UNIVERSITY OF CALIFORNIA
AT LOS ANGELES
A NAERATIVE -ESSAY
yikral ^trmatiott,
CHIEFLY EMBODIED IN
THE ACCOUNT OF AN ATTEMPT TO GIVE A LIBERAL
EDUCATION
CHILDKEN OF THE WORKING CLASSES.
BY THE
REV. S. HAWTEEY, A.M.,
ASSISTANT-MASTEE, ETON.
LONDON" :
HAMILTON, ADAMS, AND 0.
32, PATERNOSTER ROW.
1868.
5 2 4 2 8
LONnoN:
UABT S. SIOKEBBT, PBINTBB, 4a, WALBBOQK,
UANSION HOUSE. B. 0.
O
IGiV
A NAREATIVE-ESSAY
ITikral ^trntniim.
S2 Many are speaking and writing aboiit Education,
'^ — some with authority. The Education of every
% class of the community, and its bearing on the
^ national character and the future prosperity of
England, is under discussion.
First, how to promote and extend the Educa-
tion of the lower classes, and make it tell on
°° the arts and manufactures of the country.
^ Secondly, how to supply to the middle class a
CO .
^ better Education than has hitherto been within
^ their reach, and what is the character of the
Education that shall be most serviceable to them.
Thirdly, what changes and developments shall
be made in the system of Education given to the
wealthier classes of the country.
These subjects are all now under discussion,
^ and the essays and speeches bearing upon them
5 are read and thought over by those who are
^ interested in the progress and well-being of their
country.
a2
As a coiitril)utioii towards the discussion of the
foregoing questions, I give, in the following pages,
not a theory as to what ought to he done, but a
narrative of what has been done, — a narrative
— somewhat detailed — of an attempt to give a
liberal Education to boys of the working class.
The School to which I allude is not unknown
by name to friends among whom have been circu-
lated, from time to time, narratives printed with
a view of elucidating the moral system there
pursued.
This School, taking its rise from a very small
beginning twenty-one years ago, has been devel-
oping to the present time, and has been, and still
is, a source of veiy great hope, interest, and
happiness to those connected with it.
This mode of approaching a subject, w^hich may
be called the " topic of the day," will, I trust,
commend itself to many minds. A valued col-
league of the writer's (Hany Dupuis), when he
was leaving Eton for a sphere of parochial work,
said to him, " We don't want essays on Educa-
tion — WT have plenty of them. Tell us what you
have done, and how you have done it."
Harry Dupuis is no more ; but others may
share the feeling he expressed, and consider the
narrative, at this juncture, not ill-timed. For
even if it seems that the accidental circumstances
surrounding St. Mark's School are too excej^tional
to allow it to be a model, in every respect, for
schools of the poorest class, I hope it may suggest
some hmts to those engaged at this moment in
the establishment of middle-class schools.
I need not say a word about moral training
here. I have written so fully on this subject in
all the educational tracts and stories above alluded
to, that it would be superfluous to say more.
It is only necessary for me to premise that the
power of sympathy — " the contact of human
living soul with human living soul " — is pre-
supposed in all that may be said about intellectual
culture in the present Narrative-Essay.
The first detail I shall go into is about church.
By all means, where the opportunity allows, take
the boys to a service in church daily. We have
always begun the day by going to church. In
fact, the church is the first place of meeting each
morning for the boys coming from their various
homes. And here we have taken a useful hint
from the custom of public schools. Instead of
the school children being formed two and two,
and put into their seats in church like sheep into
a pen, — that is, instead of the string of boys
being passed into a seat till it is full, upon which
the next seat is opened and filled in like manner,
— each boy at the beginning of the school-time
has his place in church allotted to him.
This is the first instance I have to name of a
principle that pervades the whole of our system, —
the individualiziug each boy, and so creating a
sense of individual responsibility.
In each boy's place hangs a little bag con-
taining his hymn-book, prayer-book, and Testa-
ment, these remaining for his daily use in
church ; and, as the united cost of the three
books only amounts to the sum of sixpence, the
expense of a separate set of books for use in
church is not more than parents of the working
class are willing to afford.
Each boy, then, on coming independently from
his own home, enters church and goes at once
to his own place. We take the precaution in
arranging the places in church to intermingle in
order the elder and the younger boys. A number
of veiy little boys together are apt to be fidgety,
and the trust that is implied in placing a little
boy on either side of an elder boy begets trust-
w^orthiness.
With this precaution, and a few distinct rules
of conduct, such as would suggest themselves to
any watchful parent, the boys are very much left
to themselves ; we trust to the force of public
opinion, general habit, and a prevalent wish to do
right, for good and reverent behaviour. It does
boys much more good to see the Masters trying to
get good to themselves by following the prayers
and lessons, than to be kept in order by a Master's
eye looking about and resting on them, his own
attention being manifestly distracted thereby. It
is better even that instances of misconduct should
occur and not be seen or noticed, than that the
eye of the Master should be on the watch. And
it is obvious, that a decent reverence of manner,
produced by habit and the force of opinion and
good feeling, is far more valuable than the most
punctilious behaviour, the consequence of being
closely watched.
The daily morning service thus conducted is an
incalculable blessing to the School : it has a
gradual, quiet, but most sensible effect on the
whole tone and bearing of the boys. The service
is shortened ; it does not take more than from
fifteen to seventeen minutes. We have only one
lesson, that from the New Testament, and each
boy having his prayer-book, hymn-book, and
Testament, the burst of young fresh voices as they
read the alternate verses with the officiating
Minister, or sing the hymn (for the whole School
learn to sing by note), is animating and helpful to
one's own devotions. So is the stillness during
the reading of the lesson, each boy following it on
the pages of his own Testament.
