Practical Education, Volume II
by Maria Edgeworth · English · Gutenberg #28709 · 619,482 chars · public domain (US)
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Title: Practical Education, Volume II
Author: Maria Edgeworth
Richard Lovell Edgeworth
Release date: May 7, 2009 [eBook #28709]
Most recently updated: January 5, 2021
Language: English
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PRACTICAL EDUCATION:
BY
MARIA EDGEWORTH,
AUTHOR OF LETTERS FOR LITERARY LADIES, AND THE PARENT'S ASSISTANT, &c.
&c.
AND, BY
RICHARD LOVELL EDGEWORTH,
F. R. S. AND M. R. I. A.
IN TWO VOLUMES ... VOL. II.
SECOND AMERICAN EDITION.
PUBLISHED
BY J. FRANCIS LIPPITT, PROVIDENCE, (R. I.) AND T. B. WAIT & SONS,
BOSTON.
T. B. Wait and Sons, Printers.
1815.
CONTENTS.
Chapter Page
XIII. _On Grammar and Classical Literature_ 5
XIV. _On Geography and Chronology_ 31
XV. _On Arithmetic_ 37
XVI. _Geometry_ 54
XVII. _On Mechanics_ 57
XVIII. _Chemistry_ 85
XIX. _On Public and Private Education_ 92
XX. _On Female Accomplishments, &c._ 109
XXI. _Memory and Invention_ 138
XXII. _Taste and Imagination_ 178
XXIII. _Wit and Judgment_ 214
XXIV. _Prudence and Economy_ 248
XXV. _Summary_ 267
APPENDIX.
_Notes, containing Conversations and Anecdotes of
Children_ 283
PRACTICAL EDUCATION.
CHAPTER XIII.
ON GRAMMAR, AND CLASSICAL LITERATURE.
As long as gentlemen feel a deficiency in their own education, when
they have not a competent knowledge of the learned languages, so long
must a parent be anxious, that his son should not be exposed to the
mortification of appearing inferiour to others of his own rank. It is
in vain to urge, that language is only the key to science; that the
names of things are not the things themselves; that many of the words
in our own language convey scarcely any, or at best but imperfect,
ideas; that the true genius, pronunciation, melody, and idiom of
Greek, are unknown to the best scholars, and that it cannot reasonably
be doubted, that if Homer or Xenophon were to hear their works read by
a professor of Greek, they would mistake them for the sounds of an
unknown language. All this is true; but it is not the ambition of a
gentleman to read Greek like an ancient Grecian, but to understand it
as well as the generality of his contemporaries; to know whence the
terms of most sciences are derived, and to be able, in some degree, to
trace the progress of mankind in knowledge and refinement, by
examining the extent and combination of their different vocabularies.
In some professions, Greek is necessary; in all, a certain proficiency
of Latin is indispensable; how, therefore, to acquire this proficiency
in the one, and a sufficient knowledge of the other, with the least
labour, the least waste of time, and the least danger to the
understanding, is the material question. Some school-masters would
add, that we must expedite the business as much as possible: of this
we may be permitted to doubt. _Festina lente_ is one of the most
judicious maxims in education, and those who have sufficient strength
of mind to adhere to it, will find themselves at the goal, when their
competitors, after all their bustle, are panting for breath, or
lashing their restive steeds. We see some untutored children start
forward in learning with rapidity: they seem to acquire knowledge at
the very time it is wanted, as if by intuition; whilst others, with
whom infinite pains have been taken, continue in dull ignorance; or,
having accumulated a mass of learning, are utterly at a loss how to
display, or how to use their treasures. What is the reason of this
phenomenon? and to which class of children would a parent wish his son
to belong? In a certain number of years, after having spent eight
hours a day in "durance vile," by the influence of bodily fear, or by
the infliction of bodily punishment, a regiment of boys may be drilled
by an indefatigable usher into what are called scholars; but, perhaps,
in the whole regiment not one shall ever distinguish himself, or ever
emerge from the ranks. Can it be necessary to spend so many years, so
many of the best years of life, in toil and misery? We shall calculate
the waste of time which arises from the study of ill written, absurd
grammar, and exercise-books; from the habits of idleness contracted by
school-boys, and from the custom of allowing holydays to young
students; and we shall compare the result of this calculation with the
time really necessary for the attainment of the same quantity of
classical knowledge by rational methods. We do not enter into this
comparison with any invidious intention, but simply to quiet the
apprehensions of parents; to show them the possibility of their
children's attaining a certain portion of learning within a given
number of years, without the sacrifice of health, happiness, or the
general powers of the understanding.
At all events, may we not begin by imploring the assistance of some
able and friendly hand to reform the present generation of grammars
and school-books? For instance, is it indispensably necessary that a
boy of seven years old should learn by rote, that "relative sentences
are independent, _i. e._ no word in a relative sentence is governed
either of verb, or adjective, that stands in another sentence, or
depends upon any appurtenances of the relative; and that the English
word 'That' is always a relative when it may be turned into _which_ in
good sense, which must be tried by reading over the English sentence
_warily_, and judging how the sentence will bear it, but when it
cannot be altered, salvo sensu, it is a conjunction?" Cannot we, for
pity's sake, to assist the learner's memory, and to improve his
intellect, substitute some sentences a little more connected, and
perhaps a little more useful, than the following?
"I have been a soldier--You have babbled--Has the crow ever looked
white?--Ye have exercised--Flowers have withered--We were in a
passion--Ye lay down--Peas were parched--The lions did roar a while
ago."
In a book of Latin exercises,[1] the preface to which informs us, that
"it is intended to contain such precepts of morality and religion, as
ought most industriously to be inculcated into the heads of all
learners, contrived so as that children may, as it were, insensibly
suck in such principles as will be of use to them afterwards in the
manly conduct and ordering of their lives," we might expect somewhat
more of pure morality and sense, with rather more elegance of style,
than appear in the following sentences:
"I struck my sister with a stick, and was forced to flee into the
woods; but when I had tarried there awhile, I returned to my parents,
and submitted myself to their mercy, and they forgave me my offence."
"When my dear mother, unknown to my father, shall send me money, I
will pay my creditors their debts, and provide a supper for all my
friends in my chamber, without my brother's consent, and will make
presents to all my relations."
So the measure of maternal tenderness is the sum of money, which the
dear mother, unknown to her husband, shall send to her son; the
measure of the son's generosity is the supper he is to give to all his
friends in his chamber, exclusive of his poor brother, of whose
offence we are ignorant. His munificence is to be displayed in making
presents to all his relations, but in the mean time he might possibly
forget to pay his debts, for "justice is a slow-paced virtue, and
cannot keep pace with generosity."
A reasonable notion of punishment, and a disinterested love of truth,
is well introduced by the following picture. "My master's countenance
was greatly changed when he found his beloved son guilty of a lie.
Sometimes he was pale with anger; sometimes he was red with rage; and
in the mean time, he, poor boy, was trembling, (for what?) for fear of
punishment." Could the ideas of punishment and vengeance be more
effectually joined, than in this portrait of the master red with rage?
After truth has been thus happily recommended, comes honesty. "Many
were fellow-soldiers with valiant Jason when he stole the golden
fleece: many were companions with him, but he bore away the glory of
the enterprise."
Valour, theft, and glory, are here happily combined. It will avail us
nothing to observe, that the golden fleece has an allegorical meaning,
unless we can explain satisfactorily the nature of an allegorical
theft; though to our classical taste this valiant Jason may appear a
glorious hero, yet to the simple judgment of children, he will appear
a robber. It is fastidious, however, to object to Jason in the
exercise-book, when we consider what children are to hear, and to hear
with admiration, as they advance in their study of poetry and
mythology.
Lessons of worldly wisdom, are not forgotten in our manual, which
professes to teach "_the manly conduct and ordering of life_" to the
rising generation. "Those men," we are told, "who have the most money,
obtain the greatest honour amongst men." But then again, "a poor man
is as happy without riches, _if_ he can enjoy contentedness of mind,
as the richest earl that coveteth greater honour." It may be useful to
put young men upon their guard against hypocrites and knaves; but is
it necessary to tell school-boys, that "it concerneth me, and all men,
to look to ourselves, for the world is so full of knaves and
hypocrites, that he is hard to be found who may be trusted?" That
"they who behave themselves the most warily of all men, and live more
watchfully than others, may happen to do something, which (if it be
divulged) may very much damnify their reputation?" A knowledge of the
world may be early requisite; but is it not going too far, to assure
young people, that "the nations of the world are at this time come to
that pass of wickedness, that the earth is like hell, and many men
have degenerated into devils?"
A greater variety of ridiculous passages from this tenth edition of
Garretson's Exercise-book, might be selected for the reader's
entertainment; but the following specimens will be sufficient to
satisfy him, that by this original writer, natural history is as well
taught as morality:
Man. "Man is a creature of an upright body; he walketh upright when he
is on a journey; and when night approaches, he lieth flat, and
sleepeth."
Horses. "A journey an hundred and fifty miles long, tireth an horse
that hath not had a moderate feed of corn."
Air, Earth, Fire, and Water. "The air is nearer the earth than the
fire; but the water is placed nearest to the earth, because these two
elements compose but one body."
It is an easy task, it will be observed, to ridicule absurdity. It is
easy to pull down what has been ill built; but if we leave the ruins
for others to stumble over, we do little good to society. Parents may
reasonably say, if you take away from our children the books they
have, give them better. They are not yet to be had, but if a demand
for them be once excited, they will soon appear. Parents are now
convinced, that the first books which children read, make a lasting
impression upon them; but they do not seem to consider spelling-books,
and grammars, and exercise-books, as books, but only as tools for
different purposes: these tools are often very mischievous; if we
could improve them, we should get our work much better done. The
barbarous translations, which are put as models for imitation into the
hands of school-boys, teach them bad habits of speaking and writing,
which are sometimes incurable. For instance, in the fourteenth edition
of Clarke's Cornelius Nepos, which the preface informs us was written
by a man full of indignation for the common practices of
grammar-schools, by a man who laments that youth should spend their
time "in tossing over the leaves of a dictionary, and hammering out
such a language as the Latin," we might expect some better translation
than the following, to form the young student's style:
"No body ever heard any other entertainment for the ears at _his_
(Atticus's) meals than a reader, which we truly think very pleasant.
Nor was there ever a supper at his house without some reading, that
their guests might be entertained in their minds as well as their
stomachs; _for_ he invited those whose manners were not different from
his own."
"He (Atticus) likewise had a touch at poetry, that he might not be
unacquainted with this pleasure, we suppose. _For_ he has related in
verses the lives of those who excelled the Roman people in honour, and
the greatness of their exploits. _So_ that he has described under each
of their images, their actions and offices in no more than four or
five verses, _which_ is scarcely to be believed _that_ such great
things could be so briefly delivered."
Those who, in reading these quotations, have perhaps exclaimed, "Why
must we go through this farrago of nonsense?" should reflect, that
they have now wasted but a few minutes of their time upon what
children are doomed to study for hours and years. If a few pages
disgust, what must be the effect of volumes in the same style! and
what sort of writing can we expect from pupils who are condemned to
such reading? The analogy of ancient and modern languages, differs so
materially, that a literal translation of any ancient author, can
scarcely be tolerated. Yet, in general, young scholars are under a
necessity of _rendering_ their Latin lessons into English word for
word, faithful to the taste of their dictionaries, or the notes in
their translations. This is not likely to improve the freedom of their
English style; or, what is of much more consequence, is it likely to
preserve in the pupil's mind a taste for literature? It is not the
time that is spent in pouring over lexicons, it is not the
multiplicity of rules learnt by rote, nor yet is it the quantity of
Latin words crammed into the memory, which can give the habit of
attention or the power of voluntary exertion: without these, you will
never have time enough to teach; with them, there will always be time
enough to learn.--One half hour's vigorous application, is worth a
whole day's constrained and yawning study. If we compare what from
experience we know can be done by a child of ordinary capacity in a
given time, with what he actually does in school-hours, we shall be
convinced of the enormous waste of time incident to the common methods
of instruction. Tutors are sensible of this; but they throw the blame
upon their pupils--"You might have learned your lesson in half the
time, if you had chosen it." The children also are sensible of this;
but they are not able or willing to prevent the repetition of the
reproach. But exertion does not always depend upon the will of the
boy; it depends upon his previous habits, and upon the strength of
the immediate motive which acts upon him. Some children of quick
abilities, who have too much time allotted for their classical
studies, are so fully sensible themselves of the pernicious effect
this has upon their activity of mind, that they frequently defer
_getting their lessons_ to the last moment, that they may be forced by
a sufficient motive to exert themselves. In _classes_ at public
schools, the quick and the slow, the active and indolent, the
stumbling and sure-footed, are all yoked together, and are forced to
keep pace with one another: stupidity may sometimes be dragged along
by the vigour of genius; but genius is more frequently chained down by
the weight of stupidity. We are well aware of the difficulties with
which the public preceptor has to contend; he is often compelled by
his situation to follow ancient usage, and to continue many customs
which he wishes to see reformed. Any reformation in the manner of
instruction in these public seminaries, must be gradual, and will
necessarily follow the conviction that parents may feel of its
utility. Perhaps nothing can be immediately done, more practicably
useful, than to simplify grammar, and to lighten as much as possible
the load that is laid upon the memory. Without a multiplicity of
masters, it would be impossible to suit instruction to the different
capacities, and previous acquirements, of a variety of pupils; but in
a private education, undoubtedly the task may be rendered much easier
to the scholar and to the teacher; much jargon may be omitted; and
what appears from want of explanation to be jargon, may be rendered
intelligible by proper skill and attention. During the first lessons
in grammar, and in Latin, the pupil need not be disgusted with
literature, and we may apply all the principles which we find on other
occasions successful in the management of the attention.[2] Instead of
keeping the attention feebly obedient for an idle length of time, we
should fix if decidedly by some sufficient motive for as short a
period as may be requisite to complete the work that we would have
done. As we apprehend, that even where children are to be sent to
school, it will be a great advantage to them to have some general
notions of grammar, to lead them through the labyrinth of common
school books, we think that we shall do the public preceptor an
acceptable service, if we point out the means by which parents may,
without much labour to themselves, render the first principles of
grammar intelligible and familiar to their children.
We may observe, that children pay the strictest attention to the
analogies of the language that they speak. Where verbs are defective
or irregular, they supply the parts that are wanting with wonderful
facility, according to the common form of other verbs. They make all
verbs regular. I go_ed_, I read_ed_, I writ_ed_, &c. By a proper
application of this faculty, much time may be saved in teaching
children grammar, much perplexity, and much of that ineffectual labour
which stupifies and dispirits the understanding. By gentle degrees, a
child may be taught the relations of words to each other in common
conversation, before he is presented with the first sample of
grammatical eloquence in Lilly's Accidence. "There be eight parts of
speech." A phrase which in some parts of this kingdom would perhaps be
understood, but which to the generality of boys who go to school,
conveys no meaning, and is got by heart without reflection, and
without advantage. A child can, however, be made to understand these
formidable parts of speech, if they are properly introduced to his
acquaintance: he can comprehend, that some of the words which he hears
express _that something is done_; he will readily perceive, that if
something is done, somebody, or something must do it: he will
distinguish with much facility the word in any common sentence which
expresses an action, and that which denotes the agent. Let the reader
try the experiment immediately upon any child of six or seven years
old who has _not_ learned grammar, and he may easily ascertain the
fact.
A few months ago, Mr. ---- gave his little daughter H----, a child of
five years old, her first lesson in English grammar; but no alarming
book of grammar was produced upon the occasion, nor did the father put
on an unpropitious gravity of countenance. He explained to the smiling
child the nature of a verb, a pronoun, and a substantive.
Then he spoke a short familiar sentence, and asked H----, to try if
she could find out which word in it was a verb, which a pronoun, and
which a substantive. The little girl found them all out most
successfully, and formed no painful associations with her first
grammatical lesson. But though our pupil may easily understand, he
will easily forget our first explanations; but provided he understands
them at the moment, we should pardon his forgetfulness, and we should
patiently repeat the same exercise several days successively; a few
minutes at each lesson will be sufficient, and the simplest sentences,
such as children speak themselves, will be the best examples. Mr.
----, after having talked four or five times, for a few minutes at a
time, with his son S----, when S---- was between five and six years
old, about grammar, asked him if he knew what a pronoun meant? The boy
answered, "A word that is said instead of a substantive." As these
words might have been merely remembered by rote, the father questioned
his pupil further, and asked him to name any pronoun that he
recollected. S----immediately said, "_I_ a pronoun." "Name another,"
said his father. The boy answered after some pause, as if he doubted
whether it was or was not a pronoun, _A_. Now it would have been very
imprudent to have made a sudden exclamation at the child's mistake.
The father, without showing any surprise, gently answered, "No, my
dear, _a_ does not stand in the place of any substantive. We say _a
man_, but the word _a_ does not mean a _man_, when it is said by
itself--Does it?"
_S----._ No.
_Father._ Then try if you can find out a word that does.
_S----._ He, and _Sir_.
_Sir_ does stand, in conversation, in the place of a man, or
gentleman; therefore the boy, even by this mistake, showed that he had
formed, from the definition that had been given to him, a general idea
of the nature of a pronoun, and at all events he exercised his
understanding upon the affair, which is the principal point we ought
to have in view.
An interjection is a part of speech familiar to children. Mr. Horne
Tooke is bitter in his contempt for it, and will scarcely admit it
into civilized company. "The brutish inarticulate interjection, which
has nothing to do with speech, and is only the miserable refuge of the
speechless, has been permitted to usurp a place amongst words,
&c."--"The neighing of a horse, the lowing of a cow, the barking of a
dog, the purring of a cat; sneezing, coughing, groaning, shrieking,
and every other involuntary convulsion with oral sound, have almost as
good a title to be called parts of speech, as interjections have."
Mr. Horne Tooke would have been pleased with the sagacity of a child
of five years old (S----) who called _laughing_ an interjection. Mr.
---- gave S----a slight pinch, in order to produce "an involuntary
convulsion with oral sound." And when the interjection Oh! was uttered
by the boy, he was told by his father, that the word was an
interjection; and, that "any word or noise, that expresses a sudden
feeling of the mind, may be called an interjection." S----immediately
said, "is laughing an interjection, then?" We hope that the candid
reader will not imagine, that we produce these _sayings_ of children
of four or five years old, without some sense of the danger of
ridicule; but we wish to give some idea of the sort of simple answers
which children are likely to make in their first grammatical lessons.
If too much is expected from them, the disappointment, which must be
quickly felt, and will be quickly shown by the preceptor, will
discourage the pupil. We must repeat, that the first steps should be
frequently retraced: a child should be _for some weeks_ accustomed to
distinguish an active verb, and its agent, or nominative case, from
every other word in a sentence, before we attempt to advance. The
objects of actions are the next class of words that should be
selected.
The fanciful, or at least what appears to the moderns fanciful,
arrangement of the cases amongst grammarians, may be dispensed with
for the present. The idea, that the nominative is a direct, upright
_case_, and that the genitive declines with the smallest obliquity
from it; the dative, accusative, and ablative, falling further and
further from the perpendicularity of speech, is a species of
metaphysics not very edifying to a child. Into what absurdity men of
abilities may be led by the desire of explaining what they do not
sufficiently understand, is fully exemplified in other sciences as
well as grammar.
