presence of four
witnesses. There is another no less singular law in Sicily, according to
which any man can oblige his neighbour to sell his house, if he will pay
him three times its value. The intention of this law was, the
improvement of the towns. It was to encourage the possessors of large
houses to purchase the humble abodes of the poor.--_Count Stolberg’s
Travels._


---------------------


_Volcano in Iceland._--The Oræfa mountain is not only the loftiest in
Iceland, but has been rendered remarkable by the great devastation made
by its eruption about a century ago. Nothing can be more striking than
the account of this calamity given by Jon Thorlakson, the aged minister
of a neighbouring parish. He was in the midst of his service on the
Sabbath, when the agitation of the earth gave warning that some alarming
event was to follow. Rushing from the church, he saw a peak of the
neighbouring mountain alternately heaved up and sinking; the next day,
this portion of the mountain ran down into the plain, like melted metal
from a crucible, filling it to such a height, that, as he says, no more
of a mountain which formerly towered above it could be seen, than about
the size of a bird; volumes of water being in the mean time thrown forth
in a deluge from the crater, sweeping away whatever they encountered in
their course. The Oræfa itself then broke forth, hurling large masses of
ice to a great distance; fire burst out in every direction from its
sides; the sky was darkened by the smoke and ashes, so that the day
could hardly be distinguished from the night. This scene of horror
continued for more than three days, during which the whole region was
converted into utter desolation.--_North American Review for July_,
1832.


---------------------


_Farming in Iceland._--The most important branch of rural labour in
Iceland, is the hay-making. About the middle of July, the peasant begins
to cut down the grass of the tûn (the green around his house,) which is
immediately gathered to a convenient place, in order to dry, and, after
having been turned once or twice, is conveyed home on horseback to the
yard, where it is made up into stacks. At the poorer farms, both men and
women handle the scythe; but in general, the women only assist in making
the hay after it is cut. In many parts of the island, where there is
much hay, the peasants hire men from the fishing plains, who are paid
for their labour at the rate of thirty pounds of butter a week. They cut
by measurement; the daily task being about thirty square fathoms.
Hay-harvest being over, the sheep and cattle that had been out all
summer on the mountains are collected; the houses are put into a state
of repair for the winter; the wood needed for domestic purposes is
brought home to each farm; the turf is also taken in. During the winter,
the care of the cattle and the sheep devolves entirely on the men; and
consists chiefly in feeding and watering the former, which are kept in
the house, while the latter are turned out in the day-time to seek their
food through the snow. When the snow happens to be so deep that they
cannot scrape it away themselves, the boys do it for them; and as the
sustenance thus procured is exceedingly scanty, they generally get a
little of the meadow hay about this time. The farm hay is given to the
cows alone. All the horses, excepting perhaps a favourite riding horse,
are left to shift for themselves the whole winter, during which season
they never lie down, but rest themselves by standing in some place of
shelter.--_Henderson’s Iceland._

------------------------------------------------------------------------




⁂ The Office of the Society for the Diffusion of Useful Knowledge is at
59, Lincoln’s Inn Fields.

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Printed by WILLIAM CLOWES, Duke Street, Lambeth.

------------------------------------------------------------------------




Transcriber’s Notes


This file uses _underscores_ to indicate italic text. New original cover
art included with this eBook is granted to the public domain. Itemized
changes from the original text:

• p. 282: Replaced “n” with “in” in phrase “the war in which the human
race engages.”
• p. 282: Replaced “endered” with “rendered” in phrase “is rendered
absolutely necessary by the wants of navigators.”
• p. 282: Replaced “s” with “as” in phrase “as they come from the sea.”
• p. 283: Supplied partially misprinted words “which” and “actually” in
phrase “from which it must not be concluded that such an event
actually will take place.”
• p. 284: Added closing double quotation mark after phrase “many
thousands of years must elapse before the event can be _really_
expected.”
• p. 285: Changed “as we must first” with “we must first” in phrase “As
we cannot measure anything exactly, we must first decide what degree
of accuracy is necessary.”
• p. 286: Replaced “4/12” with “8/12” in phrase “Thus, ⅔, 4/6, 6/9,
8/12, &c. are all of the same value.”
• p. 287: Replaced “ast” with “last” in phrase “his master was at last
induced to let him off.”
• p. 287: Added comma after phrase “the Resolution and the Adventure.”
• p. 287: Added comma after phrase “after four of them had been
killed.”



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