It is a comfort to think that these boys by ear
and eye, and without the irreverent familiarity en-
gendered by using the Holy Scriptures as a school-
book, are getting day by day additional acquaint-
ance with the Word of God, at least with that
part of it most suitable for the reading of Christian
boys. Three times a year in the course of the
daily morning service do they go through the
Gospels and the Acts of the Apostles.
Now, as I am persuaded that most of what it is
the present fashion to call distressing doubts about
the very fundamentals of Christianity arises from
want of reading reverently and regularly the
Gospels, I prize this method, whereby an acquaint-
ance with the facts, the words, the spirit of the
Gospels is being very quietly and gradually, but
steadily, imparted year by year to our boys.
The reader of the morning lesson is one of
themselves. Good readers with distinct articula-
tion are chosen for the duty. Of course, if the
boys were affected and read with self-conscious-
ness, this would not answer. But in good Eng-
lish schools of a manly character, and where hard
work is done, boys are not affected or self-con-
scious. It is delightful to observe how free they
are from this fault ; I am certain all good School-
masters will heartily agree in this statement.
That being the case, there is a very great charm
in the reading of the Gospel lesson simply and re-
verently by a young boy with a clear fresh voice.
The whole congregation seems to feel it.
To the objection sometimes urged that a service
in church takes so much out of the daily school-
hours, it inay be replied, that it is an admirable
and powerful incentive to good reading for the
boys of a school to hear a chapter, which they are
following with their eyes, well read by one of them-
selves. Especially it is useful to boys in the
lower divisions who do not often come in contact
with those of the upper division, out of which the
readers in church are naturally selected : they see
the result of the rules and the method of teaching
that are applied to themselves, and this makes
them attend to those rules and do their best.
I repeat emphatically what I said many years
ago,* that the reading of the Psalms, by the boys
of a school, verse about with the officiating Cler-
gyman, and their following with their eyes on
their books the lesson which is being read by a
good reader from among themselves, will do more
to teach good reading than the same amount of
time spent in common reading lessons, or at least
it admirably supplements those lessons. But this
is altogether a minor consideration.
It is desirable that the boys should have plenty
of room allowed them. A little expense which
may make them feel that they are thought of, and
that their comfort is attended to, will not be
thrown away. Each of our boys has a separate
kneeling cushion provided for him. The silent
effect of arrangements that make boys feel that
in the house of God boys and Masters are all one
— that, one beside the other, they are praying
to and praising Him who is ^equally and infinitely
above both — is to engender a tone and feeling in
* See "Account of St. Mark's School, 1857," pages 4:2, 43.
10
reference to Divine worship just and true, and of
the highest value to the boys.
When I think of the number of newly -built or
restored churches which there are throughout the
country, many of them close to the school and
parsonage, I cannot but regret that they are not
thus utilized on week-days, and that the Clergy-
man of the parish has not the opportunity of
meeting each morning the boys and girls of his
Parochial School in his church.
In our church the seats on one side of the
centre aisle are appropriated during the week-days
to the boys ; the opposite side is sufficient for the
girls and the other attendants at the daily service.
I now leave this, the most important part of my
whole subject, with one concluding remark : I
have heard the heads of establishments say of
different social arrangements, that such or such
{e. g., the appointments of their dinner-table or
the like) were the key-stone of the discipline and
good order of their house. I say that the daily
quarter of an hour in church is the key-stone of
the moral tone of our School.
On leaving church for school the boys fall into
rank in different divisions under their respective
Masters. For it is a feature of our system, de-
rived immediately from the Public School system,
that each Master has a separate division of the
School, for which he is responsible. It cannot
11
be expected that a Master will work with energy
and hope, if he has not full credit for the success
of his work. The system, therefore, of having a
set of Assistants or Monitors, with a Head Master
exercising a general superintendence over the
whole School, I have long given up as unsatis-
factory.
Each Master is wholly responsible for the tuition
and discipline of his division. Parents look to
him and communicate with him, and the credit
for the good discipline and progress of his division
is wholly his own.
I most strongly recommend that at any school
where there is more than one Master this system
should be adopted. I am happy to say that the
Committee of the Windsor National School, in-
stead of having one Head Master to superintend
a staff of Junior Assistants and paid Monitors,
have appointed two Assistant Masters in addition
to the Head Master, each to be responsible for a
division of the School ; each Master probably to
have two " standards " out of the six under his
tuition and superintendence ; and the school-room
is being divided that each Master may have a
separate compartment for his division.
It may be mentioned here that the last week
of each school-time is devoted to an examination
in the work of the preceding half. As soon as
the examination is finished the boys separate for
the holidays ; and when the result of the exami-
12
nation is made out, the new school-list is printed,
in which the meritorious of each division are
placed in three classes according to merit, followed
by the unclassed, if any — those who have taken
a high class entitling themselves thereby to be
placed in a higher division the following school-
time.
This system is very efficacious in giving tone to
a school. The assurance that industry and pro-
gress will be rewarded by accelerated promotion
gives a healthy stimulus to exertion ; indeed,
what stimulus can be more healthy than the wish
on the part of a boy for an advancement, (which
does not necessitate the keeping back another,)
into a higher division of the School, where he
will do harder lessons and associate with more
advanced boys.