The discoveries made by the author of Epea Pteroenta, show the
difference between a vain attempt to substitute analogy and rhetoric
in the place of demonstration and common sense. When a child has been
patiently taught in conversation to analyze what he says, he will take
great pleasure in the exercise of his new talent; he will soon
discover, that the cause of the action does not always come before the
verb in a sentence, that sometimes it follows the verb. "John beats
Thomas," and "Thomas is beaten by John," he will perceive mean the
same thing; he may, with very little difficulty, be taught the
difference between a verb active and a verb passive; that one brings
first before the mind the person or thing which performs the action,
and the other represents in the first place the person or thing upon
whom the action is performed. A child of moderate capacity, after he
has been familiarized to this general idea of a verb active and
passive, and after he has been taught the names of the cases, will
probably, without much difficulty, discover that the nominative case
to a passive verb becomes the accusative case to a verb active.
"School-masters are plagued by boys." A child sees plainly, that
school-masters are the persons upon whom the action of plaguing is
performed, and he will convert the sentence readily into "boys plague
school-masters."
We need not, however, be in any hurry to teach our pupil the names of
the cases; technical grammar may be easily learned, after a general
idea of rational grammar has been obtained. For instance, _the verb_
means only _the word_, or the principal word in a sentence; a child
can easily learn this after he has learnt what is meant by a sentence;
but it would be extremely difficult to make him comprehend it before
he could distinguish a verb from a noun, and before he had any idea of
the structure of a common sentence. From easy, we should proceed to
more complicated, sentences. The grammatical construction of the
following lines, for example, may not be immediately apparent to a
child:
"What modes of sight between each vast extreme,
The mole's dim curtain, and the lynx's beam;
Of smell the headlong lioness between,
And hound sagacious on the tainted green."
"_Of Smell._" A girl of ten years old (C----) was asked if she could
tell what substantive the word "_of_" relates to; she readily
answered, "_modes_." C----had learned a general idea of grammar in
conversation, in the manner which we have described. It is asserted
from experience, that this method of instructing children in grammar
by conversation, is not only practicable, but perfectly easy, and that
the minds of children are adapted to this species of knowledge. During
life, we learn with eagerness whatever is congenial with our present
pursuits, and the acquisition of language is one of the most earnest
occupations of childhood. After distinct and ready knowledge of the
verb and nominative case has been acquired, the pupil should be taught
to distinguish the object of an action, or, in other words, the
objective or accusative case. He should be exercised in this, as in
the former lessons, repeatedly, until it becomes perfectly familiar;
and he should be encouraged to converse about these lessons, and to
make his own observations concerning grammar, without fear of the
preceptor's peremptory frown, or positive reference to "_his rules_."
A child of five years old, was asked what the word "_Here!_" meant; he
answered, "It means to give a thing."
"When I call a person, as, John! John! it seems to me," said a boy of
nine years old (S----) "it seems to me, that the vocative case is both
the verb and its accusative case." A boy who had ever been checked by
his tutor for making his own observations upon the mysterious subject
of grammar, would never have dared to have thought, or to have uttered
a new thought, so freely.--Forcing children to learn any art or
science by rote, without permitting the exercise of the understanding,
must materially injure their powers both of reasoning and of
invention. We acknowledge that Wilkins and Tooke have shown masters
how to teach grammar a little better than it was formerly taught.
Fortunately for the rising generation, all the words under the
denomination of adverbs, prepositions, and conjunctions, which were
absolute nonsense to us, may be easily explained to them, and the
commencement of instruction need no longer lay the foundation of
implicit acquiescence in nonsense. We refer to Mr. Horne Tooke's "Epea
Pteroenta," forbearing to dilate upon the principles of his work, lest
we should appear in the invidious light of authors who rob the works
of others to adorn their own. We cannot help expressing a wish, that
Mr. Horne Tooke would have the philanthropic patience to write an
elementary work in a _simple style_, unfolding his grammatical
discoveries to the rising generation.
When children have thus by gentle degrees, and by short and clear
conversations, been initiated in general grammar, and familiarized to
its technical terms, the first page of tremendous Lilly will lose much
of its horror. It has been taken for granted, that at the age of
which we have been speaking, a child can read English tolerably well,
and that he has been used to employ a dictionary. He may now proceed
to translate from some easy books a few short sentences: the first
word will probably be an adverb or conjunction; either of them may
readily be found in the Latin dictionary, and the young scholar will
exult in having translated one word of Latin; but the next word, a
substantive or verb, perhaps will elude his search. Now the grammar
may be produced, and something of the various terminations of a noun
may be explained. If _musam_ be searched for in the dictionary, it
cannot be found, but _musa_ catches the eye, and, with the assistance
of the grammar, it may be shown, that the meaning of words may be
discovered by the united helps of the dictionary and grammar. After
some days patient continuation of this exercise, the use of the
grammar, and of its uncouth collection of words and syllables, will be
apparent to the pupil: he will perceive that the grammar is a sort of
appendix to the dictionary. The grammatical formulæ may then, by
gentle degrees, be committed to memory, and when once got by heart,
should be assiduously preserved in the recollection. After the
preparation which we have recommended, the singular number of a
declension will be learnt in a few minutes by a child of ordinary
capacity, and after two or three days repetition, the plural number
may be added. The whole of the first declension should be well fixed
in the memory before a second is attempted. During this process, a few
words at every lesson may be translated from Latin to English, and
such nouns as are of the first declension, may be compared with
_musa_, and may be declined according to the same form. Tedious as
this method may appear, it will in the end be found expeditious.
Omitting some of the theoretic or didactic part of the grammar, which
should only be read, and which may be explained with care and
patience, the whole of the declensions, pronouns, conjugations, the
list of prepositions and conjunctions, interjections, some adverbs,
the concords, and common rules of syntax, may be comprised with
sufficient repetitions in about two or three hundred lessons of ten
minutes each; that is to say, ten minutes application of the scholar
in the presence of the teacher. A young boy should never be set to
learn a lesson by heart when alone. Forty hours! Is this tedious? If
you are afraid of losing time, begin a few months earlier; but begin
when you will, forty hours is surely no great waste of time: the
whole, or even half of this short time, is not spent in the labour of
getting jargon by rote; each day some slight advance is made in the
knowledge of words, and in the knowledge of their combinations. What
we insist upon is, that _nothing should be done to disgust the pupil_:
steady perseverance, with uniform gentleness, will induce habit, and
nothing should ever interrupt the regular return of the daily lesson.
If absence, business, illness, or any other cause, prevent the
attendance of the teacher, a substitute must be appointed; the idea of
relaxation on Sunday, or a holyday, should never be permitted. In most
public seminaries above one third, in some nearly one half, of the
year is permitted to idleness: it is the comparison between severe
labour and dissipation, that renders learning hateful.
Johnson is made to say by one of his female biographers,[3] that no
child loves the person who teaches him Latin; yet the author of this
chapter would not take all the doctor's fame, and all the lady's wit
and riches, in exchange for the hourly, unfeigned, unremitting
friendship, which he enjoys with a son who had no other master than
his father. So far from being laborious or troublesome, he has found
it an agreeable employment to instruct his children in grammar and the
learned languages. In the midst of a variety of other occupations,
half an hour every morning for many years, during the time of
dressing, has been allotted to the instruction of boys of different
ages in languages, and no other time has been spent in this
employment. Were it asserted that these boys made _a reasonable
progress_, the expression would convey no distinct meaning to the
reader; we shall, therefore, mention an experiment tried this morning,
November 8th, 1796, to ascertain the progress of one of these pupils.
Without previous study, he translated twenty lines of the story of
Ceyx and Alcyone, from Ovid, consulting the dictionary only twice: he
was then desired to translate the passage which he had read into
English verse; and in two or three hours he produced the following
version. Much of the time was spent in copying the lines fairly, as
this opportunity was taken of exciting his attention to writing and
spelling, to associate the habit of application with the pleasure of
voluntary exertion. The _curious_ may, if they think it worth their
while, see the various _readings_ and corrections of the translation
(V. Chapter on Conversation, and Anecdotes of Children) which were
carefully preserved, not as "_Curiosities of Literature_," but for the
sake of truth, and with a desire to show, that the pupil had the
patience to correct. A _genius_ may hit off a few tolerable lines; but
if a child is willing and able to criticise and correct what he
writes, he shows that he selects his expressions from choice, and not
from chance or imitation; and he gives to a judicious tutor the
certain promise of future improvement.
"Far in a vale there lies a cave forlorn,
Which Phoebus never enters eve or morn,
The misty clouds inhale the pitchy ground,
And twilight lingers all the vale around.
No watchful cocks Aurora's beams invite;
No dogs nor geese, the guardians of the night:
No flocks nor herds disturb the silent plains;
Within the sacred walls mute quiet reigns,
And murmuring Lethe soothing sleep invites;
In dreams again the flying past delights:
From milky flowers that near the cavern grow,
Night scatters the collected sleep below."
S----, the boy who made this translation, was just ten years old; he
had made but three previous attempts in versification; his reading in
poetry had been some of Gay's fables, parts of the Minstrel, three
odes of Gray, the Elegy in a Country Church-yard, the Tears of Old
May-day, and parts of the second volume of Dr. Darwin's Botannic
Garden; Dryden's translations of the fable of Ceyx and Alcyone he had
never seen; the book had always been locked up. Phædrus and Ovid's
Metamorphoses were the whole of his Latin erudition. These
circumstances are mentioned thus minutely, to afford the inquisitive
teacher materials for an accurate estimate of the progress made by our
method of instruction. Perhaps most boys of S----'s age, in our great
public seminaries, would, upon a similar trial, be found superior.
Competition in the art of translation is not our object; our object is
to show, that half an hour a day, steadily appropriated to grammar and
Latin, would be sufficient to secure a boy of this age, from any
danger of ignorance in classical learning; and that the ease and
shortness of his labour will prevent that disgust, which is too often
induced by forced and incessant application. We may add, that some
attention to the _manner_ in which the pupils repeat their Latin
lessons, has been found advantageous: as they were never put in bodily
fear, by the impatience of a pedagogue, they had leisure and
inclination to read and recite, without awkward gestures and
discordant tones. The whining tones and convulsive gestures often
contracted by boys during the agony of repeating their long lessons,
are not likely to be advantageous to the rising generation of orators.
Practice, and the strong motive of emulation, may, in a public
seminary, conquer these bad habits. After the pupil has learned to
speak ill, he _may_ be taught to speak well; but the chances are
against him: and why should we have the trouble of breaking bad
habits? It is much easier to prevent them. In private education, as
the preceptor has less chance of curing his pupil of the habit of
speaking ill, he should be peculiarly attentive to give the child
constant habits of speaking and reading well. It is astonishing, that
parents, who are extremely intent upon the education of their
children, should overlook some of the essential means of success. A
young man with his head full of Latin and law, will make but a poor
figure at the bar, or in parliament, if he cannot enunciate
distinctly, and if he cannot speak good English extempore, or produce
his learning and arguments with grace and propriety. It is in vain to
expect that a boy should speak well in public, who cannot, in common
conversation, utter three connected sentences without a false concord
or a provincial idiom; he may be taught with much care and cost to
speak _tripod_ sentences;[4] but bring the young orator to the test,
bring him to actual business, rouse any of his passions, throw him off
his guard, and then listen to his language; he will forget instantly
his reading master, and all his rules of pronunciation and rhetoric,
and he will speak the language to which he has been most accustomed.
No master will then be near him to regulate the pitch and tones of his
voice. We cannot believe that even Caius Gracchus could, when he was
warmed by passion, have listened to Licinius's pitch-pipe.[5] Example,
and constant attention to their manner of speaking in common
conversation, we apprehend to be the most certain methods of preparing
young men for public speakers. Much of the time that is spent in
teaching boys to walk upon stilts, might be more advantageously
employed in teaching them to walk well without them. It is all very
well whilst the pupil is under the protection of his preceptor. The
actor on the stage is admired whilst he is elevated by the cothurnus;
but young men are not to exhibit their oratorical talents always with
the advantages of stage effect and decorations. We should imagine,
that much of the diffidence felt by young men of abilities, when they
first rise to speak in public, may be attributed to their immediate
perception of the difference between scholastic exhibitions and the
real business of life; they feel that they have learned to speak two
languages, which must not, on any account, be mixed together; the one,
the vulgar language of common conversation; the other, the refined
language of oratorical composition: the first they are most inclined
to use when they are agitated; and they are agitated when they rise to
speak before numbers: consequently there is an immediate struggle
between custom and institution. Now, a young man, who in common
conversation in his own family has never been accustomed to hear or to
speak vulgar or ungrammatical language, cannot possibly apprehend that
he shall suddenly utter ridiculous expressions; he knows, that, if he
speaks at all, he shall at least speak good English; and he is not
afraid, that, if he is pursued, he shall be obliged to throw away his
cumbrous stilts. The practice of speaking in public, we are sensible,
is a great advantage; but the habit of speaking accurately in private,
is of still greater consequence: this habit depends upon the early and
persevering care of the parent and the preceptor. There is no reason
why children should not be made at the same time good scholars and
good speakers; nor is there any reason why boys, whilst they learn to
write Latin, should be suffered to forget how to write English.
It would be a great advantage to the young classical scholar, if his
Latin and English literature were mixed; the taste for ancient authors
and for modern literature, ought to be cultivated at the same time;
and the beauties of composition, characteristic of different
languages, should be familiarized to the student. Classical knowledge
and taste afford such continual and innocent sources of amusement,
that we should be extremely sorry that any of our pupils should not
enjoy them in their fullest extent; but we do not include a talent for
Latin composition amongst the _necessary_ accomplishments of a
gentleman. There are situations in life, where facility and elegance
in writing Latin may be useful, but such situations are not common;
when a young man is intended for them, he may be trained with more
particular assiduity to this art; perhaps for this purpose the true
Busbyean method is the best. The great Latin and Greek scholars of the
age, have no reason to be displeased by the assertion, that classical
proficiency equal to their own, is not a _necessary_ accomplishment in
a gentleman; if their learning become more rare, it may thence become
more valuable. We see no reason why there should not be Latinists as
well as special pleaders.
We have not laid down any course of classical study; those who
consider the order in which certain authors are read, as of material
consequence in the education of scholars, may consult Milton, Mrs.
Macaulay, "Milne's Well-bred Scholar," &c. where they will find
precise directions.
We have _lately_ seen a collection of exercises for boys,[6] which in
some measure supplies the defect of Mr. Garretson's curious
performance. We wish most earnestly that dictionaries were improved.
The author of "Stemmata Latinitatis," has conferred an essential
service on the public; but still there is wanting a dictionary for
schools, in which elegant and proper English might be substituted for
the barbarous translations now in use. Such a dictionary could not be
compiled, we should think, without an attention to the course of books
that are most commonly used in schools. The first meanings given in
the dictionary, should suit the first authors that a boy reads; this
may probably be a remote or metaphoric meaning: then the radical word
should be mentioned, and it would not cost a master any great trouble
to trace the genealogy of words to the parent stock.
Cordery is a collection of such mean sentences, and uninstructive
dialogue, as to be totally unfit for boys. Commenius's "Visible World
displayed," is far superior, and might, with proper alterations and
better prints, become a valuable _English_ school-book. Both these
books were intended for countries where the Latin language was
commonly spoken, and consequently they are filled with the terms
necessary for domestic life and conversation: for this very reason
they are not good introductions to the classics. Selections from
Bailey's Phædrus, will be proper for young beginners, upon account of
the glossary. We prefer this mode of assisting them with glossaries to
the use of translations, because they do not induce indolent habits,
and yet they prevent the pupil from having unnecessary labour.
Translations always give the pupil more trouble in the end, than they
save in the beginning. The glossary to Bailey's Phædrus, which we have
just mentioned, wants much to be modernized, and the language requires
to be improved. Mr. Valpy's "Select Sentences," would be much more
useful if they had a glossary annexed. As they are, they will,
however, be useful after Phædrus. Ovid's Metamorphoses, with all its
monstrous faults, appears to be the best introduction to the Latin
classics, and to heathen mythology. Norris's Ovid may be safely put
into the hands of children, as it is a selection of the least
exceptionable fables. To accustom boys to read poetry and prose nearly
at the same period, is advantageous. Cornelius Nepos, a _crabbed_
book, but useful from its brevity, and from its being a proper
introduction to Grecian and Roman history, may be read nearly at the
same time with Ovid's Metamorphoses. After Ovid, the pupil may begin
Virgil, postponing some of the Eclogues, and all the Georgics.
We recommend that some English books should be put into the hands of
boys whilst they are going through Phædrus, Ovid, and Cornelius Nepos,
which may suit with the ideas they acquire from these Latin authors.
Plutarch's Lives, for instance, will be useful and interesting. When
we mention Plutarch's Lives, we cannot help recollecting how many
great people have acknowledged the effect of this book in their early
education. Charles the Twelfth, Rousseau, Madame Roland, Gibbon, we
immediately remember, and we are sure we have noticed many others. An
abridgment of Plutarch, by Mrs. Helme, which we have looked into,
appears (the preface excepted) to be well written; and we see another
abridgment of Plutarch advertised, which we hope may prove
serviceable: good prints to a Plutarch for children, would be very
desirable.
As an English introduction to mythology, we recommend the first volume
of Lord Chesterfield's Letters, as a most elegant view of heathen
mythology. But if there be any danger that the first volume should
introduce the remainder of Lord Chesterfield's work to the
inexperienced reader, we should certainly forbear the experiment: it
would be far better for a young man never to be acquainted with a
single heathen deity, than to purchase Lord Chesterfield's classical
knowledge at the hazard of contamination from his detestable system of
morals. Without his Lordship's assistance, Mrs. Monsigny's Mythology
can _properly_ initiate the young pupil of either sex into the
mysteries of ancient fables. The notes to Potter's Æschylus, are also
well suited to our purpose. In Dr. Darwin's "Botanic Garden," there
are some beautiful poetic allusions to ancient gems and ancient
fables, which must fix themselves in the memory or in the imagination
of the pupil. The sooner they are read, the better; we have felt the
advantage of putting them into the hands of a boy of nine or ten years
old. The ear should be formed to English as well as to Latin poetry.
Classical poetry, without the knowledge of mythology, is
unintelligible: if children study the one, they must learn the other.
Divested of the charms of poetry, and considered without classical
prepossession, mythology presents a system of crimes and absurdities,
which no allegorical, metaphysical, or literal interpreters of modern
times, can perfectly reconcile to common sense, or common morality;
but our poets have naturalized ancient fables, so that mythology is
become essential even to modern literature. The associations of taste,
though arbitrary, are not easily changed in a nation whose literature
has attained to a certain pitch of refinement, and whose critical
judgments must consequently have been for some generations
traditional. There are subjects of popular allusion, which poets and
orators regard as common property; to dispossess them of these, seems
impracticable, after time has sanctioned the prescriptive right. But
new knowledge, and the cultivation of new sciences, present objects of
poetic allusion which, skilfully managed by men of inventive genius,
will oppose to the habitual reverence for antiquity, the charms of
novelty united to the voice of philosophy.[7]
In education we must, however, consider the actual state of manners in
that world in which our pupils are to live, as well as our wishes or
our hopes of its gradual improvement.[8] With a little care,
preceptors may manage so as to teach mythology without in the least
injuring their pupils. Children may be familiarized to the strange
manners and strange personages of ancient fable, and may consider them
as a set of beings who are not to be judged by any rules of morality,
and who have nothing in common with ourselves. The caricatura of some
of the passions, perhaps, will not shock children who are not used to
their natural appearance; they will pass over the stories of love and
jealousy, merely because they do not understand them. We should rather
leave them completely unintelligible, than attempt, like Mr. Riley, in
his mythological pocket dictionary for youth, to elucidate the whole
at once, by assuring children that Saturn was Adam, that Atlas is
Moses, and his brother Hesperus, Aaron; that Vertumnus and Pomona were
Boaz and Ruth; that Mars _corresponds_ with Joshua; that Apollo
_accords_ with David, since they both played upon the harp; that
Mercury can be no other than our Archangel Michael, since they both
have wings on their arms and feet; that, in short, to complete the
concordance, Momus is a striking likeness of Satan. The ancients, Mr.