This, of course, is none other than the system
pursued (with perhaps certain varieties of detail)
in most public, and good Grammar Schools. My
reason for naming it here is that it has been found
capable of application in a day-school for children
of tlie working class, and has been of incalculable
benefit to the school.
An observation of our former Inspector, Mr.
Bellairs, is very much in point. It is, indeed, so
very flattering, that I should hesitate to repeat it
here, if it did not give a most valuable testimony in
favour of the system of divisions which I advocate.
He had begun his inspection at the bottom of
13
the School, and worked up, taking division after
division, to the top ; when it was over, he said that
the School reminded him of nothing so much as of
a paper mill, where one sees the rough rags put in
at one end ; and each step of the process refines
and purifies the material, till the clean white paper
comes out at the other end.
The sense of trust and responsibility will make
a good Master out of an imperfect one. To call
upon him to take now this class and now that, at
the bidding of another, without his having either
responsibility or credit, will go far to spoil a good
one.
While we have been talking over these matters,
we will suppose the boys have been walking from
church to school.
When they get to school, what do they find
there ? In the first place, plenty of oxygen. The
Government requires eighty cubic feet of pure air
for each child. We give them four hundred. So
that we never, even at the end of a long day, see
any symptom of the presence of carbonic acid in
the pale face, drawn features, and languid eye.
As they enter, each boy hangs his cap and
over-coat on his own peg ; those who come from
a distance, and do not return to their homes till
the evening, drop their dinner-bags into the large
basket which the matron holds to receive them,
giving her a kindly greeting as they pass on to
their covered playground — (a grand refuge in wet
14
weather). Here a short inspection takes place to
see they are all tidy ; after which they ascend by
the diiferent staircases to their several compart-
ments of the great School.
Here again we seek to educate them to a sense
of individual responsibility by giving each boy a
locker (which, by the way, does not lock ) ; in this
he keeps and takes care of all his books, paper,
pens, and school requisites : this plan we adopt
even with the little boys, that they may early
learn to take care of their own property and to
respect that of their neighbours. Dr. Keate used
to say that a boy's bureau was his castle ; so we say
of the locker. It is poor training to take charge
of a boy's slate, book, pen, &c., to give them out
for the lesson, and then take them back. It may
look very orderly, but it is not good education.
Let the boys be treated as moral agents, not as so
many parts of a great educational mill which is
to be kept in good working order.
Another provision that works well is to have a
large tablet suspended in the compartment occu-
pied by each division, on which there is a weekly
register kept of the industry, conduct, and progress
of each boy ; a box of large printed letters and
figures, with a pot of paste and a brush, and the
help of one or two of his division, enables each
Master weekly to add on to the previous record the
result of the current week ; this register the boys
always have before their eyes. Any person inter-
15
ested in them, such as the Clergyman of the
parish, or the promoters of the School, can, at a
glance, tell how the boys are getting on. Every
week that they continue free from a blemish for
inattention, irregularity, and the like, makes
them all the more anxious to keep free from
blemish the next week. And, as they see their
marks for school and home lessons groiv weekly, they
are all the more anxious they should keep on
growing.
It is pleasant, when a half holiday at Eton allows
me to do so, to go to the School and see who
deserves a shake of the hand or a pat on the
back for his sustained good conduct and industry
through the school-time. Weekly reports are
also sent home, and much valued ; and the
periodical meeting of parents, when the final re-
sult of the weekly register and of the examina-
tion at the end of the school-time is given out,
is a most festive and happy day with us.
At the end of the covered playground we have
a row of warm baths, and all boys must either be
washed all over at home at least weekly, or have
a bath at school. Practically, the baths at
school are a real delight and enjoyment to all,
and a great source of health. I am afraid to
say how much the rate of mortality was decreased
at the Hanwell District School by the introduction
of soap and warm water.
But of all the arrangements at St. Mark's,
16
none is more valuable, morally or socially, than
the provisions for the boys' retiring closets. So
valuable are they, that I hope no reader of these
pages who is building a school, or altering school
premises, will omit to come and see, or make
inquiries about what Mr. Street has done for us
in this respect.
We now come to the vexata questio, the chief
subject of discussion in all the daily speeches and
essays one meets with on Education. By what
studies shall we inform boys' minds, and culti-
vate their intellects ? Of course, all agree that
the foundation of Eeading, Writing, and Arith-
metic must be first laid. Of these, I have not
much to say. But, as I wish to be useful, I will
say a few words on each of these heads.
I. Beading. — The rule for attaining the art of
clear, articulate Beading is a very short one —
FINISH YOUR WORDS.
Do not let the last consonant be divided from its
own word and tacked on to the next following, —
for instance, do not let the words " dwelt in " be
read as though they were written " dwel tin."
Expression, force, and propriety in Beading must
be gained by a general quickening of the faculties.
— (See Appendix A.)
II. For Writing, a short, good rule, which we
17
owe to Mr Harris, the old Writing Master at Eton,
is, 23oint the knuckle of your fore-finger to the
ceiling. A pleasant occasional exercise is to ba-
lance a halfpenny on the knuckle of the fore-finger ;
if it does not slip off till the end of the copy,
let it then slip into the writer's pocket. — (See
Appendix B.)
III. Arithmetic. — Prolonged experience teaches
me that explanation of principles in teaching
Arithmetic may he easily overdone. I have erred
myself in overdoing explanation again and again.
G-ive out the rule ; let them write it out, learn it,
and do a number of examples by it. An occa-
sional pithy and pointed explanation of a principle
is all very good, especially when accompanied by
some practical illustration.
For instance, — a square of ginger-bread or a
plate of apples is admirably useful to illustrate
the definitions and fundamental rules of vulgar
fractions, especially if the " parts into which the
unit is divided" are at the close of the lesson
shared amongst the members of the class; but
lengthened explanations children cannot follow. —
(See Appendix C.)
Any account of the Education given at St.
Mark's School would be very incomplete without
a reference to Music. I will here, then, intro-
duce parenthetically what I have to say. Singing
by note is taught as part of the school business to
18
every boy. All that I said in the *' Account of
St. Mark's School," pubhshcd m 1856, I endorse
now.
As to the intellectual, moral, and social benefit
of the study, I am fortunate in being able to leave
to others less prejudiced than myself to say if
they think that the experiment has been a success.
The CoUege of Eton, in instituting a choir
of their own for their chapel services, have done
me the honour to take their choristers from St.
Mark's, and have endowed the School with twelve
choral scholarships. Simultaneously with this
step, they have appointed as their organist, and
as the head of the music at Eton, the Rev. G. L.
Hayne, Mus. D., Oxon., himself an old Etonian.
Now, Dr. Ha}Tie is in daily intercourse with
these choristers, and he can therefore, better
than any one else, measure them musically,
mentally, and morally. To him with confidence
I leave it to say if he thinks that the result of our
having made music at St. Mark's a study, not a
pastime, is good.
To resume : — The foundation of reading, writ-
ing, and arithmetic being well laid, what next ?
Is it to be History ? Geography ? the knowledge
of common things ? an insight into the interesting
discoveries of our age ? My experience tells me,
No. These are not mental cultivators. These are
not what dig, plough, harrow the brain. These
are rather of the nature of seeds which, when
19
thrown into ground previously prepared, take root,
grow, and bear fruit. Then what is the mental
cultivator that is to prepare the ground ? Lan-
guage, I should say undoubtedly. Is it to be
English or Latin ? I answer, both.
Our Schoolmasters having been trained at St.
Mark's and Culham Training Colleges, there is
naturally far more attention paid to the study of
English with us than at regular classical schools.
English words are analysed, their formation and
meaning traced, synonymous words are examined
and distinguished, metaphorical sentences are put
into common language : the analysis of sentences
also is a favourite exercise, and the boys seem to
get a very intelligent knowledge of the structure
of language thereby.
Eeading lessons, as in schools for their class and
age, form a prominent item in the work of each
day, and through their reading lessons they get
an extensive acquaintance with good English au-
thors ; for not only are School Beading Books now
very good, and improving every year, but AUman,
(by his circulating library for schools,) and other
enterprising publishers, enable us to put standard
authors into our boys' hands, such as " The Tales
of a Grandfather," "Bobinson Crusoe," "The Fool
of Quality," (that grand old book full of generosity
and chivalry, without a shadow of modern flip-
pancy,) Shakespear, of course, and Sir Walter
B 2
20
Scott's Poems and Novels,* the sentiment and
romance of which form a good antidote to the
slang and flippancy in which much of the modern
writing which comes within the reach of school-
boys is steeped.
Speaking of these matters, I cannot omit to
record the great benefit which Mr. Warbnrton
conferred upon the School when he was our In-
spector. He not only told us that we should find
the learning — with perfect accuracy — good and
choice pieces of English to be spoken with great
care, good articulation, and proper emphasis, a
valuable educational exercise — but he further
found time, amidst his avocations as Queen's
Inspector, to gather for us and copy with his own
hand a long manuscript of most choice pieces
of English,— " The Battle of the Nile," "The
Mining Adventure in Peru," " Physical Geogra-
phy," " St. Peter's Chapel in the Tower," " Ma-
terial Progress," "The Earl of Warwick," &c., culled
from such writers as Macaulay, Dr. Arnold, S. T.
* It may not be amiss to remind my readers that Sir
Walter Scott's Novels may be liad for sixpence each complete
work ; of course, they are in paper covers ; but if before the
book is given out as a reading book a few holes are stabbed in
it with a bookbinder's awl, as near the back as possible, (for
there is very little margin,) and a bit of strong carpet-thread or
wax-end be drawn in and out through the holes tightly, the book
will never fall to pieces, and will last, as a reading book, as
long as if it were bound.
21
Coleridge, Soutliey, and his own poor brother, will
fix him for a long time in our memories.
We found his words most true. His pieces of
English, in style most beautiful, and breathing
manly and heroic sentiments, have been a precious
possession to the School. I can testify that this
most kind act of his has done the School the
greatest good both intellectual and moral ; and I
would venture to suggest that if he would add
other pieces to those which he has selected for
us, and were to publish them in a book, he would
be conferring a benefit on other schools which is
now confined to ourselves.
I trust all this will satisfy Professor Seeley that
English is not overlooked, but neither am I dis-
posed to forego Latin. At least, we have begun it
with our lads at St. Mark's School, three years
earlier than the age which he names (fourteen)
for beginning Latin ; and, I cannot help seeing,
with the best result.
Shall I be called a " Philistine " if I urge that
Latin is a fine thing for " evening lessons ? "
There is something very definite in committing to
memory a page of accidence, and in a Latin
exercise or translation, VN^hich has to be done,
written out fair, examined, have its faults marked
and corrected. I have never been able to make
English such a good old-fashioned lesson as this —
boys cannot always be learning choice bits of
poetry, and to be told to look over so many pages
22
of s}Tionymes, or of history, geography, &c., is not
detiiiitc Hkc a Latin exorcise.