Riley allows, have so much disfigured these personages, that it is
hard to know many of the portraits again at first sight; however, he
is persuaded that "the young student will find a peculiar
gratification in tracing the likeness," and he has kindly furnished us
with a catalogue to explain the exhibition, and to guide us through
his new pantheon.
As books of reference, the convenient size, and compressed
information, of _pocket_ mythological dictionaries, will recommend
them to general use; but we object to the miserable prints with which
they are sometimes disgraced. The first impression made upon the
imagination[9] of children, is of the utmost consequence to their
future taste. The beautiful engravings[10] in Spence's Polymetis, will
introduce the heathen deities in their most graceful and picturesque
forms to the fancy. The language of Spence, though classical, is not
entirely free from pedantic affectation, and his dialogues are,
perhaps, too stiff and long winded for our young pupils. But a parent
or preceptor can easily select the useful explanations; and in
turning over the prints, they can easily associate some general
notion of the history and attributes of the gods and goddesses with
their forms: the little eager spectators will, as they crowd round the
book, acquire imperceptibly all the necessary knowledge of mythology,
imbibe the first pleasing ideas of taste, and store their imagination
with classic imagery. The same precautions that are necessary to
educate the eye, are also necessary to form the ear and understanding
of taste. The first mythological descriptions which our pupils read,
should be the best in their kind. Compare the following account of
Europa in a pocket dictionary, with her figure in a poetical
gem--"Europa, the daughter of Agenor, king of the Phoenicians, and
sister of Cadmus. This princess was so beautiful, that, they say, one
of the companions of Juno had robbed her of a pot of paint to bestow
on this lady, which rendered her so handsome. She was beloved of
Jupiter, who assumed the shape of a bull to run away with her, swam
over the sea with her on his back, and carried her into that part of
the world now called Europe, from her name." So far the dictionary;
now for the poet.
"Now lows a milk-white bull on Afric's strand,
And crops with dancing head the daisy'd land;
With rosy wreathes Europa's hand adorns
His fringed forehead and his pearly horns;
Light on his back the sportive damsel bounds,
And, pleas'd, he moves along the flowery grounds;
Bears with slow step his beauteous prize aloof,
Dips in the lucid flood his ivory hoof;
Then wets his velvet knees, and wading laves
His silky sides, amid the dimpling waves.
While her fond train with beckoning hands deplore,
Strain their blue eyes, and shriek along the shore:
Beneath her robe she draws her snowy feet,
And, half reclining on her ermine seat,
Round his rais'd neck her radiant arms she throws,
And rests her fair cheek on his curled brows;
Her yellow tresses wave on wanton gales,
And high in air her azure mantle sails."[11]
FOOTNOTES:
[1] Garretson's Exercises, the tenth edition.
[2] V. Chapter on Attention.
[3] Mrs. Piozzi.
[4] V. Blair.
[5] V. Plutarch.
[6] Valpy's Exercises.
[7] V. Darwin's Poetry.
[8] Since the above was written, we have seen a letter from Dr. Aikin
to his son on the _morality_ and _poetic merit_ of the fable of Circe,
which convinces us that the observations that we have hazarded are not
premature.
[9] Chapter on Imagination.
[10] We speak of these engravings as _beautiful_, for the times in
which they were done; modern artists have arrived at higher
perfection.
[11] Darwin. V. Botanic Garden.
CHAPTER XIV.
ON GEOGRAPHY AND CHRONOLOGY.
The usual manner of teaching Geography and Chronology, may, perhaps,
be necessary in public seminaries, where a number of boys are to learn
the same thing at the same time; but what is learned in this manner,
is not permanent; something besides merely committing names and dates
to the memory, is requisite to make a useful impression upon the
memory. For the truth of this observation, an appeal is made to the
reader. Let him recollect, whether the Geography and Chronology which
he learned whilst a boy, are what he now remembers--Whether he has not
obtained his present knowledge from other sources than the tasks of
early years. When business, or conversation, calls upon us to furnish
facts accurate as to place and time, we retrace our former
heterogeneous acquirements, and select those circumstances which are
connected with our present pursuit, and thus we form, as it were, a
nucleus round which other facts insensibly arrange themselves. Perhaps
no two men in the world, who are well versed in these studies, connect
their knowledge in the same manner. Relation to some particular
country, some favourite history, some distinguished person, forms the
connection which guides our recollection, and which arranges our
increasing nomenclature. By attending to what passes in our own minds,
we may learn an effectual method of teaching without pain, and without
any extraordinary burden to the memory, all that is useful of these
sciences. The details of history should be marked by a few
chronological æras, and by a few general ideas of geography. When
these have been once completely associated in the mind, there is
little danger of their being ever disunited: the sight of any country
will recall its history, and even from representations in a map, or on
the globe, when the mind is wakened by any recent event, a long train
of concomitant ideas will recur.
The use of technical helps to the memory, has been condemned by many,
and certainly, when they are employed as artifices to supply the place
of real knowledge, they are contemptible; but when they are used as
indexes to facts that have been really collected in the mind; when
they serve to arrange the materials of knowledge in appropriate
classes, and to give a sure and rapid clue to recollection, they are
of real advantage to the understanding. Indeed, they are now so
common, that pretenders cannot build the slightest reputation upon
their foundation. Were an orator to attempt a display of long
chronological accuracy, he might be wofully confounded by his
opponent's applying at the first pause,
[12]Els_luk_ he would have said!
Ample materials are furnished in Gray's Memoria Technica, from which a
short and useful selection may be made, according to the purposes
which are in view. For children, the little ballad of the Chapter of
Kings, will not be found beneath the notice of mothers who attend to
education. If the technical terminations of Gray are inserted, they
will never be forgotten, or may be easily recalled.[13] We scarcely
ever forget a ballad if the tune is popular.
For pupils at a more advanced age, it will be found advantageous to
employ technical helps of a more scientific construction. Priestley's
Chart of Biography may, from time to time, be hung in their view.
Smaller charts, upon the same plan, might be provided with a few names
as land-marks; these may be filled up by the pupil with such names as
he selects from history; they may be bound in octavo, like maps, by
the middle, so as to unfold both ways--Thirty-nine inches by nine will
be a convenient size. Prints, maps, and medals, which are part of the
constant furniture of a room, are seldom attended to by young people;
but when circumstances excite an interest upon any particular subject,
then is the moment to produce the symbols which record and communicate
knowledge.
Mrs. Radcliffe, in her judicious and picturesque Tour through Germany,
tells us, that in passing through the apartments of a palace which the
archduchess Maria Christiana, the sister of the late unfortunate queen
of France, had left a few hours before, she saw spread upon a table a
map of all the countries then included in the seat of the war. The
positions of the several corps of the allied armies were marked upon
this chart with small pieces of various coloured wax. Can it be
doubted, that the strong interest which this princess must have taken
in the subject, would for ever impress upon her memory the geography
of this part of the world?
How many people are there who have become geographers since the
beginning of the present war. Even the common newspapers disseminate
this species of knowledge, and those who scarcely knew the situation
of Brest harbour a few years ago, have consulted the map with that
eagerness which approaching danger excites; they consequently will
tenaciously remember all the geographical knowledge they have thus
acquired. The art of creating an interest in the study of geography,
depends upon the dexterity with which passing circumstances are seized
by a preceptor in conversation. What are maps or medals, statues or
pictures, but technical helps to memory? If a mother possess good
prints, or casts of ancient gems, let them be shown to any persons of
taste and knowledge who visit her; their attention leads that of our
pupils; imitation and sympathy are the parents of taste, and taste
reads in the monuments of art whatever history has recorded.
In the Adele and Theodore of Madame de Silleri, a number of
adventitious helps are described for teaching history and chronology.
There can be no doubt that these are useful; and although such an
apparatus cannot be procured by private families, fortunately the
print-shops of every provincial town, and of the capital in
particular, furnish even to the passenger a continual succession of
instruction. Might not prints, assorted for the purposes which we have
mentioned, be _lent_ at circulating libraries?
To assist our pupils in geography, we prefer a globe to common maps.
Might not a cheap, portable, and convenient globe, be made of oiled
silk, to be inflated by a common pair of bellows? Mathematical
exactness is not requisite for our purpose, and though we could not
pretend to the precision of our best globes, yet a balloon of this
sort would compensate by its size and convenience for its inaccuracy.
It might be hung by a line from its north pole, to a hook screwed into
the horizontal architrave of a door or window; and another string from
its south pole might be fastened at a proper angle to the floor, to
give the requisite elevation to the axis of the globe. An idea of the
different projections of the sphere, may be easily acquired from this
globe in its flaccid state, and any part of it might be consulted as a
map, if it were laid upon a convex board of a convenient size.
Impressions from the plates which are used for common globes, might be
taken to try this idea without any great trouble or expense; but we
wish to employ a much larger scale, and to have them five or six feet
diameter. The inside of a globe of this sort might be easily
illuminated, and this would add much to the novelty and beauty of its
appearance.
In the country, with the assistance of a common carpenter and
plasterer, a large globe of lath and plaster may be made for the
instruction and entertainment of a numerous family of children. Upon
this they should leisurely delineate from time to time, by their given
latitudes and longitudes, such places as they become acquainted with
in reading or conversation. The capital city, for instance, of the
different countries of Europe, the rivers, and the neighbouring towns,
until at last the outline might be added: for the sake of convenience,
the lines, &c. may be first delineated upon a piece of paper, from
which they may be accurately transferred to their proper places on the
globe, by the intervention of black-leaded paper, or by pricking the
lines through the paper, and pouncing powdered blue through the holes
upon the surface of the globe.
We enter into this detail because we are convinced, that every
addition to the active manual employment of children, is of
consequence, not only to their improvement, but to their happiness.
Another invention has occurred to us for teaching geography and
history together. Priestley's Chart of History, though constructed
with great ingenuity, does not invite the attention of young people:
there is an intricacy in the detail which is not obvious at first. To
remedy what appears to us a difficulty, we propose that eight and
twenty, or perhaps thirty, octavo maps of the globe should be
engraved; upon these should be traced, in succession, the different
situations of the different countries of the world, as to power and
extent, during each respective century: different colours might denote
the principal divisions of the world in each of these maps; the same
colour always denoting the same country, with the addition of one
strong colour; red, for instance, to distinguish that country which
had at each period the principal dominion. On the upper and lower
margin in these maps, the names of illustrious persons might be
engraven in the manner of the biographical chart; and the reigning
opinions of each century should also be inserted. Thus history,
chronology, and geography, would appear at once to the eye in their
proper order, and regular succession, divided into centuries and
periods, which easily occur to recollection.
We forbear to expatiate upon this subject, as it has not been actually
submitted to experiment; carefully avoiding in the whole of this work
to recommend any mode of instruction which we have not actually put in
practice. For this reason, we have not spoken of the abbé Gaultier's
method of teaching geography, as we have only been able to obtain
accounts of it from the public papers, and from reviews; we are,
however, disposed to think favourably beforehand, of any mode which
unites amusement with instruction. We cannot forbear recommending, in
the strongest manner, a few pages of Rollin in his "Thoughts upon
Education,"[14] which we think contain an excellent specimen of the
manner in which a well informed preceptor might lead his pupils a
geographical, historical, botanical, and physiological tour upon the
artificial globe.
We conclude this chapter of hints, by repeating what we have before
asserted, that though technical assistance may be of ready use to
those who are really acquainted with that knowledge to which it
refers, it never can supply the place of accurate information.
The causes of the rise and fall of empires, the progress of human
knowledge, and the great discoveries of superior minds, are the real
links which connect the chain of political knowledge.
FOOTNOTES:
[12] V. Gray's Memoria Technica, and the Critic.
[13] Instead of
William the conqueror long did reign, And William his son by an arrow
was slain.
Read,
William the Con_sau_ long did reign, And Ruf_koi_ his son by an arrow
was slain.
And so on from Gray's Memoria Technica to the end of the chapter.
[14] Page 24.
CHAPTER XV.
ON ARITHMETIC.
The man who is ignorant that two and two make four, is stigmatized
with the character of hopeless stupidity; except, as Swift has
remarked, in the arithmetic of the customs, where two and two do not
always make the same sum.
We must not judge of the understanding of a child by this test, for
many children of quick abilities do not immediately assent to this
proposition when it is first laid before them. "Two and two make
four," says the tutor. "Well, child, why do you stare so?"
The child stares because the word _make_ is in this sentence used in a
sense which is quite new to him; he knows what it is to make a bow,
and to make a noise, but how this active verb is applicable in the
present case, where there is no agent to perform the action, he cannot
clearly comprehend. "Two and two _are_ four," is more intelligible;
but even this assertion, the child, for want of a distinct notion of
the sense in which the word _are_ is used, does not understand. "Two
and two _are called_ four," is, perhaps, the most accurate phrase a
tutor can use; but even these words will convey no meaning until they
have been associated with the pupil's perceptions. When he has once
perceived the combination of the numbers with real objects, it will
then be easy to teach him that the words _are called_, _are_, and
_make_, in the foregoing proposition, are synonymous terms.
We have chosen the first simple instance we could recollect, to show
how difficult the words we generally use in teaching arithmetic, must
be to our young pupils. It would be an unprofitable task to enumerate
all the puzzling technical terms which, in their earliest lessons,
children are obliged to hear, without being able to understand.
It is not from want of capacity that so many children are deficient in
arithmetical skill; and it is absurd to say, "such a child has no
genius for arithmetic. Such a child cannot be made to comprehend any
thing about numbers." These assertions prove nothing, but that the
persons who make them, are ignorant of the art of teaching. A child's
seeming stupidity in learning arithmetic, may, perhaps, be a proof of
intelligence and good sense. It is easy to make a boy, who does not
reason, repeat by rote any technical rules which a common
writing-master, with magisterial solemnity, may lay down for him; but
a child who reasons, will not be thus easily managed; he stops,
frowns, hesitates, questions his master, is wretched and refractory,
until he can discover why he is to proceed in such and such a manner;
he is not content with seeing his preceptor make figures and lines
upon a slate, and perform wondrous operations with the self-complacent
dexterity of a conjurer. A sensible boy is not satisfied with merely
seeing the total of a given sum, or the answer to a given question,
_come out right_; he insists upon knowing why it is right. He is not
content to be led to the treasures of science blindfold; he would tear
the bandage from his eyes, that he might know the way to them again.
That many children, who have been thought to be slow in learning
arithmetic, have, after their escape from the hands of pedagogues,
become remarkable for their quickness, is a fact sufficiently proved
by experience. We shall only mention one instance, which we happened
to meet with whilst we were writing this chapter. John Ludwig, a Saxon
peasant, was dismissed from school when he was a child, after four
years ineffectual struggle to learn the common rules of arithmetic. He
had been, during this time, beaten and scolded in vain. He spent
several subsequent years in common country labour, but at length some
accidental circumstances excited his ambition, and he became expert in
all the common rules, and mastered the rule of three and fractions, by
the help of an old school book, in the course of one year. He
afterwards taught himself geometry, and raised himself, by the force
of his abilities and perseverance, from obscurity to fame.
We should like to see the book which helped Mr. Ludwig to conquer his
difficulties. Introductions to Arithmetic are, often, calculated
rather for adepts in science, than for the ignorant. We do not pretend
to have discovered any shorter method than what is common, of teaching
these sciences; but, in conformity with the principles which are laid
down in the former part of this work, we have endeavoured to teach
their rudiments without disgusting our pupils, and without habituating
them to be contented with merely technical operations.
In arithmetic, as in every other branch of education, the principal
object should be, to preserve the understanding from implicit belief;
to invigorate its powers; to associate pleasure with literature, and
to induce the laudable ambition of progressive improvement.
As soon as a child can read, he should be accustomed to count, and to
have the names of numbers early connected in his mind with the
combinations which they represent. For this purpose, he should be
taught to add first by things, and afterwards by signs or figures. He
should be taught to form combinations of things by adding them
together one after another. At the same time that he acquires the
names that have been given to these combinations, he should be taught
the figures or symbols that represent them. For example, when it is
familiar to the child, that one almond, and one almond, are called two
almonds; that one almond, and two almonds, are called three almonds,
and so on, he should be taught to distinguish the figures that
represent these assemblages; that 3 means one and two, &c. Each
operation of arithmetic should proceed in this manner, from
individuals to the abstract notation of signs.
One of the earliest operations of the reasoning faculty, is
abstraction; that is to say, the power of classing a number of
individuals under one name. Young children call strangers either men
or women; even the most ignorant savages[15] have a propensity to
generalize.
We may err either by accustoming our pupils too much to the
consideration of tangible substances when we teach them arithmetic, or
by turning their attention too much to signs. The art of forming a
sound and active understanding, consists in the due mixture of facts
and reflection. Dr. Reid has, in his "Essay on the Intellectual Powers
of Man," page 297, pointed out, with great ingenuity, the admirable
economy of nature in limiting the powers of reasoning during the first
years of infancy. This is the season for cultivating the senses, and
whoever, at this early age, endeavours to force the tender shoots of
reason, will repent his rashness.
In the chapter "on Toys," we have recommended the use of plain,
regular solids, cubes, globes, &c. made of wood, as playthings for
children, instead of uncouth figures of men, women and animals. For
teaching arithmetic, half inch cubes, which can be easily grasped by
infant fingers, may be employed with great advantage; they can be
easily arranged in various combinations; the eye can easily take in a
sufficient number of them at once, and the mind is insensibly led to
consider the assemblages in which they may be grouped, not only as
they relate to number, but as they relate to quantity or shape;
besides, the terms which are borrowed from some of these shapes, as
squares, cubes, &c. will become familiar. As these children advance in
arithmetic to square or cube, a number will be more intelligible to
them than to a person who has been taught these words merely as the
formula of certain rules. In arithmetic, the first lessons should be
short and simple; two cubes placed _above_ each other, will soon be
called two; if placed in any other situations near each other, they
will still be called two; but it is advantageous to accustom our
little pupils to place the cubes with which they are taught in
succession, either by placing them upon one another, or laying in
columns upon a table, beginning to count from the cube next to them,
as we cast up in addition. For this purpose, a board about six inches
long, and five broad, divided into columns perpendicularly by slips of
wood three eighths of an inch wide, and one eighth of an inch thick,
will be found useful; and if a few cubes of colours _different from
those already mentioned_, with numbers on their six sides, are
procured, they may be of great service. Our cubes should be placed,
from time to time, in a different order, or promiscuously; but when
any arithmetical operations are to be performed with them, it is best
to preserve the established arrangement.
One cube and one other, are called two.
Two what?
Two cubes.
One glass, and one glass, are called two glasses. One raisin, and one
raisin, are called two raisins, &c. One cube, and one glass, are
called what? _Two things_ or two.
By a process of this sort, the meaning of the abstract term _two_ may
be taught. A child will perceive the word _two_, means the same as the
words _one and one_; and when we say one and one are called two,
unless he is prejudiced by something else that is said to him, he will
understand nothing more than that there are two names for the same
thing.
"One, and one, and one, are called three," is the same as saying "that
three is the name for one, and one, and one." "Two and one are three,"
is also the same as saying "that three is the name of _two and one_."