But, besides this, I am persuaded that the in-
flections of Latin give quite a new view of the
reahty of concords. And, as an instrument for
cultivating the mental faculties, what can be
better than an exercise that requires a simul-
taneous effort to get number, gender, case, tense,
mood, person, all right together. To an educated
person all this seems to come intuitively, but it
should not be forgotten that to get each of them
right requires a separate mental effort when a boy
is constructing a Latin sentence.
The boys like their Latin lesson ; they are
interested and animated by it ; a little know-
ledge of Latin they find a great help in pulling
English words to pieces ; and they analyse the
structure of sentences in the English fashion all
the better from parsing their Latin lesson.
With regard to grammar. "Whether they first
read the progressive sentences in their elementary
Latin-books and build up for themselves (under
the teacher's guidance) laws, rules of construction,
or take the law at the hands of those who have
travelled over the ground before them, and trace
its action in the structure of the sentences framed
for them, and subsequently in those authors
whose writings they may read, is a question which
I do not think worth fighting about.
What is wanted is that their knowledge of
23
language slionld be systematic, drawn up in
orderly array, under well-defined rules wliicli they
can apply. And it is not less valuable surely,
as an intellectual exercise, than the arrangement of
stones, or flowers, or insects, in classified order.
It is but a little way that we go in Latin, but
every step seems to be valuable, per se. Of course,
we do not touch verses, that is beyond us. But
finding, as we do in familiar intercourse with these
boys, that ready discernment, quickness of ap-
prehension and thought, the power of taking in
and estimating what is said, of reading a glance
of the eye, seeing the point of a joke, or detecting
covert irony : — in a word, a general mental acumen
is developed by their study of language, I feel
disposed to say, if Latin, so far as we go at St.
Mark's, gives this mental activity, why should not
the good effect of the exercise go on if the boys
were able to advance yet further ? What if in
addition to getting mood, tense, person, number,
gender, case of a sentence, all right, they were still
further required to bring out the sentence subject
to metrical rules and the rhythm and poiiit of
verse ?
Are we quite sure that the Remove and Fourth-
form boy is not deriving intellectual profit from
that "worry and torture of brain" which makes
him knit his brow, bite his pen, and turn from
Gradus to Dictionary and back again from
Dictionary to Gradus ? Especially as it is an
24
exercise that is enlivened, I contend, from time
to time, with pleasurable emotion. Who cannot
call to mind his looking back on a couplet which
he hoped was rather good, and the thought
arising, " I wonder what my tutor will say to that
verse ? "
How long this work should continue, at what
time, if a boy does not become a good composer,
verse -making should be given up, I do not pretend
to say. But this I do say, before we give up
verses as mental cultivation and training, let us
see that we have something to put in their place
that will do intellectually the same or more
good.
Mr. Farrar, I suppose, will answer with an un-
hesitating voice, " Science will do it." And very
beautiful is the posy of scientific flowerets which he
gathered from the fields of modern discovery, and
presented to his charmed audience at the British
Institution. With such art and grace were they
entwined, that I could not but ask myself, How
much of his power in running down verses does
Mr. Farrar owe to his having worked at verses ?
Is he not somewhat in the position of a Swiss
mountaineer who, having by hard labour reached
some Alpine eminence, now luxuriates in the
charms of his high position, and despises, flings
away the good staff which helped him to sur-
mount the rugged difficulties of the ascent, and
enabled him to crown the height ?
25
In like manner those brilliant speeches of
Mr. Lowe, with which he is shaking the country's
traditional opinions about Education, are not their
wit, vivacity, and power due to that intellectual
training which he would bring into disrepute ?
His enthusiastic audiences, who are exulting in
his slashing cuts and telling hits, do not reflect
that his sword was sharpened and his arrow
pointed by that very engine the cumbrous inu-
tility of which they are laughing at.
My reason for not using science, I ought rather
to say scientific informatioup as an instrument of
intellectual Education, I have stated above. In-
ordinary hands it is not a good instrument for
cultivating the mental faculties.
I have on all occasions" expressed my contempt
and abhorrence of that species of mental training
which was in vogue in our advanced, sharp
National Schools some fifteen to twenty-five years
ago, — a training which consisted in putting into
minds not prepared to receive them — and wholly
incapable of digesting and assimilating them — the
facts of geography and history, and crude morsels
of scientific and miscellaneous knowledge.
I got a lesson when I was a very young school-
boy, which I have never forgotten. We had
taken a wood-pidgeon's nest, and brought home
in pride a fine, vigorous, young bird nearly fledged,
* See " Account of St. Mark's School, 1857," pages 27, 28, and
" Eeminiscences of a French Eton," page 74.
26
It was our ambition to rear it. We went out and
bought some beans, dry liorse beans, opened its
beak, and slipped one and another and another of
the beans down its gullet. Thinking that we had
given it a good meal, we left it for the night to
digest its food. The next morning we hurried to
see our bird ; the result may be anticipated. It
was lying at the bottom of its cage with an ex-
tended crop, dead. We had given it food which it
was not able to digest, and so had killed it.
When I have listened to a National School-
master giving to school-children crude morsels of
scientific and miscellaneous Imowledge, which
they gulped down, indeed, but were clearly unable
to digest, "It is hcans," I have said to myself,
" that he is cramming down their throats : instead
of nourishing them, he is intellectually killing
them."