Three is also the name of one and two; the word three has, therefore,
three meanings; it means one, and one, and one; _also_, two and one;
also, one and two. He will see that any two of the cubes may be put
together, as it were, in one parcel, and that this parcel may be
called _two_; and he will also see that this parcel, when joined to
another single cube, will _make_ three, and that the sum will be the
same, whether the single cube, or the two cubes, be named first.
In a similar manner, the combinations which form _four_, may be
considered. One, and one, and one, and one, are four.
One and three are four.
Two and two are four.
Three and one are four.
All these assertions mean the same thing, and the term _four_ is
equally applicable to each of them; when, therefore, we say that two
and two are four, the child may be easily led to perceive, and indeed
to _see_, that it means the same thing as saying one _two_, and one
_two_, which is the same thing as saying two _two's_, or saying the
word _two_ two times. Our pupil should be suffered to rest here, and
we should not, at present, attempt to lead him further towards that
compendious method of addition which we call multiplication; but the
foundation is laid by giving him this view of the relation between two
and two in forming four.
There is an enumeration in the note[16] of the different combinations
which compose the rest of the Arabic notation, which consists only of
nine characters.
Before we proceed to the number ten, or to the new series of
numeration which succeeds to it, we should make our pupils perfectly
masters of the combinations which we have mentioned, both in the
direct order in which they are arranged, and in various modes of
succession; by these means, not only the addition, but the
subtraction, of numbers as far as nine, will be perfectly familiar to
them.
It has been observed before, that counting by realities, and by
signs, should be taught at the same time, so that the ear, the eye,
and the mind, should keep pace with one another; and that technical
habits should be acquired without injury to the understanding. If a
child begins between four and five years of age, he may be allowed
half a year for this essential, preliminary step in arithmetic; four
or five minutes application every day, will be sufficient to teach him
not only the relations of the first decade in numeration, but also how
to write figures with accuracy and expedition.
The next step, is, by far the most difficult in the science of
arithmetic; in treatises upon the subject, it is concisely passed over
under the title of Numeration; but it requires no small degree of care
to make it intelligible to children, and we therefore recommend, that,
besides direct instruction upon the subject, the child should be led,
by degrees, to understand the nature of classification in general.
Botany and natural history, though they are not pursued as sciences,
are, notwithstanding, the daily occupation and amusement of children,
and they supply constant examples of classification. In conversation,
these may be familiarly pointed out; a grove, a flock, &c. are
constantly before the eyes of our pupil, and he comprehends as well as
we do what is meant by two groves, two flocks, &c. The trees that form
the grove are each of them individuals; but let their numbers be what
they may when they are considered as a grove, the grove is but one,
and may be thought of and spoken of distinctly, without any relation
to the number of single trees which it contains. From these, and
similar observations, a child may be led to consider _ten_ as the name
for a _whole_, an _integer_; a _one_, which may be represented by the
figure (1): this same figure may also stand for a hundred, or a
thousand, as he will readily perceive hereafter. Indeed, the term one
hundred will become familiar to him in conversation long before he
comprehends that the word _ten_ is used as an aggregate term, like a
dozen, or a thousand. We do not use the word ten as the French do _une
dizaine_; ten does not, therefore, present the idea of an integer till
we learn arithmetic. This is a defect in our language, which has
arisen from the use of duodecimal numeration; the analogies existing
between the names of other numbers in progression, is broken by the
terms eleven and twelve. _Thirteen_, _fourteen_, &c. are so obviously
compounded of three and ten, and four and ten, as to strike the ears
of children immediately, and when they advance as far as twenty, they
readily perceive that a new series of units begins, and proceeds to
thirty, and that thirty, forty, &c. mean three tens, four tens, &c. In
pointing out these analogies to children, they become interested and
attentive, they show that species of pleasure which arises from the
perception of _aptitude_, or of truth. It can scarcely be denied that
such a pleasure exists independently of every view of utility and
fame; and when we can once excite this feeling in the minds of our
young pupils at any period of their education, we may be certain of
success.
As soon as distinct notions have been acquired of the manner in which
a collection of ten units becomes a new unit of a higher order, our
pupil may be led to observe the utility of this invention by various
examples, before he applies it to the rules of arithmetic. Let him
count as far as ten with black pebbles,[17] for instance; let him lay
aside a white pebble to represent the collection of ten; he may count
another series of ten black pebbles, and lay aside another white one;
and so on, till he has collected ten white pebbles: as _each_ of the
ten white pebbles represents ten black pebbles, he will have counted
one hundred; and the ten white pebbles may now be represented by a
single red one, which will stand for one hundred. This large number,
which it takes up so much time to count, and which could not be
comprehended at one view, is represented by a single sign. Here the
difference of colour forms the distinction: difference in shape, or
size, would answer the same purpose, as in the Roman notation X for
ten, L for fifty, C for one hundred, &c. All this is fully within the
comprehension of a child of six years old, and will lead him to the
value of written figures by the _place_ which they hold when compared
with one another. Indeed he may be led to invent this arrangement, a
circumstance which would encourage him in every part of his education.
When once he clearly comprehends that the third place, counting from
the right, contains only figures which represent hundreds, &c. he will
have conquered one of the greatest difficulties of arithmetic. If a
paper ruled with several perpendicular lines, a quarter of an inch
asunder, be shown to him, he will see that the spaces or columns
between these lines would distinguish the value of figures written in
them, without the use of the sign (0) and he will see that (0) or
zero, serves only to mark the place or situation of the neighbouring
figures.
An idea of decimal arithmetic, but without detail, may now be given to
him, as it will not appear extraordinary to _him_ that a unit should
represent ten by having its place, or column changed; and nothing more
is necessary in decimal arithmetic, than to consider that figure which
represented, at one time, an integer, or whole, as representing at
another time the number of _tenth parts_ into which that whole may
have been broken.
Our pupil may next be taught what is called numeration, which he
cannot fail to understand, and in which he should be frequently
exercised. Common addition will be easily understood by a child who
distinctly perceives that the perpendicular columns, or places in
which figures are written, may distinguish their value under various
different denominations, as gallons, furlongs, shillings, &c. We
should not tease children with long sums in avoirdupois weight, or
load their frail memories with tables of long-measure, and
dry-measure, and ale-measure in the country, and ale-measure in
London; only let them cast up a few sums in different denominations,
with the tables before them, and let the practice of addition be
preserved in their minds by short sums every day, and when they are
between six and seven years old, they will be sufficiently masters of
the first and most useful rule of arithmetic.
To children who have been trained in this manner, subtraction will be
quite easy; care, however, should be taken to give them a clear notion
of the mystery of _borrowing_ and _paying_, which is inculcated in
teaching subtraction.
From 94
Subtract 46
"Six from four I can't, but six from ten, and four remains; four and
four _is_ eight."
And then, "One that I borrowed and four are five, five from nine, and
four remains."
This is the formula; but is it ever explained--or can it be? Certainly
not without some alteration. A child sees that six cannot be
subtracted (taken) from four: more especially a child who is
familiarly acquainted with the component parts of the names six and
four: he sees that the sum 46 is less than the sum 94, and he knows
that the lesser sum may be subtracted from the greater; but he does
not perceive the means of separating them figure by figure. Tell him,
that though six cannot be deducted from four, yet it can from
fourteen, and that if one of the tens which are contained in the (9)
ninety in the uppermost row of the second column, be supposed to be
taken away, or borrowed, from the ninety, and added to the four, the
nine will be reduced to 8 (eighty), and the four will become fourteen.
_Our_ pupil will comprehend this most readily; he will see that 6,
which could not be subtracted from 4, may be subtracted from fourteen,
and he will remember that the 9 in the next column is to be considered
as only (8). To avoid confusion, he may draw a stroke across the (9)
and write 8 over[18] it [8 over (9)] and proceed to the remainder of
the operation. This method for beginners is certainly very distinct,
and may for some time, be employed with advantage; and after its
rationale has become familiar, we may explain the common method which
depends upon this consideration.
"If one number is to be deducted from another, the remainder will be
the same, whether we add any given number to the smaller number, or
take away the same given number from the larger." For instance:
Let the larger number be 9
And the smaller 4
If you deduct 3 from the larger it will be 6
From this subtract the smaller 4
--
The remainder will be 2
--
Or if you add 3 to the smaller number, it
will be 7
--
Subtract this from the larger number 9
7
--
The remainder will be 2
Now in the common method of subtraction, the _one_ which is borrowed
is taken from the uppermost figure in the adjoining column, and
instead of altering that figure to _one_ less, we add one to the
lowest figure, which, as we have just shown, will have the same
effect. The terms, however, that are commonly used in performing this
operation, are improper. To say "one that I borrowed, and four"
(meaning the lowest figure in the adjoining column) implies the idea
that what was borrowed is now to be repaid to that lowest figure,
which is not the fact. As to multiplication, we have little to say.
Our pupil should be furnished, in the first instance, with a table
containing the addition of the different units, which form the
different products of the multiplication table: these he should, from
time to time, add up as an exercise in addition; and it should be
frequently pointed out to him, that adding these figures so many times
over, is the same as multiplying them by the number of times that they
are added; as three times 3 means 3 added three times. Here one of the
figures represents a quantity, the other does not represent a
quantity, it denotes nothing but the times, or frequency of
repetition. Young people, as they advance, are apt to confound these
signs, and to imagine, for instance, in the rule of three, &c. that
the sums which they multiply together, mean quantities; that 40 yards
of linen may be multiplied by three and six-pence, &c.--an idea from
which the misstatements in sums that are intricate, frequently arise.
We have heard that the multiplication table has been set, like the
Chapter of Kings, to a cheerful tune. This is a species of technical
memory which we have long practised, and which can do no harm to the
understanding; it prevents the mind from no beneficial exertion, and
may save much irksome labour. It is certainly to be wished, that our
pupil should be expert in the multiplication table; if the cubes which
we have formerly mentioned, be employed for this purpose, the notion
of _squaring_ figures will be introduced at the same time that the
multiplication table is committed to memory.
In division, what is called the Italian method of arranging the
divisor and quotient, appears to be preferable to the common one, as
it places them in such a manner as to be easily multiplied by each
other, and as it agrees with algebraic notation.
The usual method is this:
Divisor
71)83467(1175
Italian method:
Dividend
83467| 71
| ----
| 1175
The rule of three is commonly taught in a manner merely technical:
that it may be learned in this manner, so as to answer the common
purposes of life, there can be no doubt; and nothing is further from
our design, than to depreciate any mode of instruction which has been
sanctioned by experience: but our purpose is to point out methods of
conveying instruction that shall improve the reasoning faculty, and
habituate our pupil to think upon every subject. We wish, therefore,
to point out the course which the mind would follow to solve problems
relative to proportion without the rule, and to turn our pupil's
attention to the circumstances in which the rule assists us.
The calculation of the price of any commodity, or the measure of any
quantity, where the first term is one, may be always stated as a sum
in the rule of three; but as this statement retards, instead of
expediting the operation, it is never practised.
If one yard costs a shilling, how much will three yards cost?
The mind immediately perceives, that the price added three times
together, or multiplied by three, gives the answer. If a certain
number of apples are to be equally distributed amongst a certain
number of boys, if the share of one is one apple, the share of ten or
twenty is plainly equal to ten or twenty. But if we state that the
share of three boys is twelve apples, and ask what number will be
sufficient for nine boys, the answer is not obvious; it requires
consideration. Ask our pupil what made it so easy to answer the last
question, he will readily say, "Because I knew what was the share of
one."
Then you could answer this new question if you knew the share of one
boy?
Yes.
Cannot you find out what the share of one boy is when the share of
three boys is twelve?
Four.
What number of apples then will be enough, at the same rate, for nine
boys?
Nine times four, that is thirty-six.
In this process he does nothing more than divide the second number by
the first, and multiply the quotient by the third; 12 divided by 3 is
4, which multiplied by 9 is 36. And this is, in truth, the foundation
of the rule; for though the golden rule facilitates calculation, and
contributes admirably to our convenience, it is not absolutely
necessary to the solution of questions relating to proportion.
Again, "If the share of three boys is five apples, how many will be
sufficient for nine?"
Our pupil will attempt to proceed as in the former question, and will
begin by endeavouring to find out the share of one of the three boys;
but this is not quite so easy; he will see that each is to have one
apple, and part of another; but it will cost him some pains to
determine exactly how much. When at length he finds that one and
two-thirds is the share of one boy, before he can answer the question,
he must multiply one and two-thirds by nine, which is an operation _in
fractions_, a rule of which he at present knows nothing. But if he
begins by multiplying the second, instead of dividing it previously by
the first number, he will avoid the embarrassment occasioned by
fractional parts, and will easily solve the question.
3 : 5 : 9 : 15
Multiply 5
by 9
--
it makes 45
which product 45, divided by 3, gives 15.
Here our pupil perceives, that if a given number, 12, for instance, is
to be divided by one number, and multiplied by another, _it will come
to the same thing_, whether he begins by dividing the given number, or
by multiplying it.
12 divided by 4 is 3, which
multiplied by 6 is 18;
And
12 multiplied by 6 is 72, which
divided by 4 is 18.
We recommend it to preceptors not to fatigue the memories of their
young pupils with sums which are difficult only from the number of
figures which they require, but rather to give examples _in practice_,
where aliquot parts are to be considered, and where their ingenuity
may be employed without exhausting their patience. A variety of
arithmetical questions occur in common conversation, and from common
incidents; these should be made a subject of inquiry, and our pupils,
amongst others, should try their skill: in short, whatever can be
taught in conversation, is clear gain in instruction.
We should observe, that every explanation upon these subjects should
be recurred to from time to time, perhaps every two or three months;
as there are no circumstances in the business of every day, which
recall abstract speculations to the minds of children; and the pupil
who understands them to-day, may, without any deficiency of memory,
forget them entirely in a few weeks. Indeed, the perception of the
chain of reasoning, which connects demonstration, is what makes it
truly advantageous in education. Whoever has occasion, in the business
of life, to make use of the rule of three, may learn it effectually in
a month as well as in ten years; but the habit of reasoning cannot be
acquired late in life without _unusual_ labour, and uncommon
fortitude.
FOOTNOTES:
[15] V. A strange instance quoted by Mr. Stewart, "On the Human Mind,"
page 152.
[16]
NOTE.
1 Two is 1 the - name for 2 =
1 1 1 1 2 - - 3 3 = =
1 1 1 1 1 1 2 1 2 3 2 - - - - 4 4 4 4 = = = =
1 1 1 1 1 1 1 1 1 1 1 2 3 1 2 3 4 2 2 - - - - - - 5 5 5 5 5 5 = = = =
= =
1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 3 4 2 3 1 2 3 4 5 2 2 2 2
3 3 - - - - - - - - - - - 6 6 6 6 6 6 6 6 6 6 6 = = = = = = = = = = =
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 2 3 4
5 2 3 4 1 2 3 4 5 6 2 2 2 2 2 3 3 3 - - - - - - - - - - - - - - 7 7 7
7 7 7 7 7 7 7 7 7 7 7 = = = = = = = = = = = = = =
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1
2 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 4 1 2 3 4 5 6 7 2 2 2 3 3 3 3 3 -
- - - - - - - - - - - - - - 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 = = = = = =
= = = = = = = = =
1 1 2 1 1 5 2 2 3 4 2 2 3 4 4 4 4 5 6 - - - - - - - 8 8 8 8 8 8 8 = =
= = = = =
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
1 2 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 1 2 3
4 5 6 7 8 2 2 2 3 3 3 3 - - - - - - - - - - - - - - - 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 = = = = = = = = = = = = = = =
1 1 1 1 1 1 2 3 1 2 1 1 2 1 1 2 1 3 3 4 4 5 6 2 2 4 5 2 2 2 2 3 3 3 3
3 3 4 4 4 4 5 5 6 7 - - - - - - - - - - - - - - 9 9 9 9 9 9 9 9 9 9 9
9 9 9 = = = = = = = = = = = = = =
[17] The word calculate is derived from the Latin calculus, a pebble.
[18] This method is recommended in the Cours de Math, par Camus, p.
38.
CHAPTER XVI.
GEOMETRY.
There is certainly no royal road to geometry, but the way may be
rendered easy and pleasant by timely preparations for the journey.
Without any previous knowledge of the country, or of its peculiar
language, how can we expect that our young traveller should advance
with facility or pleasure? We are anxious that our pupil should
acquire a taste for accurate reasoning, and we resort to Geometry, as
the most perfect, and the purest series of ratiocination which has
been invented. Let us, then, sedulously avoid whatever may disgust
him; let his first steps be easy, and successful; let them be
frequently repeated until he can trace them without a guide.
We have recommended in the chapter upon Toys, that children should,
from their earliest years, be accustomed to the shape of what are
commonly called regular solids; they should also be accustomed to the
figures in mathematical diagrams. To these should be added their
respective names, and the whole language of the science should be
rendered as familiar as possible.
Mr. Donne, an ingenious mathematician of Bristol, has published a
prospectus of an Essay on Mechanical Geometry: he has executed, and
employed with success, models in wood and metal for demonstrating
propositions in geometry in a _palpable_ manner. We have endeavoured,
in vain, to procure a set of these models for our own pupils, but we
have no doubt of their entire utility.
What has been acquired in childhood, should not be suffered to escape
the memory. Dionysius[19] had mathematical diagrams described upon
the floors of his apartments, and thus recalled their demonstrations
to his memory. The slightest addition that can be conceived, if it be
continued daily, will imperceptibly, not only preserve what has been
already acquired, but will, in a few years, amount to as large a stock
of mathematical knowledge as we could wish. It is not our object to
make mathematicians, but to make it easy to our pupil to become a
mathematician, if his interest, or his ambition, make it desirable;
and, above all, to habituate him to clear reasoning, and close
attention. And we may here remark, that an early acquaintance with the
accuracy of mathematical demonstration, does not, within our
experience, contract the powers of the imagination. On the contrary,
we think that a young lady of twelve years old, who is now no more,
and who had an uncommon propensity to mathematical reasoning, had an
imagination remarkably vivid and inventive.[20]
We have accustomed our pupils to form in their minds the conception of
figures generated from points and lines, and surfaces supposed to move
in different directions, and with different velocities. It may be
thought, that this would be a difficult occupation for young minds;
but, upon trial, it will be found not only easy to them, but
entertaining. In their subsequent studies, it will be of material
advantage; it will facilitate their progress not only in pure
mathematics, but in mechanics and astronomy, and in every operation of
the mind which requires exact reflection.
To demand steady thought from a person who has not been trained to it,
is one of the most unprofitable and dangerous requisitions that can be
made in education.
"Full in the midst of Euclid dip at once,
And petrify a genius to a dunce."
In the usual commencement of mathematical studies, the learner is
required to admit that a point, of which he sees the prototype, a dot
before him, has neither length, breadth, nor thickness. This, surely,
is a degree of faith not absolutely necessary for the neophyte in
science. It is an absurdity which has, with much success, been
attacked in "Observations on the Nature of Demonstrative Evidence," by
Doctor Beddoes.
We agree with the doctor as to the impropriety of calling a visible
dot, a point without dimensions. But, notwithstanding the high respect
which the author commands by a steady pursuit of truth on all subjects
of human knowledge, we cannot avoid protesting against part of the
doctrine which he has endeavoured to inculcate. That the names point,
radius, &c. are derived from sensible objects, need not be disputed;
but surely the word centre can be understood by the human mind without
the presence of any visible or tangible substance.
Where two lines meet, their junction cannot have dimensions;
where two radii of a circle meet, they constitute the centre,
and the name centre may be used for ever without any relation
to a tangible or visible point. The word boundary, in like manner,
means the extreme limit we call a line; but to assert that it has
thickness, would, from the very terms which are used to describe it,
be a direct contradiction. Bishop Berkely, Mr. Walton, Philathetes
Cantabrigiensis, and Mr. Benjamin Robins, published several pamphlets
upon this subject about half a century ago. No man had a more
penetrating mind than Berkely; but we apprehend that Mr. Robins closed
the dispute against him. This is not meant as an appeal to authority,
but to apprize such of our readers as wish to consider the argument,
where they may meet an accurate investigation of the subject. It is
sufficient for our purpose, to warn preceptors not to insist upon
their pupils' acquiescence in the dogma, that a point, represented by
a dot, is without dimensions; and at the same time to profess, that we
understand distinctly what is meant by mathematicians when they speak
of length without breadth, and of a superfices without depth;
expressions which, to our minds, convey a meaning as distinct as the
name of any visible or tangible substance in nature, whose varieties
from shade, distance, colour, smoothness, heat, &c. are infinite, and
not to be comprehended in any definition.
In fact, this is a dispute merely about words, and as the extension of
the art of printing puts it in the power of every man to propose and
to defend his opinions at length, and at leisure, the best friends may
support different sides of a question with mutual regard, and the most
violent enemies with civility and decorum. Can we believe that Tycho
Brahe lost half his nose in a dispute with a Danish nobleman about a
mathematical demonstration?
FOOTNOTES:
[19] Plutarch.--Life of Dion.
[20] V. Rivuletta, a little story written _entirely_ by her in 1786.
CHAPTER XVII.
ON MECHANICS.
Parents are anxious that children should be conversant with Mechanics,
and with what are called the Mechanic Powers. Certainly no species of
knowledge is better suited to the taste and capacity of youth, and yet
it seldom forms a part of early instruction. Every body talks of the
lever, the wedge, and the pulley, but most people perceive, that the
notions which they have of their respective uses, are unsatisfactory,
and indistinct; and many endeavour, at a late period of life, to
acquire a scientific and exact knowledge of the effects that are
produced by implements which are in every body's hands, or that are
absolutely necessary in the daily occupations of mankind.
An itinerant lecturer seldom fails of having a numerous and attentive
auditory; and if he does not communicate much of that knowledge which
he endeavours to explain, it is not to be attributed either to his
want of skill, or to the insufficiency of his apparatus, but to the
novelty of the terms which he is obliged to use. Ignorance of the
language in which any science is taught, is an insuperable bar to its
being suddenly acquired; besides a precise knowledge of the meaning of
terms, we must have an instantaneous idea excited in our minds
whenever they are repeated; and, as this can be acquired only by
practice, it is impossible that philosophical lectures can be of much
service to those who are not familiarly acquainted with the technical
language in which they are delivered; and yet there is scarcely any
subject of human inquiry more obvious to the understanding, than the
laws of mechanics. Only a small portion of geometry is necessary to
the learner, if he even wishes to become master of the more difficult
problems which are usually contained in a course of lectures, and most
of what is practically useful, may be acquired by any person who is
expert in common arithmetic.
But we cannot proceed a single step without deviating from common
language; if the theory of the balance, or the lever, is to be
explained, we immediately speak of _space_ and _time_. To persons not
versed in literature, it is probable that these terms appear more
simple and unintelligible than they do to a man who has read Locke,
and other metaphysical writers. The term _space_ to the bulk of
mankind, conveys the idea of an interval; they consider the word
_time_ as representing a definite number of years, days, or minutes;
but the metaphysician, when he hears the words _space_ and _time_,
immediately takes the alarm, and recurs to the abstract notions which
are associated with these terms; he perceives difficulties unknown to
the unlearned, and feels a confusion of ideas which distracts his
attention. The lecturer proceeds with confidence, never supposing
that his audience can be puzzled by such common terms. He means by
_space_, the distance from the place whence a body begins to fall, to
the place where its motion ceases; and by time, he means the number of
seconds, or of any determinate divisions of _civil_ time which elapse
from the commencement of any motion to its end; or, in other words,
the duration of any given motion. After this has been frequently
repeated, any intelligent person perceives the sense in which they are
used by the tenour of the discourse; but in the interim, the greatest
part of what he has heard, cannot have been understood, and the
premises upon which every subsequent demonstration is founded, are
unknown to him. If this be true, when it is affirmed of two terms
only, what must be the situation of those to whom eight or ten unknown
technical terms occur at the commencement of a lecture? A complete
knowledge, such a knowledge as is not only full, but familiar, of all
the common terms made use of in theoretic and practical mechanics, is,
therefore, absolutely necessary before any person can attend public
lectures in natural philosophy with advantage.
What has been said of public lectures, may, with equal propriety, be
applied to private instruction; and it is probable, that inattention
to this circumstance is the reason why so few people have distinct
notions of natural philosophy. Learning by rote, or even reading
repeatedly, definitions of the technical terms of any science, must
undoubtedly facilitate its acquirement; but conversation, with the
habit of explaining the meaning of words, and the structure of common
domestic implements, to children, is the sure and effectual method of
preparing the mind for the acquirement of science.
The ancients, in learning this species of knowledge, had an advantage
of which we are deprived: many of their terms of science were the
common names of familiar objects. How few do we meet who have a
distinct notion of the words radius, angle, or valve. A Roman peasant
knew what a radius or a valve meant, in their original signification,
as well as a modern professor; he knew that a valve was a door, and a
radius a spoke of a wheel; but an English child finds it as difficult
to remember the meaning of the word angle, as the word parabola. An
angle is usually confounded, by those who are ignorant of geometry and
mechanics, with the word triangle, and the long reasoning of many a
laborious instructer has been confounded by this popular mistake. When
a glass pump is shown to an admiring spectator, he is desired to watch
the motion of the valves: he looks "above, about, and underneath;"
but, ignorant of the word _valve_, he looks in vain. Had he been
desired to look at the motion of the little doors that opened and
shut, as the handle of the pump was moved up and down, he would have
followed the lecturer with ease, and would have understood all his
subsequent reasoning. If a child attempts to push any thing heavier
than himself, his feet slide away from it, and the object can be moved
only at intervals, and by sudden starts; but if he be desired to prop
his feet against the wall, he finds it easy to push what before eluded
his little strength. Here the use of a fulcrum, or fixed point, by
means of which bodies may be moved, is distinctly understood. If two
boys lay a board across a narrow block of wood, or stone, and balance
each other at the opposite ends of it, they acquire another idea of a
centre of motion. If a poker is rested against a bar of a grate, and
employed to lift up the coals, the same notion of a centre is recalled
to their minds. If a boy, sitting upon a plank, a sofa, or form, be
lifted up by another boy's applying his strength at one end of the
seat, whilst the other end of the seat rests on the ground, it will be
readily perceived by them, that the point of rest, or centre of
motion, or fulcrum, is the ground, and that the fulcrum is not, as in
the first instance, between the force that lifts, and the thing that
is lifted; the fulcrum is at one end, the force which is exerted acts
at the other end, and the weight is in the middle. In trying, these
simple experiments, the terms _fulcrum_, _centre of motion_, &c.
should be constantly employed, and in a very short time they would be
as familiar to a boy of eight years old as to any philosopher. If for
some years the same words frequently recur to him in the same sense,
is it to be supposed that a lecture upon the balance and the lever
would be as unintelligible to him as to persons of good abilities, who
at a more advanced age hear these terms from the mouth of a lecturer?
A boy in such circumstances would appear as if he had a genius for
mechanics, when, perhaps, he might have less taste for the science,
and less capacity, than the generality of the audience. Trifling as it
may at first appear, it will not be found a trifling advantage, in the
progress of education, to attend to this circumstance. A distinct
knowledge of a few terms, assists a learner in his first attempts;
finding these successful, he advances with confidence, and acquires
new ideas without difficulty or disgust. Rousseau, with his usual
eloquence, has inculcated the necessity of annexing ideas to words; he
declaims against the splendid ignorance of men who speak by rote, and
who are rich in words amidst the most deplorable poverty of ideas. To
store the memory of his pupil with images of things, he is willing to
neglect, and leave to hazard, his acquirement of language. It requires
no elaborate argument to prove that a boy, whose mind was stored with
accurate images of external objects, of experimental knowledge, and
who had acquired habitual dexterity, but who was unacquainted with the
usual signs by which ideas are expressed, would be incapable of
accurate reasoning, or would, at best, reason only upon particulars.
Without general terms, he could not abstract; he could not, until his
vocabulary was enlarged, and familiar to him, reason upon general
topics, or draw conclusions from general principles: in short, he
would be in the situation of those who, in the solution of difficult
and complicated questions relative to quantity, are obliged to employ
tedious and perplexed calculations, instead of the clear and
comprehensive methods that unfold themselves by the use of signs in
algebra.
It is not necessary, in teaching children the technical language of
any art or science, that we should pursue the same order that is
requisite in teaching the science itself. Order is required in
reasoning, because all reasoning is employed in deducing propositions
from one another in a regular series; but where terms are employed
merely as names, this order may be dispensed with. It is, however, of
great consequence to seize the proper time for introducing a new term;
a moment when attention is awake, and when accident has produced some
particular interest in the object. In every family, opportunities of
this sort occur without any preparation, and such opportunities are
far preferable to a formal lecture and a splendid apparatus for the
first lessons in natural philosophy and chemistry. If the pump
belonging to the house is out of order, and the pump-maker is set to
work, an excellent opportunity presents itself for variety of
instruction. The centre pin of the handle is taken out, and a long rod
is drawn up by degrees, at the end of which a round piece of wood is
seen partly covered with leather. Your pupil immediately asks the name
of it, and the pump-maker prevents your answer, by informing little
master that it is called a sucker. You show it to the child, he
handles it, feels whether the leather is hard or soft, and at length
discovers that there is a hole through it which is covered with a
little flap or door. This, he learns from the workmen, is called a
clack. The child should now be permitted to plunge _the piston_ (by
which name it should _now_ be called) into a tub of water; in drawing
it backwards and forwards, he will perceive that the clack, which
should now be called the valve, opens and shuts as the piston is drawn
backwards and forwards. It will be better not to inform the child how
this mechanism is employed in the pump. If the names sucker and
piston, clack and valve, are fixed in his memory, it will be
sufficient for his first lesson. At another opportunity, he should be
present when the fixed or lower valve of the pump is drawn up; he will
examine it, and find that it is similar to the valve of the piston; if
he sees it put down into the pump, and sees the piston put into its
place, and set to work, the names that he has learned will be fixed
more deeply in his mind, and he will have some general notion of the
whole apparatus. From time to time these names should be recalled to
his memory on suitable occasions, but he should not be asked to repeat
them by rote. What has been said, is not intended as a lesson for a
child in mechanics, but as a sketch of a method of teaching which has
been employed with success.
Whatever repairs are carried on in a house, children should be
permitted to see: whilst every body about them seems interested, they
become attentive from sympathy; and whenever action accompanies
instruction, it is sure to make an impression. If a lock is out of
order, when it is taken off, show it to your pupil; point out some of
its principal parts, and name them; then put it into the hands of a
child, and let him manage it as he pleases. Locks are full of oil, and
black with dust and iron; but if children have been taught habits of
neatness, they may be clock-makers and white-smiths, without spoiling
their clothes, or the furniture of a house. Upon every occasion of
this sort, technical terms should be made familiar; they are of great
use in the every-day business of life, and are peculiarly serviceable
in giving orders to workmen, who, when they are spoken to in a
language that they are used to, comprehend what is said to them, and
work with alacrity.
An early use of a rule and pencil, and easy access to prints of
machines, of architecture, and of the implements of trades, are of
obvious use in this part of education. The machines published by the
Society of Arts in London; the prints in Desaguliers, Emerson, le
Spectacle de la Nature, Machines approuvées par l'Académie, Chambers's
Dictionary, Berthoud sur l'Horlogerie, Dictionaire des Arts et des
Métiers, may, in succession, be put into the hands of children. The
most simple should be first selected, and the pupils should be
accustomed to attend minutely to one print before another is given to
them. A proper person should carefully point out and explain to them
the first prints that they examine; they may afterwards be left to
themselves.
To understand prints of machines, a previous knowledge of what is
meant by an elevation, a profile, a section, a perspective view, and a
(vue d'oiseau) bird's eye view, is necessary. To obtain distinct ideas
of sections, a few models of common furniture, as chests of drawers,
bellows, grates, &c. may be provided, and may be cut asunder in
different directions. Children easily comprehend this part of drawing,
and its uses, which may be pointed out in books of architecture; its
application to the common business of life, is so various and
immediate, as to fix it for ever in the memory; besides, the habit of
abstraction, which is acquired by drawing the sections of complicated
architecture or machinery, is highly advantageous to the mind. The
parts which we wish to express, are concealed, and are suggested
partly by the elevation or profile of the figure, and partly by the
connection between the end proposed in the construction of the
building, machine, &c. and the means which are adapted to effect it.
A knowledge of perspective, is to be acquired by an operation of the
mind directly opposite to what is necessary in delineating the
sections of bodies; the mind must here be intent only upon the objects
that are delineated upon the retina, exactly what we see; it must
forget or suspend the knowledge which it has acquired from experience,
and must see with the eye of childhood, no further than the surface.
Every person, who is accustomed to drawing in perspective, sees
external nature, when he pleases, merely as a picture: this habit
contributes much to form a taste for the fine arts; it may, however,
be carried to excess. There are improvers who prefer the most dreary
ruin to an elegant and convenient mansion, and who prefer a blasted
stump to the glorious foliage of the oak.
Perspective is not, however, recommended merely as a means of
improving the taste, but as it is useful in facilitating the knowledge
of mechanics. When once children are familiarly acquainted with
perspective, and with the representations of machines by elevations,
sections, &c. prints will supply them with an extensive variety of
information; and when they see real machines, their structure and uses
will be easily comprehended. The noise, the seeming confusion, and the
size of several machines, make it difficult to comprehend and combine
their various parts, without much time, and repeated examination; the
reduced size of prints lays the whole at once before the eye, and
tends to facilitate not only comprehension, but contrivance. Whoever
can delineate progressively as he invents, saves much labour, much
time, and the hazard of confusion. Various contrivances have been
employed to facilitate drawing in perspective, as may be seen in
"Cabinet de Servier, Memoires of the French Academy, Philosophical
Transactions, and lately in the Repertory of Arts." The following is
simple, cheap, and _portable_.
PLATE 1. FIG. 1.
A B C, three mahogany boards, two, four, and six inches long, and of
the same breadth respectively, so as to double in the manner
represented.
PLATE 1. FIG. 2.
The part A is screwed, or _clamped_ to a table of a convenient height,
and a sheet of paper, one edge of which is put under the piece A, will
be held fast to the table.
The index P is to be set (at pleasure) with it sharp point to any
part of an object which the eye sees through E, the eye-piece.
The machine is now to be doubled as in Fig. 2, taking care that the
index be not disturbed; the point, which was before perpendicular,
will then approach the paper horizontally, and the place to which it
points on the paper, must be marked with a pencil. The machine must be
again unfolded, and another point of the object is to be ascertained
in the same manner as before; the space between these points may be
then connected with a line; fresh points should then be taken, marked
with a pencil, and connected with a line; and so on successively,
until the whole object is delineated.
Besides the common terms of art, the technical terms of science
should, by degrees, be rendered familiar to our pupils. Amongst these
the words Space and Time occur, as we have observed, the soonest, and
are of the greatest importance. Without exact definitions, or abstract
reasonings, a general notion of the use of these terms may be
inculcated by employing them frequently in conversation, and by
applying them to things and circumstances which occur without
preparation, and about which children are interested, or occupied.
"There is a great space left between the words in that printing." The
child understands, that _space_ in this sentence means white paper
between black letters. "You should leave a greater space between the
flowers which you are planting"--he knows that you mean more _ground_.
"There is a great space between that boat and the ship"--space of
water. "I hope the hawk will not be able to catch that pigeon, there
is a great space between them"--space of air. "The men who are pulling
that sack of corn into the granary, have raised it through half the
space between the door and the ground." A child cannot be at any loss
for the meaning of the word space in these or any other practical
examples which may occur; but he should also be used to the word space
as a technical expression, and then he will not be confused or stopped
by a new term when employed in mechanics.
The word _time_ may be used in the same manner upon numberless
occasions to express the duration of any movement which is performed
by the force of men, or horses, wind, water, or any mechanical power.
"Did the horses in the mill we saw yesterday, go as fast as the horses
which are drawing the chaise?" "No, not as fast as the horses go at
present on level ground; but they went as fast as the chaise-horses do
when they go up hill, or as fast as horses draw a waggon."
"How many times do the sails of that wind-mill go round in a minute?
Let us count; I will look at my watch; do you count how often the
sails go round; wait until that broken arm is uppermost, and when you
say _now_, I will begin to count the _time_; when a minute has past, I
will tell you."
After a few trials, this experiment will become easy to a child of
eight or nine years old; he may sometimes attend to the watch, and at
other times count the turns of the sails; he may easily be made to
apply this to a horse-mill, or to a water-mill, a corn-fan, or any
machine that has a rotatory motion; he will be entertained with his
new employment; he will compare the _velocities_ of different
machines; the meaning of this word will be easily added to his
vocabulary.
"Does that part of the arms of the wind-mill which is near the
_axle-tree_, or _centre_, I mean that part which has no cloth or sail
upon it, go as fast as the ends of the arms that are the farthest from
the centre?"
"No, not near so fast."
"But that part goes as often round in a minute as the rest of the
sail."
"Yes, but it does not go as fast."
"How so?"
"It does not go so _far_ round."
"No, it does not. The _extremities_ of the _sails go through more
space in the same time_ than the part near the centre."
By conversations like these, the technical meaning of the word
_velocity_ may be made quite familiar to a child much younger than
what has been mentioned; he may not only comprehend that velocity
means time and space considered together, but if he is sufficiently
advanced in arithmetic, he may be readily taught how to express and
compare in numbers _velocities_ composed of certain portions of time
and space. He will not inquire about the abstract meaning of the word
_space_; he has seen space measured on paper, on timber, on the water,
in the air, and he perceives distinctly that it is a term equally
applicable to all distances that can exist between objects of any
sort, or that he can see, feel, or imagine.
Momentum, a less common word, the meaning of which is not quite so
easy to convey to a child, may, by degrees, be explained to him: at
every instant he feels the effect of momentum in his own motions, and
in the motions of every thing that strikes against him; his feelings
and experience require only proper terms to become the subject of his
conversation. When he begins to inquire, it is the proper time to
instruct him. For instance, a boy of ten years old, who had acquired
the meaning of some other terms in science, this morning asked the
meaning of the word momentum; he was desired to explain what he
thought it meant.
He answered, "Force."
"What do you mean by force?"
"Effort."
"Of what?"
"Of gravity."
"Do you mean that force by which a body is drawn down to the earth?"
"No."
"Would a feather, if it were moving with the greatest conceivable
swiftness or velocity, throw down a castle?"
"No."[21]
"Would a mountain torn up by the roots, as fabled in Milton, if it
moved with the least conceivable velocity, throw down a castle?"
"Yes, I think it would."