If, during these last twenty and more years, St.
Mark's has sent out into the world young men
able and intelligent, fitted to be good and useful
men, it is because this practice I reprobate is
there eschewed ; the aim of the School being not
so much to impart knowledge as to develope the
boys' faculties, and to teach them how to learn.
Now, in answer to the cry for science, which
resounds in the present day, I fear a recurrence
in schools of a higher rank to the bad system
which has been of late years wisely abandoned in
schools for the lower class.
27
Another danger to be apprehended is this, that
boys, finding that they are to be released from
severer study on the ground of its being dis-
tasteful, more and more will find severe study
distasteful, and that thus our English boys will
lose some of that mental vigour which they now
have, and take with them into the affairs of
life the weakness which belongs to discursive and
superficial men.
To follow out one subject in which the learner
feels interest is a splendid Education. " One
subject thoroughly," says Professor Tulloch, most
wisely.
What man is there of any class more worthy
of respect than the mechanic, who, after his hours
of toil, takes up a study or pursuit by wiiich he
may educate himself — be it a branch of mathema-
tics or philology, — engineering, drawing, flowers,
stones, or beetles. And the inquiring mind and
persevering spirit which the artisan shows in thus
educating himself is met with in other classes
and in different conditions of life.
I recollect being once for some days wind-bound
in one of the least interesting spots I remember
to have visited, — the island of Alderney.
Among the few families that were to be found
on the island, I had the pleasure of meeting a
lady who had turned the dull island into a para-
dise of beauty and interest. Folio after folio she
showed me containing treasures of beauty in form
28
and colour, such as I had no idea existed on
earth. In fact, she hved in a world of beauty
and order; her knowledge was extensive and
accurate, her conversation was as instructive as it
was charming and animated. I found she was
in correspondence with men of European cele-
brity. How was all this brought about ? Why,
she had gone to the bottom of sea-iceed !
Another vision of past days now comes up before
my mind. I was in abookseller's shop inPaternoster
Row. An old pupil accosted me. We kept together
a good part of the day, talking of old days and
many things. I found he was in quest of books,
learned, rare, old, to assist him in disentangling
some intricate point of historical geography.
He accompanied me to the station, and then
left me to return to his quarters. He was in the
Grenadier Guards and was stationed at the Tower.
My old pupil has since risen to an exalted
position in the country, deservedly honoured,
admired, I might add, beloved by a large circle
of friends. When I hear him extolled by those
who know him, I think of the day when I watched
the young officer of the Guards returning to the
Tower to meet the learned books he had ordered,
which were to help him in his careful search after
truth.
Here are instances of the highest and most
valuable kind of Education ; but the Alderney lady,
the young Guardsman, the Manchester artisan,
29
are not common types of their several classes.
They are exceptional cases. They re-appear, at
intervals, as Eton or other public schools-hoys,
hut these are just the boys who give us no trouble
or anxiety ; they would make themselves under
any system. "We get great credit, indeed, and
praise for their success, but it is credit which we
only partially deserve : on the other hand, we
deserve a great deal of credit in cases where we
get little or none. I mean in the case of boys of
no intellectual or moral power, whom, by care, and
patience, and fellow-feeling, we have led to use self-
control ; whose weak or dormant faculties we have
called out, and whom we send out into the world
not indeed to shine, but to stand on a higher
intellectual and moral level than they would have
reached had they not passed through our hands.
Now, it is these last that form the bulk of
humanity ; it is for them, and not for exceptional
cases, that we must legislate and form our plans.
And it is for the mass that I fear, when I hear
the cry that boys should be freed from the severer
labour of studying language if it is distasteful,
and therefore, it is said, unprofitable, and should
learn, instead, something about the wonders which
science has achieved within the present century.
Suppose them freed from verse-making, and from
learning about ye and civ and allowed, instead,
to learn about the electric telegraph, the light-
ning conductor, the electric light, the Davy
30
Safety Lamp, chloroform, and vaccination, (for
these — deprived of the poetic imagery with which
he surrounds them — are the subjects whicli
Mr. Farrar puts in the place of the idol worshipped
in the shape of classics,) would there not be a
great danger of the boys becoming less vigorous-
minded than they are ?
Certain of them I grant might, and doubtless
would, educate themselves by botany, chemistry,
electricity, and the like. But it will be those who
have an inquiring mind, and a decided love for the
science which they take in hand. But how will it
be with the mass ? Will their becoming acquainted
with a string of scientific results stand them
instead of the mental training they now get ?
Am I satisfied with the training we now give
to boys through our own subjects ? By no means.
But do not let us therefore begin on another tack ;
let us try to do, what we do, better.
And notwithstanding the imperfection of our
teaching and the idleness of the boys, what are
the intellectual characteristics of the pupils which
the public schools of England turn out ? Is not
their apprehension quick, and discernment ready
and correct ? Do they not take in, w^eigh, and set
at its true value what is said, with a perfectly
marvellous quickness and unerring instinct ? If
an observation is just, in good taste, well-timed,
do they not feel that it is so, and respond ? If
not, do they not detect the weakness or fallacy
31
instantly, and . eschew it ? Will they tolerate
verbiage ? Have they not a fine sense of the
ridiculous ?