The difference between an uniform, and an uniformly accelerated
motion, the measure of the velocity of falling bodies, the composition
of motions communicated to the same body in different directions at
the same time, and the cause of the curvilinear track of projectiles,
seem, at first, intricate subjects, and above the capacity of boys of
ten or twelve years old; but by short and well-timed lessons, they may
be explained without confounding or fatiguing their attention. We
tried another experiment whilst this chapter was writing, to determine
whether we had asserted too much upon this subject. After a
conversation between two boys upon the descent of bodies towards the
earth, and upon the measure of the increasing velocity with which they
fall, they were desired, with a view to ascertain whether they
understood what was said, to invent a machine which should show the
difference between an uniform and an accelerated velocity, and in
particular to show, by occular demonstration, "that if one body moves
in a given time through a given space, with an uniform motion, and if
another body moves through the same space in the same time with an
uniformly accelerated motion, the uniform motion of the one will be
equal to half the accelerated motion of the other." The eldest boy,
H----, thirteen years old, invented and executed the following machine
for this purpose:
Plate I, Fig. 3. _b_ is a bracket 9 inches by 5, consisting of a back
and two sides of hard wood: two inches from the back two slits are
made in the sides of the bracket half an inch deep, and an eighth of
an inch wide, to receive the two wire pivots of a roller; which roller
is composed of a cylinder, three inches long and half an inch
diameter; and a cone three inches long and one inch diameter in its
largest part or base. The cylinder and cone are not separate, but are
turned out of one piece; a string is fastened to the cone at its base
_a_, with a bullet or any other small weight at the other end of it;
and another string and weight are fastened to the cylinder at _c_; the
pivot _p_ of wire is bent into the form of a handle; if the handle is
turned either way, the strings will be respectively wound up upon the
cone and cylinder; their lengths should now be adjusted, so that when
the string on the cone is wound up as far as the cone will permit, the
two weights may be at an equal distance from the bottom of the
bracket, which bottom we suppose to be parallel with the pivots; the
bracket should now be fastened against a wall, at such a height as to
let the weights lightly touch the floor when the strings are unwound:
silk or _bobbin_ is a proper kind of string for this purpose, as it is
woven or plaited, and therefore is not liable to twist. When the
strings are wound up to their greatest heights, if the handle be
suddenly let go, both the weights will begin to fall at the same
moment; but the weight 1, will descend at first but slowly, and will
pass through but small space compared with the weight 2. As they
descend further, No. 2 still continues to get before No. 1; but after
some time, No. 1 begins to overtake No. 2, and at last they come to
the ground together. If this machine is required to show exactly the
space that a falling body would describe in given times, the cone and
cylinder must have grooves cut spirally upon their circumference, to
direct the string with precision. To describe these spiral lines,
became a new subject of inquiry. The young mechanics were again eager
to exert their powers of invention; the eldest invented a machine upon
the same principle as that which is used by the best workmen for
cutting clock fusees; and it is described in Berthoud. The youngest
invented the engine delineated, Plate 1, Fig. 4.
The roller or cone (or both together) which it is required to cut
spirally, must be furnished with a handle, and a toothed wheel _w_,
which turns a smaller wheel or pinion _w_. This pinion carries with it
a screw _s_, which draws forward the puppet _p_, in which the
graver of chisel _g_ slides _without shake_. This graver has a point
or edge shaped properly to form the spiral groove, with a shoulder to
regulate the depth of the groove. The iron rod _r_, which is firmly
fastened in the puppet, slides through mortices at _mm_, and guides
the puppet in a straight line.
[Illustration: Plate 1.]
The rest of the machine is intelligible from the drawing.
A simple method of showing the nature of compound forces was thought
of at the same time. An ivory ball was placed at the corner of a board
sixteen inches broad, and two feet long; two other similar balls were
let fall down inclined troughs against the first ball in different
directions, but at the same time. One fell in a direction parallel to
the length of the board; the other ball fell back in a direction
parallel to its breadth. By raising the troughs, such a force was
communicated to each of the falling balls, as was sufficient to drive
the ball that was at rest to that side or end of the board which was
opposite, or at right angles, to the line of its motion.
When both balls were let fall together, they drove the ball that was
at rest diagonally, so as to reach the opposite corner. If the same
board were placed as an inclined plane, at an angle of five or six
degrees, a ball placed at one of its uppermost corners, would fall
with an accelerated motion in a direct line; but if another ball were
made (by descending through an inclined trough) to strike the first
ball at right angles to the line of its former descent, at the moment
when it began to descend, it would not, as in the former experiment,
move diagonally, but would describe a curve.
The reason why it describes a curve, and why that curve is not
circular, was easily understood. Children who are thus induced to
invent machines or apparatus for explaining and demonstrating the laws
of mechanism, not only fix indelibly those laws in their own minds,
but enlarge their powers of invention, and preserve a certain
originality of thought, which leads to new discoveries.
We therefore strongly recommend it to teachers, to use as few precepts
as possible in the rudiments of science, and to encourage their pupils
to use their own understandings as they advance. In mechanism, a
general view of the powers and uses of engines is all that need be
taught; where more is necessary, such a foundation, with the
assistance of good books, and the examination of good machinery, will
perfect the knowledge of theory and facilitate practice.
At first we should not encumber our pupils with accurate
demonstration. The application of mathematics to mechanics is
undoubtedly of the highest use, and has opened a source of ingenious
and important inquiry. Archimedes, the greatest name amongst mechanic
philosophers, scorned the mere practical application of his sublime
discoveries, and at the moment when the most stupendous effects were
producing by his engines, he was so deeply absorbed in abstract
speculation as to be insensible to the fear of death. We do not mean,
therefore, to undervalue either the application of strict
demonstration to problems in mechanics, or the exhibition of the most
accurate machinery in philosophical lectures; but we wish to point out
a method of giving a general notion of the mechanical organs to our
pupils, which shall be immediately obvious to their comprehension, and
which may serve as a sure foundation for future improvement. We are
told by a vulgar proverb, that though we believe what we see, we have
yet a higher belief in what we _feel_. This adage is particularly
applicable to mechanics. When a person perceives the effect of his own
bodily exertions with different engines, and when he can compare in a
rough manner their relative advantages, he is not disposed to reject
their assistance, or expect more than is reasonable from their
application. The young theorist in mechanics thinks he can produce a
perpetual motion! When he has been accustomed to refer to the plain
dictates of common sense and experience, on this, as well as on every
other subject, he will not easily be led astray by visionary theories.
[Illustration: Plate 2.]
To bring the sense of feeling to our assistance in teaching the uses
of the mechanic powers, the following apparatus was constructed, to
which we have given the name Panorganon.
It is composed of two principal parts: a frame to contain the moving
machinery; and a _capstan_ or _windlass_, which is erected on a _sill_
or plank, that is sunk a few inches into the ground: the frame is by
this means, and by six braces or props, rendered steady. The cross
rail, or _transom_, is strengthened by braces and a king-post to make
it lighter and cheaper. The _capstan_ consists of an upright shaft,
upon which are fixed two _drums_; about which a rope may be wound up,
and two levers or arms by which it may be turned round. There is also
a screw of iron coiled round the lower part of the shaft, to show the
properties of the screw as a mechanic power. The rope which goes round
the _drum_ passes over one of the pulleys near to the top of the
frame, and under another pulley near the bottom of the frame. As two
_drums_ of different sizes are employed, it is necessary to have an
upright roller to conduct the rope in a proper direction to the
pulleys, when either of the _drums_ is used. Near the frame, and in
the direction in which the rope runs, is laid a platform or road of
deal boards, one board in breadth, and twenty or thirty feet long,
upon which a small sledge loaded with different weights may be drawn.
Plate 2. Fig. 1.
F. F. The frame.
b. b. Braces to keep the frame steady.
a. a. a. Angular braces to strengthen the transom; and also a
_king-post_.
S. A round, taper shaft, strengthened above and below the mortises
with iron hoops.
L L. Two arms, or levers, by which the shaft, &c. are to be moved
round.
D D. The drum, which has two rims of different circumferences.
R. The roller to conduct the rope.
P. The pulley, round which the rope passes to the larger drum.
P 2. Another pulley to answer to the smaller drum.
P 3. A pulley through which the rope passes when experiments are tried
with levers, &c.
P 4. Another pulley through which the rope passes when the sledge is
used.
Ro. The road of deal boards for the sledge to move on.
Sl. The sledge, with pieces of hard wood attached to it, to guide it
on the road.
_Uses of the Panorganon._
As this machine is to be moved by the force of men or children, and as
their force varies not only with the strength and weight of each
individual, but also according to the different manner in which that
strength or weight is applied; it is, in the first place, requisite to
establish one determinate mode of applying human force to the machine;
and also a method of determining the relative force of each individual
whose strength is applied to it.
_To estimate the force with which a person can draw horizontally by a
rope over his shoulder._
EXPERIMENT I.
Hang a common long scale-beam (without scales or chains) from the top
or _transom_ of the frame, so as that one end of it may come within an
inch of one side or post of the machine. Tie a rope to the hook of the
scale-beam, where the chains of the scale are usually hung, and pass
it through the pulley P 3, which is about four feet from the ground;
let the person pull this rope from 1 towards 2, turning his back to
the machine, and pulling the rope over his shoulder--Pl. 2. Fig. 6. As
the pulley may be either too high or too low to permit the rope to be
horizontal, the person who pulls it should be placed ten or fifteen
feet from the machine, which will lessen the angular direction of the
cord, and the inaccuracy of the experiment. Hang weights to the other
end of the scale-beam, until the person who pulls can but just walk
forward, pulling fairly without propping his feet against any thing.
This weight will estimate the force with which he can draw
horizontally by a rope over his shoulder.[22] Let a child who tries
this, walk on the board with dry shoes; let him afterwards chalk his
shoes, and afterwards try it with his shoes soaped: he will find that
he can pull with different degrees of force in these different
circumstances; but when he tries the following experiments, let his
shoes be always dry, that his force may be always the same.
_To show the power of the three different sorts of levers._
EXPERIMENT II.
Instead of putting the cord that comes from the scale-beam, as in the
last experiment, over the shoulder of the boy, hook it to the end 1 of
the lever L, Fig. 2. Plate 2. This lever is passed through a
socket--Plate 2. Fig. 3.--in which it can be shifted from one of its
ends towards the other, and can be fastened at any place by the screw
of the socket. This socket has two gudgeons, upon which it, and the
lever which it contains, can turn. This socket and its gudgeons can be
lifted out of the holes in which it plays, between the rail R R, Plate
2. Fig. 2. and may be put into other holes at R R, Fig. 5. Loop
another rope to the other end of this lever, and let the boy pull as
before. Perhaps it should be pointed out, that the boy must walk in a
direction contrary to that in which he walked before, viz. from 1
towards 3. The height to which the weight ascends, and the distance to
which the boy advances, should be carefully marked and measured; and
it will be found, that he can raise the weight to the same height,
advancing through the same space as in the former experiment. In this
case, as both ends of the lever moved through equal spaces, the lever
only changed the direction of the motion, and added no mechanical
power to the direct strength of the boy.
EXPERIMENT III.
Shift the lever to its extremity in the _socket_; the middle of the
lever will be now opposite to the pulley, Pl. 2. Fig. 4.--hook to it
the rope that goes through the pulley P 3, and fasten to the other end
of the lever the rope by which the boy is to pull. This will be _a
lever of the second kind_, as it is called in books of mechanics; in
using which, _the resistance is placed between the centre of motion or
fulcrum, and the moving power_. He will now raise double the weight
that he did in Experiment II, and he will advance through double the
space.
EXPERIMENT IV.
Shift the lever, and the socket which forms the axis (without shifting
the lever from the place in which it was in the socket in the last
experiment) to the holes that are prepared for it at R R, Plate 2.
Fig. 5. The free end of the lever E will now be opposite to the rope,
and to the pulley (over which the rope comes from the scale-beam.)
Hook this rope to it, and hook the rope by which the boy pulls, to the
middle of the lever. The effect will now be different from what it was
in the two last experiments; the boy will advance only half as far,
and will raise only half as much weight as before. This is called _a
lever of the third sort_. The first and second kinds of levers are
used in quarrying; and the operations of many tools may be referred to
them. The third kind of lever is employed but seldom, but its
properties may be observed with advantage whilst a long ladder is
raised, as the man who raises it, is obliged to exert an increasing
force until the ladder is nearly perpendicular. When this lever is
used, it is obvious, from what has been said, that the power must
always pass through less space than the thing which is to be moved; it
can never, therefore, be of service in gaining power. But the object
of some machines, is to increase velocity, instead of obtaining power,
as in a sledge-hammer moved by mill-work. (V. the plates in Emerson's
Mechanics, No. 236.)
The experiments upon levers may be varied at pleasure, increasing or
diminishing the mechanical advantage, so as to balance the power and
the resistance, to accustom the learners to calculate the relation
between the power and the effect in different circumstances; always
pointing out, that whatever excess there is in the power,[23] or in
the resistance, is always compensated by the difference of space
through which the inferiour passes.
The experiments which we have mentioned, are sufficiently satisfactory
to a pupil, as to the immediate relation between the power and the
resistance; but the different spaces through which the power and the
resistance move when one exceeds the other, cannot be obvious, without
they pass through much larger spaces than levers will permit.
EXPERIMENT V.
Place the sledge on the farthest end of the wooden road--Plate 2. Fig.
1.--fasten a rope to the sledge, and conduct it through the lowest
pulley P 4, and through the pulley P 3, so as that the boy may be
enabled to draw it by the rope passed over his shoulder. The sledge
must now be loaded, until the boy can but just advance with short
steps steadily upon the wooden road; this must be done with care, as
there will be but just room for him beside the rope. He will meet the
sledge exactly on the middle of the road, from which he must step
aside to pass the sledge. Let the time of this experiment be noted. It
is obvious that the boy and the sledge move with equal velocity; there
is, therefore, no mechanical advantage obtained by the pulleys. The
weight that he can draw will be about half a hundred, if he weigh
about nine stone; but the exact force with which the boy draws, is to
be known by Experiment I.
_The wheel and axle._
This organ is usually called in mechanics, _The axis in peritrochio_.
A _hard_ name, which might well be spared, as the word windlass or
capstan would convey a more distinct idea to our pupils.
EXPERIMENT VI.
To the largest drum, Plate 2. Fig. 1. fasten a cord, and pass it
through the pulley P downwards, and through the pulley P 4 to the
sledge placed at the end of the wooden road, which is farthest from
the machine. Let the boy, by a rope fastened to the extremity of one
of the arms of the capstan, and passed over his shoulder, draw the
capstan round; he will wind the rope round the drum, and draw the
sledge upon its road. To make the sledge advance twenty-four feet upon
its road, the boy must have walked circularly 144 feet, which is six
times as far, and he will be able to draw about three hundred weight,
which is six times as much as in the last experiment.
It may now be pointed out, that the difference of space, passed
through by the power in this experiment, is exactly equal to the
difference of weight, which the boy could draw without the capstan.
EXPERIMENT VII.
Let the rope be now attached to the smaller drum; the boy will draw
nearly twice as much weight upon the sledge as before, and will go
through double the space.
EXPERIMENT VIII.
Where there are a number of boys, let five or six of them, whose power
of drawing (estimated as in Experiment I) amounts to six times as much
as the force of the boy at the capstan, pull at the end of the rope
which _was_ fastened to the sledge; they will balance the force of the
boy at the capstan: either they, or he, by a sudden pull, may advance,
but if they pull fairly, there will be no advantage on either part. In
this experiment, the rope should pass through the pulley P 3, and
should be coiled round the larger drum. And it must be also observed,
that in all experiments upon the motion of bodies, in which there is
much friction, as where a sledge is employed, the results are never so
uniform as in other circumstances.
_The Pulley._
Upon the pulley we shall say little, as it is in every body's hands,
and experiments may be tried upon it without any particular apparatus.
It should, however, be distinctly inculcated, that the power is not
increased by a fixed pulley. For this purpose, a wheel without a rim,
or, to speak with more propriety, a number of spokes fixed in a nave,
should be employed. (Plate 2. Fig. 9.) Pieces like the heads of
crutches should be fixed at the ends of these spokes, to receive a
piece of girth-web, which is used instead of a cord, because a cord
would be unsteady; and a strap of iron with a hook to it should play
upon the centre, by which it may at times be suspended, and from which
at other times a weight may be hung.
EXPERIMENT IX.
Let the skeleton of a pulley be hung by the iron strap from the
transom of the frame; fasten a piece of web to one of the radii, and
another to the end of the opposite radius. If two boys of equal weight
pull these pieces of girth-web, they will balance each other; or two
equal weights hung to these webs, will be in equilibrio. If a piece
of girth-web be put round the uppermost radius, two equal weights hung
at the ends of it will remain immoveable; but if either of them be
pulled, or if a small additional weight be added to either of them, it
will descend, and the web will apply itself successively to the
ascending radii, and will detach itself from those that are
descending. If this movement be carefully considered, it will be
perceived, that the web, in unfolding itself, acts in the same manner
upon the radii as two ropes would if they were hung to the extremities
of the opposite radii in succession. The two radii which are opposite,
may be considered as a lever of the first sort, where the centre is in
the middle of the lever; as each end moves through an equal space,
there is no mechanical advantage. But if this skeleton-pulley be
employed as a common _block_ or _tackle_, its motions and properties
will be entirely different.
EXPERIMENT X. PLATE 2. FIG. 9.
Nail a piece of girth-web to a post, at the distance of three or four
feet from the ground; fasten the other end of it to one of the radii.
Fasten another piece of web to the opposite radius, and let a boy hold
the skeleton-pulley suspended by the web; hook weights to the strap
that hangs from the centre. The end of the radius to which the fixed
girth-web is fastened, will remain immoveable; but, if the boy pulls
the web which he holds in his hand upwards, he will be able to lift
nearly double the weight, which he can raise from the ground by a
simple rope, without the machine, and he will perceive that his hand
moves through twice as great a space as the weight ascends: he has,
therefore, the mechanical advantage which he would have by a lever of
the second sort, as in Experiment III. Let a piece of web be put round
the under radii, let one end of it be nailed to the post, and the
other be held by the boy, and it will represent the application of a
rope to a moveable pulley; if its motion be carefully considered, it
will appear that the radii, as they successively apply themselves to
the web, represent a series of levers of the second kind. A pulley is
nothing more than an infinite number of such levers; the cord at one
end of the diameter serving as a fulcrum for the _organ_ during its
progress. If this _skeleton-pulley_ be used horizontally, instead of
perpendicularly, the circumstances which have been mentioned, will
appear more obvious.
Upon the wooden road lay down a piece of girth-web; nail one end of it
to the road; place the pulley upon the web at the other end of the
board, and, bringing the web over the radii, let the boy, taking hold
of it, draw the loaded sledge fastened to the hook at the centre of
the pulley: he will draw nearly twice as much in this manner as he
could without the pulley.[24]
Here the web lying on the road, shows more distinctly, that it is
quiescent where the lowest radius touches it; and if the radii, as
they tread upon it, are observed, their points will appear at rest,
whilst the centre of the pulley will go as fast as the sledge, and the
top of each radius successively (and the boy's hand which unfolds the
web) will move twice as fast as the centre of the pulley and the
sledge.
If a person, holding a stick in his hand, observes the relative
motions of the top, and the middle, and the bottom of the stick,
whilst he inclines it, he will see that the bottom of the stick has no
motion on the ground, and that the middle has only half the motion of
the top. This property of the pulley has been dwelt upon, because it
elucidates the motion of a wheel rolling upon the ground; and it
explains a common paradox, which appears at first inexplicable. "The
bottom of a rolling wheel never moves _upon_ the road." This is
asserted only of a wheel moving over hard ground, which, in fact, may
be considered rather as laying down its circumference upon the road,
than as moving upon it.
_The inclined Plane and the Wedge._
The _inclined plane_ is to be next considered. When a heavy body is to
be raised, it is often convenient to lay a sloping artificial road of
planks, up which it may be pushed or drawn. This mechanical power,
however, is but of little service without the assistance of wheels or
rollers; we shall, therefore, speak of it as it is applied in another
manner, under the name of _the wedge_, which is, in fact, a moving
inclined plane; but if it is required to explain the properties of the
inclined plane by the panorganon, the wooden road may be raised and
set to any inclination that is required, and the sledge may be drawn
upon it as in the former experiments.
Let one end of a lever, N. Plate 2. Fig. 7. with a wheel at one end of
it, be hinged to the post of the frame, by means of a gudgeon driven
or screwed into the post. To prevent this lever from deviating
sideways, let a slip of wood be connected with it by a nail, which
shall be fast in the lever, but which moves freely in a hole in the
rail. The other end of this slip must be fastened to a stake driven
into the ground at three or four feet from the lever, at one side of
it, and towards the end in which the wheel is fixed (Plate 2. Fig 10.
which is a _vue d'oiseau_) in the same manner as the treadle of a
common lathe is managed, and as the treadle of a loom is sometimes
guided.[25]
EXPERIMENT XI.
Under the wheel of this lever place an inclined plane or half-wedge
(Plate 2. Fig. 7.) on the wooden road, with rollers under it, to
prevent friction;[26] fasten a rope to the foremost end of the wedge,
and pass it through the pulleys (P 4. and P 3.) as in the fifth
experiment. Let a boy draw the sledge by this rope over his shoulder,
and he will find, that as it advances it will raise the weight
upwards; the wedge is five feet long, and elevated one foot. Now, if
the perpendicular ascent of the weight, and the space through which he
advances, be compared, he will find, that the space through which he
has passed will be five times as great as that through which the
weight has ascended; and that _this_ wedge has enabled him to raise
five times as much as he could raise without it, if his strength were
applied, as in Experiment I, without any mechanical advantage. By
making this wedge in two parts hinged together, with a graduated piece
to keep them asunder, the wedge may be adjusted to any given
obliquity; and it will be always found, that the mechanical advantage
of the wedge may be ascertained by comparing its perpendicular
elevation with its base. If the base of the wedge is 2, 3, 4, 5, or
any other number of times greater than its height, it will enable the
boy to raise respectively 2, 3, 4, or 5 times more weight than he
could do in Experiment I, by which his power is estimated.
_The Screw._
_The screw_ is an inclined plane wound round a cylinder; the height of
all its revolutions round the cylinder taken together, compared with
the space through which the power that turns it passes, is the measure
of its _mechanical advantage_.[27] Let the lever, used in the last
experiment, be turned in such a manner as to reach from its gudgeon to
the shaft of the Panorganon, guided by an attendant lever as before.
(Plate 2. Fig. 8.) Let the wheel rest upon the lowest _helix_ or
thread of the screw: as the arms of the shaft are turned round, the
wheel will ascend, and carry up the weight which is fastened to the
lever.[28] As the situation of the screw prevents the weight from
being suspended exactly from the centre of the screw, proper allowance
must be made for this in estimating the force of the screw, or
determining the mechanical advantage gained by the lever: this can be
done by measuring the perpendicular ascent of the weight, which in all
cases is better, and more expeditious, than measuring the parts of a
machine, and estimating its force by calculation; because the
different diameters of ropes, and other small circumstances, are
frequently mistaken in estimates.
The space passed through by the moving power, and by that which it
moves, are infallible data for estimating the powers of engines. Two
material subjects of experiments, yet remain for the Panorganon;
friction, and wheels of carriages: but we have already extended this
article far beyond its just proportion to similar chapters in this
work. We repeat, that it is not intended in this, or in any other part
of our design, to write treatises upon science; but merely to point
out methods for initiating young people in the rudiments of knowledge,
and of giving them a clear and distinct view of those principles upon
which they are founded. No preceptor, who has had experience, will
cavil at the superficial knowledge of a boy of twelve or thirteen upon
these subjects; he will perceive, that the general view, which we wish
to give our pupils of the useful arts and sciences, must certainly
tend to form a taste for literature and investigation. The _sciolist_
has learned only to _talk_--we wish to teach our pupils to _think_,
upon the various objects of human speculation.
The Panorganon may be employed in trying the resistance of air and
water; the force of different muscles; and in a great variety of
amusing and useful experiments. In academies, and private families, it
may be erected in the place allotted for amusement, where it will
furnish entertainment for many a vacant hour. When it has lost its
novelty, the shaft may from time to time be taken down, and a swing
may be suspended in its place. It may be constructed at the expense of
five or six pounds: that which stands before our window, was made for
less than three guineas, as we had many of the materials beside us for
other purposes.
FOOTNOTES:
[21] When this question was sometime afterwards repeated to S----, he
observed, that the feather would throw down the castle, if its
swiftness were so great as to make up for its want of weight.
[22] Were it thought necessary to make these experiments perfectly
accurate, a segment of a pulley, the radius of which is half the
length of the scale-beam, should be attached to the end of the beam;
upon which the cord may apply itself, and the pulley (P 3) should be
raised or lowered, to bring the rope horizontally from the man's
shoulder when in the attitude of drawing.
[23] The word _power_ is here used in a popular sense, to denote the
strength or efficacy that is employed to produce an effect by means of
any engine.
[24] In all these experiments with the skeleton-pulley, somebody must
keep it in its proper direction; as from its structure, which is
contrived for illustration, not for practical use, it cannot retain
its proper situation without assistance.
[25] In a loom this secondary lever is called _a lamb_, by mistake,
for _lam_; from _lamina_, a slip of wood.
[26] There should be three rollers used; one of them must be placed
before the sledge, under which it will easily find its place, if the
bottom of the sledge near the foremost end is a little sloped upwards.
To retain this foremost roller in its place until the sledge meets it,
it should be stuck lightly on the road with two small bits of wax or
pitch.
[27] _Mechanical advantage_ is not a proper term, but our language is
deficient in proper technical terms. The word _power_ is used so
indiscriminately, that it is scarcely possible to convey our meaning,
without employing it more strictly.
[28] In this experiment, the boy should pull as near as possible to
the shaft, within a foot of it, for instance, else he will have such
mechanical advantage as cannot be counterbalanced by any weight which
the machine would be strong enough to bear.
CHAPTER XVIII.
CHEMISTRY.
In the first attempts to teach chemistry to children, objects should
be selected, the principal properties of which may be easily
discriminated by the senses of touch, taste or smell; and such terms
should be employed as do not require accurate definition.
When a child has been caught in a shower of snow, he goes to the fire
to warm and dry himself. After he has been before the fire for some
time, instead of becoming dry, he finds that he is wetter than he was
before: water drops from his hat and clothes, and the snow with which
he was covered disappears. If you ask him what has become of the snow,
and why he has become wetter, he cannot tell you. Give him a tea-cup
of snow, desire him to place it before the fire, he perceives that the
snow melts, that it becomes water. If he puts his finger into the
water, he finds that it is warmer than snow; he then perceives that
the fire which warmed him, warmed likewise the snow, which then
became water; or, in other words, he discovers, that the heat which
came from the fire goes into the snow and melts it: he thus acquires
the idea of the dissolution of snow by heat.
If the cup containing the water, or melted snow, be taken from the
fire, and put out of the window on a frosty day, he perceives, that in
time the water grows colder; that a thin, brittle skin spreads over
it; which grows thicker by degrees, till at length all the water
becomes ice; and if the cup be again put before the fire, the ice
returns to water. Thus he discovers, that by diminishing the heat of
water, it becomes ice; by adding heat to ice, it becomes water.
A child watches the drops of melted sealing-wax as they fall upon
paper. When he sees you stir the wax about, and perceives, that what
was formerly hard, now becomes soft and very hot, he will apply his
former knowledge of the effects of heat upon ice and snow, and he will
tell you that the heat of the candle melts the wax. By these means,
the principle of the solution of bodies by heat, will be imprinted
upon his memory; and you may now enlarge his ideas of solution.
When a lump of sugar is put into a dish of hot tea, a child sees that
it becomes less and less, till at last it disappears. What has become
of the sugar? Your pupil will say that it is melted by the heat of the
tea: but if it be put into cold tea, or cold water, he will find that
it dissolves, though more slowly. You should then show him some fine
sand, some clay, and chalk, thrown into water; and he will perceive
the difference between mechanical mixture and diffusion, or chemical
mixture. Chemical mixture, as that of sugar in water, depends upon the
attraction that subsists between the parts of the solid and fluid
which are combined. Mechanical mixture is only the suspension of the
parts of a solid in a fluid. When fine sand, chalk, or clay, are put
into water, the water continues for some time turbid or muddy; but by
degrees the sand, &c. falls to the bottom, and the water becomes
clear. In the chemical mixture of sugar and water, there is no
muddiness, the fluid is clear and transparent, even whilst it is
stirred, and when it is at rest, there is no sediment, the sugar is
joined with the water; a new, fluid substance, is formed out of the
two simple bodies sugar and water, and though the parts which compose
the mixture are not discernible to the eye, yet they are perceptible
by the taste.
After he has observed the mixture, the child should be asked, whether
he knows any method by which he can separate the sugar from the water.
In the boiling of a kettle of water, he has seen the steam which
issues from the mouth of the vessel; he knows that the steam is formed
by the heat from the fire, which joining with the water drives its
parts further asunder, and makes it take another form, that of vapour
or steam. He may apply this knowledge to the separation of the sugar
and water; he may turn the water into steam, and the sugar will be
left in the vessel in a solid form. If, instead of evaporating the
water, the boy had added a greater quantity of sugar to the mixture,
he would have seen, that after a certain time, the water would have
dissolved no more of the sugar; the superfluous sugar would fall to
the bottom of the vessel as the sand had done: the pupil should then
be told that the liquid is _saturated_ with the solid.
By these simple experiments, a child may acquire a general knowledge
of solution, evaporation, and saturation, without the formality of a
lecture, or the apparatus of a chemist. In all your attempts to
instruct him in chemistry, the greatest care should be taken that he
should completely understand one experiment, before you proceed to
another. The common metaphorical expression, that the mind should have
time to digest the food which it receives, is founded upon fact and
observation.
Our pupil should see the solution of a variety of substances in
fluids, as salt in water; marble, chalk, or alkalies, in acids; and
camphire in spirits of wine: this last experiment he may try by
himself, as it is not dangerous. Certainly many experiments are
dangerous, and therefore unfit for children; but others may be
selected, which they may safely try without any assistance; and the
dangerous experiments may, when they are necessary, be shown to them
by some careful person. Their first experiments should be such as they
can readily execute, and of which the result may probably be
successful: this success will please and interest the pupils, and will
encourage them to perseverance.
A child may have some spirit of wine and some camphire given to him;
the camphire will dissolve in the spirit of wine, till the spirit is
saturated; but then he will be at a loss how to separate them again.
To separate them, he must pour into the mixture a considerable
quantity of water; he will immediately see the liquor, which was
transparent, become muddy and white: this is owing to the separation
of the camphire from the spirit; the camphire falls to the bottom of
the vessel in the form of a curd. If the child had weighed the
camphire, both before and after its solution, he would have found the
result nearly the same. He should be informed, that this _chemical
operation_ (for technical terms should now be used) is called
_precipitation_: the substance that is separated from the mixture by
the introduction of another body, is cast down, or precipitated from
the mixture. In this instance, the spirit of wine attracted the
camphire, and therefore dissolved it. When the water was poured in,
the spirit of wine attracted the water more strongly than it did the
camphire; the camphire being let loose, fell to the bottom of the
vessel.
The pupil has now been shown two methods, by which a solid may be
separated from a fluid in which it has been dissolved.
A still should now be produced, and the pupil should be instructed in
the nature of distillation. By experiments he will learn the
difference between the _volatility_ of different bodies; or, in other
words, he will learn that some are made fluid, or are turned into
vapour, by a greater or less degree of heat than others. The degrees
of heat should be shown to him by the thermometer, and the use of the
thermometer, and its nature, should be explained. As the pupil already
knows that most bodies expand by heat, he will readily understand,
that an increase of heat extends the mercury in the bulb of the
thermometer, which, having no other space for its expansion, rises in
the small glass tube; and that the degree of heat to which it is
exposed, is marked by the figures on the scale of the instrument.
The business of distillation, is to separate the more volatile from
the less volatile of two bodies. The whole mixture is put into a
vessel, under which there is fire: the most volatile liquor begins
first to turn into vapour, and rises into a higher vessel, which,
being kept cold by water or snow, condenses the evaporated fluid;
after it has been condensed, it drops into another vessel. In the
experiment that the child has just tried, after having separated the
camphire from the spirit of wine by precipitation, he may separate the
spirit from the water by distillation. When the substance that rises,
or that is separated from other bodies by heat, is a solid, or when
what is collected after the operation, is solid, the process is not
called distillation, but sublimation.
Our pupil may next be made acquainted with the general qualities of
acids and alkalies. For instructing him in this part of chemistry,
definition should as much as possible be avoided; example, and occular
demonstration, should be pursued. Who would begin to explain by words
the difference between an acid and an alkali, when these can be shown
by experiments upon the substances themselves? The first great
difference which is perceptible between an acid and an alkali, is
their taste. Let a child have a distinct perception of the difference
of their tastes; let him be able to distinguish them when his eyes
are shut; let him taste the strongest of each so as not to hurt him,
and when he has once acquired distinct notions of the pungent taste of
an alkali, and of the sour taste of an acid, he will never forget the
difference. He must afterwards see the effects of an acid and alkali
on the blue colour of vegetables at _separate times_, and not on the
same day; by these means he will more easily remember the experiments,
and he will not confound their different results. The blue colour of
vegetables is turned red by acids, and green by alkalies. Let your
pupil take a radish, and scrape off the blue part into water; it
should be left for some time, until the water becomes of a blue
colour: let him pour some of this liquor into two glasses; add vinegar
or lemon juice to one of them, and the liquor will become red;
dissolve some alkali in water, and pour this into the other glass, and
the dissolved radish will become green. If into the red mixture alkali
be poured, the colour will change into green; and if into the liquor
which was made green, acid be poured, the colour will change to red:
thus alternately you may pour acid or alkali, and produce a red or
green colour successively. Paper stained with the blue colour of
vegetables, is called _test_ paper; this is changed by the least
powerful of the acids or alkalies, and will, therefore, be peculiarly
useful in the first experiments of our young pupils. A child should
for safety use the weakest acids in his first trials, but he should be
shown that the effects are similar, whatever acids we employ; only the
colour will be darker when we make use of the strong, than when we use
the weak acids. By degrees the pupil should be accustomed to employ
the strong acids; such as the vitriolic, the nitric, and the muriatic,
which three are called fossil acids, to distinguish them from the
vegetable, or weaker acids. We may be permitted to advise the young
chemist to acquire the habit of wiping the neck of the vessel out of
which he pours any strong acid, as the drops of the liquor will not
then burn his hand when he takes hold of the bottle; nor will they
injure the table upon which he is at work. This custom, trivial as it
may seem, is of advantage, as it gives an appearance of order, and of
ease, and steadiness, which are all necessary in trying chemical
experiments. The little pupil may be told, that the custom which we
have just mentioned, is the constant practice of the great chemist,
Dr. Black.
We should take care how we first use the term _salt_ in speaking to
children, lest they should acquire indistinct ideas: he should be
told, that the kind of salt which he eats is not the only salt in the
world; he may be put in mind of the kind of salts which he has,
perhaps, smelt in smelling-bottles; and he should be further told,
that there are a number of earthy, alkaline, and metallic salts, with
which he will in time become acquainted.
When an acid is put upon an alkali, or upon limestone, chalk, or
marle, a bubbling may be observed, and a noise is heard; a child
should be told, that this is called _effervescence_. After some time
the effervescence ceases, and the limestone, &c. is dissolved in the
acid. This effervescence, the child should be informed, arises from
the escape of a considerable quantity of a particular sort of air,
called fixed air, or carbonic acid gas. In the solution of the lime in
the acid, the lime and acid have an attraction for one another; but as
the present mixture has no attraction for the gas, it escapes, and in
rising, forms the bubbling or effervescence. This may be proved to a
child, by showing him, that if an acid is poured upon caustic lime
(lime which has had this gas taken from it by fire) there will be no
effervescence.
There are various other chemical experiments with which children may
amuse themselves; they may be employed in analyzing marle, or clays;
they may be provided with materials for making ink or soap. It should
be pointed out to them, that the common domestic and culinary
operations of making butter and cheese, baking, brewing, &c. are all
chemical processes. We hope the reader will not imagine, that we have
in this slight sketch pretended to point out the _best_ experiments
which can be devised for children; we have only offered a few of the
simplest which occurred to us, that parents may not, at the conclusion
of this chapter, exclaim, "What is to be done? How are we to _begin_?
What experiments are suited to children? If we knew, our children
should try them."
It is of little consequence what particular experiment is selected for
the first; we only wish to show, that the minds of children may be
turned to this subject; and that, by accustoming them to observation,
we give them not only the power of learning what has been already
discovered, but of adding, as they grow older, something to the
general stock of human knowledge.
CHAPTER XIX.
ON PUBLIC AND PRIVATE EDUCATION.
The anxious parent, after what has been said concerning tasks and
classical literature, will inquire whether the whole plan of education
recommended in the following pages, is intended to relate to public or
to private education. It is intended to relate to both. It is not
usual to send children to school before they are eight or nine years
old: our first object is to show how education may be conducted to
that age in such a manner, that children may be well prepared for the
acquisition of all the knowledge usually taught at schools, and may be
perfectly free from many of the faults that pupils sometimes have
acquired before they are sent to any public seminary. It is obvious,
that public preceptors would be saved much useless labour and anxiety,
were parents to take some pains in the previous instruction of their
children; and more especially, if they were to prevent them from
learning a taste for total idleness, or habits of obstinacy and of
falsehood, which can scarcely be conquered by the utmost care and
vigilance. We can assure parents, from experience, that if they pursue
steadily a proper plan with regard to the understanding and the moral
habits, they will not have much trouble with the education of their
children after the age we have mentioned, as long as they continue to
instruct them at home; and if they send them to public schools, their
superiority in intellect and in conduct will quickly appear. Though we
have been principally attentive to all the circumstances which can be
essential to the management of young people during the first nine or
ten years of their lives, we have by no means confined our
observations to this period alone; but we have endeavoured to lay
before parents a general view of the human mind (as far as it relates
to our subject) of proper methods of teaching, and of the objects of
rational instruction--so that they may extend the principles which we
have laid down, through all the succeeding periods of education, and
may apply them as it may best suit their peculiar situations, or their
peculiar wishes. We are fully conscious, that we have executed but
very imperfectly even our own design; that experimental education is
yet but in its infancy, and that boundless space for improvement
remains; but we flatter ourselves, that attentive parents and
preceptors will consider with candour the practical assistance which
is offered to them, especially as we have endeavoured to express our
opinions without dogmatical presumption, and without the illiberal
exclusion of any existing institutions or prevailing systems. People
who, even with the best intentions, attack with violence any of these,
and who do not consider what is practicable, as well as what ought to
be done, are not likely to persuade, or to convince mankind to
increase the general sum of happiness, or their own portion of
felicity. Those who really desire to be of service to society, should
point out decidedly, but with temperate indulgence for the feelings
and opinions of others, whatever appears to them absurd or
reprehensible in any prevailing customs: having done this, they will
rest in the persuasion that what is most reasonable, will ultimately
prevail.