When Mr. Hullah was giving singing lessons at
Eton, he made two observations on the charac-
teristics of his Eton class which showed his
penetration. Eirst, that they seemed all one,
bound together as by a three-fold cord ; compared
to them, his other classes appeared encircled by
a rope of sand.
His second observation was, that, in teaching
them, he was baffled by the quickness of their ap-
prehension. Before he had finished his sentence,
he felt that they had hold of it, and had time to
become distracted and inattentive, while he was
adding such further explanation as he commonly
gave to his classes.
And as we trace them on in life, I cannot but
think that we see these intellectual characteristics
of public school-boys developing themselves. Who
shall say how much the quick appreciation of
practical good sense v/hicli characterizes the
House of Commons, its intolerance of humbug,
its admirable instincts, and the other kindred
qualities in which the country feels both pride and
confidence, are due to the large number of public
school-men which it contains ?
Look, on the other hand, at those wiio have not
been under the training of our public schools, nor
have formed themselves, by some study or pur-
S2
suit, of a solid, vigorous character, but, instead,
have dabbled in science, — men who have left the
beaten track of classics and mathematics for the
flowery meads of scientific discovery. They are
not a numerous class, and are still rather un-
English. But here and there they may be found.
I dare say most people have one or two specimens
of the class before their mind's eye. If so, they
can say whether I overdraw their characteristics
in describing them as self-complacent and self-
conscious ; wanting in manliness, in vigour of
mind, and in sound judgment ; mouthy-talkers,
without the sense to know that they are dull ; even
in their own subjects apt to be hazy, and when
talking of one scientific subject, to confound and
jumble it with another : a public school-man may
very possibly be profoundly ignorant of both ; but
he honestly says so, while the sciolist indulges in
grandiloquent twaddle about what he does not
understand.
I leave it to English parents to say into which
of these two types of men they would like to see
their sons grow up.
But are public school-men to be profoundly
ignorant about the various interesting and marvel-
lous discoveries which modern science is daily
making, and their application to the comforts and
conveniences of life ? Is the choice of necessity
to be between ignorance and sciolism ? By no
means.
S3
In advocating the study of language as the best
means of educing the mental powers, — of doing
the work of digging and harrowing the brain, I
have said only half my say. A mind educated by
classics alone is only half educated. There is a
book the study and understanding of which will
make the education complete. No one who is
master of that book can ever be a sciolist, and
he will be mentally prepared by it to survey
and firmly to grasp all branches of natural
science : he will find it a master-key that unlocks
aU such knowledge. His mind, imbued with
that book, will deal with scientific subjects in a
manner in which, without the knowledge of that
book, it never would have done : — and that book
is Euclid.
But are we met in limine with a difficulty ?
Is this first step, the mastery of Euclid, so difiicult
a step, that it cannot be taken by the average of
our school-boys ? Is it necessary that they shall
give up the attempt ? must they be satisfied with a
humbler and more incomplete and unsatisfactory
acquaintance with natural science ?
Mr. Wilson inserts, in his very interesting
essay on a Liberal Education, a note, over which
I have thought much since reading it. He writes
as follows : — " The extreme repulsiveness of
Euclid to almost every boy is a complete proof, if,
indeed, other proofs were wanting, that the
ordinary methods of studying geometry at pre-
34
paratory and public schools are wholly erroneous."
Mr. Wilson speaks with deserved weight and
authority. But I must say that the extreme re-
pulsiveness of Euclid to almost every boy is not a
fact which has come under my own observation.
And holding as I do most firmly that a man is
not perfectly educated unless to classical study he
adds the mastering of Euclid ; — and that any one
who has mastered Euclid has hereby the best of
all preparations for a profitable study of all
branches of natural science, I feel almost bound
to speak, — to say what my experience is, — and to
add some hints that I hope may be useful.
It was in the year 1836 that I began to teach
Euclid at Eton, and I have been teaching it ever
since. Among the brightest and most interesting
hours of my life have been those that I have spent
in initiating boys, even boys of very weak mental
power, into the knowledge of Euclid. I make
this statement because I think it stands to reason
that this would not have been the case if the
study had proved repulsive to our pupils.
The first steps to many minds, I grant, are
difficult, — to some, very difficult. But the teacher
is cheered on by the thought that the more
difficult the appreciation of geometrical reasoning
is to a boy's mind, the more does that mind
stand in need of Euclid ; the more good is he
doing to the boy in trying to make him understand
it.
35
In looking back through years of experience, I
feel borne out in saying that at Eton we do not
find Euclid, as a rule, a repulsive study.
Boys of very low mental calibre have taken to
it, have been interested in it, attracted by it, and
have said to me again and again, "It's the best
thing we do at Eton."
The Euclid hour is always a bright one.
Whether we are taking the first steps with feeble
pupils ; or breaking fresh ground with a more ad-
vanced class ; or, recapitulating, we are linking on
proposition to proposition ; or, reversing the opera-
tion, we are tracing a proposition backward,
through those on which it depends, to lirst
principles ; or lastly, are setting the class to work
their brains on riders and exercises, — every
phase of Euclid teaching is pleasant in the retro-
spect.
Of course, I have had my disappointments — what
Master has not ? — in boys not using the personal
effort necessary to reproduce what they have
learned. Many have done so, and many a time I
have had to thank them for giving me a satis-
faction, one of the greatest a teacher can have,
that of finding that pupils retain and have made
their own what he has taught them.