Mankind, at least the prudent and rational part of mankind, have an
aversion to pull down, till they have a moral certainty that they can
build up a better edifice than that which has been destroyed. Would
you, says an eminent writer, convince me, that the house I live in is
a bad one, and would you persuade me to quit it; build a better in my
neighbourhood; I shall be very ready to go into it, and shall return
you my very sincere thanks. Till another house be ready, a wise man
will stay in his old one, however inconvenient its arrangement,
however seducing the plans of the enthusiastic projector. We do not
set up for projectors, or reformers: we wish to keep steadily in view
the actual state of things, as well as our own hopes of progressive
improvement; and to seize and combine all that can be immediately
serviceable: all that can assist, without precipitating improvements.
Every well informed parent, and every liberal school-master, must be
sensible, that there are many circumstances in the management of
public education which might be condemned with reason; that too much
time is sacrificed to the study of the learned languages; that too
little attention is paid to the general improvement of the
understanding and formation of the moral character; that a
school-master cannot pay attention to the temper or habits of each of
his numerous scholars; and that parents, during that portion of the
year which their children spend with them, are not sufficiently
solicitous to co-operate with the views of the school-master; so that
the public is counteracted by the private education. These, and many
other things, we have heard objected to schools; but what are we to
put in the place of schools? How are vast numbers who are occupied
themselves in public or professional pursuits, how are men in business
or in trade, artists or manufacturers, to educate their families, when
they have not time to attend to them; when they may not think
themselves perfectly prepared to undertake the classical instruction
and entire education of several boys; and when, perhaps, they may not
be in circumstances to engage the assistance of such a preceptor as
they could approve? It is obvious, that if in such situations parents
were to attempt to educate their children at home, they would harass
themselves, and probably spoil their pupils irrecoverably. It would,
therefore, be in every respect impolitic and cruel to disgust those
with public schools, who have no other resource for the education of
their families. There is another reason which has perhaps operated
upon many in the middle ranks of life unperceived, and which
determines them in favour of public education. Persons of narrow
fortune, or persons who have acquired wealth in business, are often
desirous of breeding up their sons to the liberal professions: and
they are conscious that the company, the language, and the style of
life, which their children would be accustomed to at home, are beneath
what would be suited to their future professions. Public schools
efface this rusticity, and correct the faults of provincial dialect:
in this point of view they are highly advantageous. We strongly
recommend it to such parents to send their children to large public
schools, to Rugby, Eton, or Westminster; not to any small school; much
less to one in their own neighbourhood. Small schools are apt to be
filled with persons of nearly the same stations, and out of the same
neighbourhood: from this circumstance, they contribute to perpetuate
uncouth antiquated idioms, and many of those obscure prejudices which
cloud the intellect in the future business of life.
Whilst we admit the necessity which compels the largest portion of
society to prefer public seminaries of education, it is incumbent upon
us to caution parents from expecting that the moral character, the
understandings, or the tempers of their children, should be improved
at large schools; there the learned languages, we acknowledge, are
successfully taught. Many satisfy themselves with the assertion, that
public education is the least troublesome, that a boy once sent to
school is settled for several years of life, and will require only
short returns of parental care twice a year at the holydays. It is
hardly to be supposed, that those who think in this manner, should
have paid any anxious, or at least any judicious attention to the
education of their children, previously to sending them to school. It
is not likely that they should be very solicitous about the
commencement of an education which they never meant to finish: they
would think, that what could be done during the first few years of
life, is of little consequence; that children from four to seven years
old are too young to be taught; and that a school would speedily
supply all deficiencies, and correct all those faults which begin at
that age to be troublesome at home. Thus to a public school, as to a
general infirmary for mental disease, all desperate subjects are sent,
as the last resource. They take with them the contagion of their
vices, which quickly runs through the whole tribe of their companions,
especially amongst those who happen to be nearly of their own age,
whose sympathy peculiarly exposes them to the danger of infection. We
are often told, that as young people have the strongest sympathy with
each other, they will learn most effectually from each other's
example. They do learn quickly from example, and this is one of the
dangers of a public school: a danger which is not necessary, but
incidental; a danger against which no school-master can possibly
guard, but which parents can, by the previous education of the pupils,
prevent. Boys are led, driven, or carried to school; and in a
school-room they first meet with those who are to be their fellow
prisoners. They do not come with fresh unprejudiced minds to commence
their course of social education; they bring with them all the ideas
and habits which they have already learned at their respective homes.
It is highly unreasonable to expect, that all these habits should be
reformed by a public preceptor. If he had patience, how could he have
time for such an undertaking? Those who have never attempted to break
a pupil of any one bad habit, have no idea of the degree of patience
requisite to success. We once heard an officer of dragoons assert,
that he would rather break twenty horses of their bad habits, than one
man of his. The proportionate difficulty of teaching boys, may be
easily calculated.
It is sometimes asserted, that the novelty of a school life, the
change of situation, alters the habits, and forms in boys a new
character. Habits of eight or nine years standing, cannot be
instantaneously, perhaps can never be radically, destroyed; they will
mix themselves imperceptibly with the new ideas which are planted in
their minds, and though these may strike the eye by the rapidity of
their growth, the others, which have taken a strong root, will not
easily be dispossessed of the soil. In this new character, as it is
called, there will, to a discerning eye, appear a strong mixture of
the old disposition. The boy, who at home lived with his father's
servants, and was never taught to have any species of literature, will
not acquire a taste for it at school, merely by being compelled to
learn his lessons; the boy, who at home was suffered to be the little
tyrant of a family, will, it is true, be forced to submit to superior
strength or superior numbers at school;[29] but does it improve the
temper to practise alternately the habits of a tyrant and a slave? The
lesson which experience usually teaches to the temper of a school-boy,
is, that strength, and power, and cunning, will inevitably govern in
society: as to reason, it is out of the question, it would be hissed
or laughed out of the company. With respect to social virtues, they
are commonly amongst school-boys so much mixed with party spirit, that
they mislead even the best dispositions. A boy at home, whose
pleasures are all immediately connected with the idea of self, will
not feel a sudden enlargement of mind from entering a public school.
He will, probably, preserve his selfish character in his new society;
or, even suppose he catches that of his companions, the progress is
not great in moral education from selfishness to spirit of party: the
one is a despicable, the other a dangerous, principle of action. It
has been observed, that what we are when we are twenty, depends on
what we were when we were ten years old. What a young man is at
college, depends upon what he was at school; and what he is at school,
depends upon what he was before he went to school. In his father's
house, the first important lessons, those which decide his future
abilities and character, must be learned. We have repeated this idea,
and placed it in different points of view, in hopes that it will catch
and fix the attention. Suppose that parents educated their children
well for the first eight or nine years of their lives, and then sent
them all to public seminaries, what a difference this must immediately
make in public education: the boys would be disposed to improve
themselves with all the ardour which the most sanguine preceptor would
desire; their tutors would find that there was nothing to be
_unlearned_; no habits of idleness to conquer; no perverse stupidity
would provoke them; no capricious contempt of application would appear
in pupils of the quickest abilities. The moral education could then be
made a part of the preceptor's care, with some hopes of success; the
pupils would all have learned the first necessary moral principles and
habits; they would, consequently, be all fit companions for each
other; in each other's society they would continue to be governed by
the same ideas of right and wrong by which they had been governed all
their lives; they would not have any new character to learn; they
would improve, by mixing with numbers, in the social virtues, without
learning party spirit; and though they would love their companions,
they would not, therefore, combine together to treat their instructers
as pedagogues and tyrants. This may be thought an Utopian idea of a
school; indeed it is very improbable, that out of the numbers of
parents who send their children to large schools, many should suddenly
be much moved, by any thing that we can say, to persuade them to take
serious trouble in their previous instruction. But much may be
effected by gradual attempts. Ten well educated boys, sent to a public
seminary at nine or ten years old, would, probably, far surpass their
competitors in every respect; they would inspire others with so much
emulation, would do their parents and preceptors so much credit, that
numbers would eagerly inquire into the causes of their superiority;
and these boys would, perhaps, do more good by their example, than by
their actual acquirements. We do not mean to promise, that a boy
judiciously educated, shall appear at ten years old a prodigy of
learning; far from it: we should not even estimate his capacity, or
the chain of his future progress, by the quantity of knowledge stored
in his memory, by the number of Latin lines he had got by rote, by his
expertness in repeating the rules of his grammar, by his pointing out
a number of places readily in a map, or even by his knowing the
latitude and longitude of all the capital cities in Europe; these are
all useful articles of knowledge: but they are not the test of a good
education. We should rather, if we were to examine a boy of ten years
old, for the credit of his parents, produce proofs of his being able
to reason accurately, of his quickness in invention, of his habits of
industry and application, of his having learned to generalize his
ideas, and to apply his observations and his principles: if we found
that he had learned all, or any of these things, we should be in
little pain about grammar, or geography, or even Latin; we should be
tolerably certain that he would not long remain deficient in any of
these; we should know that he would overtake and surpass a competitor
who had only been technically taught, as certainly as that the giant
would overtake the panting dwarf, who might have many miles the start
of him in the race. We do not mean to say, that a boy should not be
taught the principles of grammar, and some knowledge of geography, at
the same time that his understanding is cultivated in the most
enlarged manner: these objects are not incompatible, and we
particularly recommend it to _parents who intend to send their
children to school_, early to give them confidence in themselves, by
securing the rudiments of literary education; otherwise their pupils,
with a real superiority of understanding, may feel depressed, and may,
perhaps, be despised, when they mix at a public school with numbers
who will estimate their abilities merely by their proficiency in
particular studies.
Mr. Frend,[30] in recommending the study of arithmetic for young
people, has very sensibly remarked, that boys bred up in public
schools, are apt to compare themselves with each other merely as
classical scholars; and, when they afterwards go into the world
excellent Greek and Latin scholars, are much astonished to perceive,
that many of the companions whom they had under-valued at school, get
before them when they come to actual business, and to active life.
Many, in the pursuit of their classical studies, have neglected all
other knowledge, especially that of arithmetic, that useful, essential
branch of knowledge, without which neither the abstract sciences nor
practical arts can be taught. The precision which the habit of
applying the common rules of arithmetic, gives to the understanding,
is highly advantageous, particularly to young people of vivacity, or,
as others would say, of genius. The influence which the habit of
estimating has upon that part of the moral character called prudence,
is of material consequence. We shall further explain upon this subject
when we speak of the means of teaching arithmetic and reasoning to
children; we only mention the general ideas here, to induce
intelligent parents to attend early to these particulars. If they mean
to send their children to public classical schools, it must be
peculiarly advantageous to teach them early the rudiments of
arithmetic, and to give them the habit of applying their knowledge in
the common business of life. We forbear to enumerate other useful
things, which might easily be taught to young people before they leave
home, because we do not wish to terrify with the apprehension, that a
perplexing variety of things are to be taught. One thing well taught,
is better than a hundred taught imperfectly.
The effect of the pains which are taken in the first nine or ten years
of a child's life, may not be apparent immediately to the view, but it
will gradually become visible. To careless observers, two boys of nine
years old, who have been very differently educated, may appear nearly
alike in abilities, in temper, and in the promise of future character.
Send them both to a large public school, let them be placed in the
same new situation, and exposed to the same trials, the difference
will then appear: the difference in a few years will be such as to
strike every eye, and people will wonder what can have produced in so
short a time such an amazing change. In the Hindoo art of dyeing, the
same liquors communicate different colours to particular spots,
according to the several bases previously applied: to the ignorant
eye, no difference is discernible in the ground, nor can the design be
distinctly traced till the air, and light, and open exposure, bring
out the bright and permanent colours to the wondering eye of the
spectator.
Besides bestowing some attention upon early education, parents, who
send their children to school, may much assist the public preceptor
by judicious conduct towards children during that portion of the year
which is usually spent at home.[31] Mistaken parental fondness,
delights to make the period of time which children spend at home, as
striking a contrast as possible with that which they pass at school.
The holydays are made a jubilee, or rather resemble the Saturnalia.
Even if parents do not wish to represent a school-master as a tyrant,
they are by no means displeased to observe, that he is not the friend
or favourite of their children. They put themselves in mean
competition with him for their affection, instead of co-operating with
him in all his views for their advantage. How is it possible, that any
master can long retain the wish or the hope of succeeding in any plan
of education, if he perceives that his pupils are but partially under
his government; if his influence over their minds be counteracted from
time to time by the superior influence of their parents? An influence
which he must not wish to destroy. To him is left the power to punish,
it is true; but parents reserve to themselves the privilege to reward.
The ancients did not suppose, that even Jupiter could govern the world
without the command of pain and pleasure. Upon the vases near his
throne, depended his influence over mankind.
And what are these holyday delights? And in what consists parental
rewards? In dissipation and idleness. With these are consequently
associated the idea of happiness and the name of pleasure; the name is
often sufficient, without the reality. During the vacation, children
have a glimpse of what is called _the world_; and then are sent back
to their prison with heads full of visions of liberty, and with a
second-sight of the blessed lives which they are to lead when they
have left school for ever. What man of sense, who has studied the
human mind, who knows that the success of any plan of education must
depend upon the concurrence of every person, and every circumstance,
for years together, to the same point, would undertake any thing more
than the partial instruction of pupils, whose leading associations and
habits must be perpetually broken? When the work of school is undone
during the holydays, what hand could have the patience perpetually to
repair the web?
During the vacations spent at home, children may be made extremely
happy in the society and in the affections of their friends, but they
need not be taught, that idleness is pleasure: on the contrary,
occupation should, by all possible methods, be rendered agreeable to
them; their school acquisitions, their knowledge and taste, should be
drawn out in conversation, and they should be made to feel the value
of what they have been taught; by these means, there would be some
connection, some unity of design, preserved in their education. Their
school-masters and tutors should never become the theme of insipid
ridicule; nor should parents ever put their influence in competition
with that of a preceptor: on the contrary, his pupils should uniformly
perceive, that from his authority there is no appeal, except to the
superior power of reason, which should be the avowed arbiter to which
all should be submitted.
Some of the dangerous effects of that mixed society at schools, of
which we have complained, may be counteracted by the judicious conduct
of parents during the time which children spend at home. A better view
of society, more enlarged ideas of friendship and of justice, may be
given to young people, and the vile principle of party spirit may be
treated with just contempt and ridicule. Some standard, some rules may
be taught to them, by which they may judge of character independently
of prejudice, or childish prepossession.
"I do not like you, Doctor Fell;
The reason why, I cannot tell:
But this I know full well,
I do not like you, Doctor Fell"--
is an exact specimen of the usual mode of reasoning, of the usual
method in which an ill educated school-boy expresses his opinion and
feelings about all persons, and all things. "The reason why," should
always be inquired whenever children express preference or aversion.
To connect the idea of childhood with that of inferiority and
contempt, is unjust and impolitic; it should not be made a reproach to
young people to be young, nor should it be pointed out to them, that
when they are some years older, they will be more respected; the
degree of respect which they really command, whether in youth or age,
will depend upon their own conduct, their knowledge, and their powers
of being useful and agreeable to others. If they are convinced of
this, children will not at eight years old long to be fifteen, or at
fifteen to be one and twenty; proper subordination would be preserved,
and the scale of happiness would not have a forced and false
connection with that of age. If parents did not first excite foolish
wishes in the minds of their children, and then imprudently promise
that these wishes shall be gratified at certain periods of their
existence, children would not be impatient to pass over the years of
childhood; those years which idle boys wish to pass over as quickly as
possible, men without occupation regret as the happiest of their
existence. To a child, who has been promised that he shall put on
manly apparel on his next birthday, the pace of time is slow and heavy
until that happy era arrive. Fix the day when a boy shall leave
school, and he wishes instantly to mount the chariot, and lash the
horses of the sun. Nor when he enters the world, will his restless
spirit be satisfied; the first step gained, he looks anxiously forward
to the height of manly elevation,
"And the brisk minor pants for twenty-one"
These juvenile anticipations diminish the real happiness of life;
those who are in continual expectation, never enjoy the present; the
habit of expectation is dangerous to the mind, it suspends all
industry, all voluntary exertion. Young men, who early acquire this
habit, find existence insipid to them without the immediate stimuli of
hope and fear: no matter what the object is, they must have something
to sigh for; a curricle, a cockade, or an opera-dancer.
Much may be done by education to prevent this boyish restlessness.
Parents should refrain from those imprudent promises, and slight
inuendoes, which the youthful imagination always misunderstands and
exaggerates.--Never let the moment in which a young man quits a
seminary of education, be represented as a moment in which all
instruction, labour, and restraints, cease. The idea, that he must
restrain and instruct himself, that he must complete his own
education, should be excited in a young man's mind; nor should he be
suffered to imagine that his education is finished, because he has
attained to some given age.
When a common school-boy bids adieu to that school which he has been
taught to consider as a prison, he exults in his escape from books and
masters, and from all the moral and intellectual discipline, to which
he imagines that it is the peculiar disgrace and misery of childhood
to be condemned. He is impatient to be thought a man, but his ideas of
the manly character are erroneous, consequently his ambition will only
mislead him. From his companions whilst at school, from his father's
acquaintance, and his father's servants, with whom he has been
suffered to consort during the vacations, he has collected imperfect
notions of life, fashion, and society. These do not mix well in his
mind with the examples and precepts of Greek and Roman virtue: a
temporary enthusiasm may have been kindled in his soul by the
eloquence of antiquity; but, for want of sympathy, this enthusiasm
necessarily dies away. His heroes are not the heroes of the present
times; the maxims of his sages are not easily introduced into the
conversation of the day. At the tea-table he now seldom hears even
the name of Plato; and he often blushes for not knowing a line from a
popular English poet, whilst he could repeat a cento from Horace,
Virgil, and Homer; or an antistrophe from Æschylus or Euripides. He
feels ashamed to produce the knowledge he has acquired, because he has
not learned sufficient address to produce it without pedantry. On his
entrance into the world, there remains in his mind no grateful, no
affectionate, no respectful remembrance of those under whose care he
has passed so many years of his life. He has escaped from the
restraints imposed by his school-master, and the connection is
dissolved for ever.
But when a son separates from his father, if he has been well
educated, he wishes to continue his own education: the course of his
ideas is not suddenly broken; what he has been, joins immediately with
what he is to be; his knowledge applies to real life, it is such as he
can use in all companies; there is no sudden metamorphosis in any of
the objects of his ambition; the boy and man are the same individual.
Pleasure will not influence him merely by her name, or by the contrast
of her appearance with the rigid discipline of scholastic learning; he
will feel the difference between pleasure and happiness, and his early
taste for domestic life will remain or return upon his mind. His old
precepts and new motives are not at war with each other; his
experience will confirm his education, and external circumstances will
call forth his latent virtues. When he looks back, he can trace the
gradual growth of his knowledge; when he looks forward, it is with the
delightful hope of progressive improvement. A desire in some degree to
repay the care, to deserve the esteem, to fulfil the animating
prophecies, or to justify the fond hopes of the parent who has watched
over his education, is one of the strongest motives to an ingenuous
young man; it is an incentive to exertion in every honourable pursuit.
A son who has been judiciously and kindly educated, will feel the
value of his father's friendship. The perception, that no man can be
more entirely interested in every thing that concerns him, the idea,
that no one more than his father can share in his glory or in his
disgrace, will press upon his heart, will rest upon his understanding.
Upon these ideas, upon this common family interest, the real strength
of the connection between a father and his son depends. No public
preceptor can have the same advantages; his connection with his pupil
is not necessarily formed to last.
After having spoken with freedom, but we hope with moderation, of
public schools, we may, perhaps, be asked our opinion of universities.
Are universities the most splendid repositories
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