But, whether the boys of a class be studiously
disposed or otherwise, I cannot call to mind any
to whom Euclid could rightly be said to be a repul-
sive study. If ever I say to a class, ''What shall
c 2
36
we have to-day ? " I am sure the cry will be,
"Euclid."-
And turning from my experience of Etonians to
boys of a totally different class and station.
I have now fresh in my recollection the heart-
felt pleasure of a weekly evening meeting through
last school-time with a party of St. Mark's school-
boys, whom Mr. Blythe (the Head Master of the
School) sent to me for a weekly lesson in Euclid.
They were boys of ages ranging from 12 to 15.
I took them through the third book of Euclid :
we only used enunciation books. I set before
them what had to be proved, and left them to
find out the demonstration, helping them if
necessary by giving the figure, and referring them
to the propositions on which the proof depended.
I do not know that there was a demonstration
that they did not make out for themselves. Each
would look keenly at the black board where the
figure was drawn, and give me a nod when he had
made out the demonstration. Then came the
comparing notes, and great was the fun and
hearty the laughter if one made a slip, or assumed
what he had no right to do. The school-time
was cro^vned by as beautiful a Euclid-paper from
* May I take the observation that has been made to me
more than once by a Cambridge tutor, " that in looking over
Examination papers, it is refreshing to come on an Eton man's
Euclid," as a corroboration of my assertion that Euclid is not
found repulsive by our Eton pxipils 1
37
almost every one of them as I ever looked
over.
It was only last night that one of them, who
is leaving school, came with his father, to give
me (according to om* custom) his photograph and
take leave. His manly workman father stood
beside him, and the tears found a channel for
themselves down his furrowed cheeks, tears of
thankfulness at the thought of what St. Mark's
had done for his son.
Nor were the boys who formed this evening class
more than good boys of average ability. The
very boy who took leave yesterday (he will not
be angry with me for saying so), Avlien he be-
gan Euclid, used to jumble the data and qucesita
in admired confusion in his brain. I thought at
one time (good boy as he always was) he would
never master Euclid, but I found him last school-
time as sharp and clear-headed as any of the party.
He would " spot " the false step in the reasoning
as quickly as any one of them.
And not only is the Euclid lesson an interest
full of charm, whether with my Etonian pupils, or
with mechanics' children at St. Mark's. It forms
a bond of firm friendship in after life. How often,
amidst the mountains and valleys of Switzerland,
do I find my hand grasped, and, looking up,
I see an animated face, radiant with pleasant
memories ! " What, don't you know me ? I am one
of your old fMva-Tat," — alluding to a long and
38
growing list that used to hang up in the mathe-
matical school of " the Initiated," that is, of those
who understood and could apply the fourth pro-
position of the first book. These were my iJ^varat,,
The Platonic motto " /i^^Set? dyecofMerp'nTo^ elairco" stand-
ing at the head of the list, shut out the inofanum
vuJgus ; and hearty, nay, vehement sometimes,
were the struggles to get into it.
All this I feel to be very outspoken ; but the
matter in discussion is too interesting and im-
portant for me to be squeamish about speaking
out.
And if we do interest boys in Euclid, and make
them like it, only think what we are doing for
them. Lund, in his Preface to his Geometry,
says : — " Next to the Bible, Euclid is the most
wonderful book in the world." I prefer to place
the Bible in a category by itself, and, drawing no
comparison between it and any other book,
simply to say, Euclid is the most wonderful book
ever written by man. Undoubtedly it is so. It
is the book which has moulded European thought
from generation to generation.
Even in those nations who have given up
Euclid as a text book, the mind has been trained
to habits of thought by the rigour and precision
of geometrical reasoning of which Euclid is the
father. But we Englishmen, with our stability
of taste, and our love of linking ourselves on with
the traditions of the past, stiU use the very text
39
of Euclid for mental discipline and training. We
value its calmness, its dignity, its permanence.
We find Euclid to be a book the tendency of
which is eminently to give what St. James calls
"the meekness of wisdom:" there is no self-
consciousness, or conceit, or affectation in the
quickened intelligence which its study imparts.
For myself, I can safely say that I can re-
member few hours of greater enjoyment than
those in which — shutting out the noise, eager-
ness, and contention of the outward world, and
taking up a book which has held its ground for
more than two thousand years — I have endea-
voured, by its help, to open the minds of the
young, to bring out those faculties which God has
given them, by the calm and unimpassioned inves-
tigation of truth, for truth's sake, to which its
pages guide us.
It was a happy day for me, and a proud day,
when a party of my old H'VaTaL who had entered
into the Indian Civil Service, presented to me a
copy of a Euclid which they had translated into
Hindustanee, as the surest and best way of bring-
ing the Asiatic mind and mode of thought into
conformity with the European.
Again, as I have said, Euclid is the true en-
trance to the natural sciences, — and a noble en-
trance it is, — how much better to enter on them
thus, than to scramble up in some other way !
What, for instance, is the greatest and most
40
elevating of all the natural sciences ? It is that,
incontestably, which issues in the researches and
discoveries of Physical Astronomy.
When we have made a pupil appreciate Euclid,
we have placed his foot firmly on the first step
of that great intellectual ladder which leads by
natural and continuous sequence, step by step, up
to the highest researches of celestial mechanics.
The highest steps of this ladder no man has ever
reached ; but the most highly gifted among man-
kind are those that have climbed highest upon it,
and are climbing still.
Terrestrial and celestial mechanics are one
harmonious whole, one continuous, unbroken rise.
All matter obeys in its moiivement the same
laws. *' La courbe," says La Place, — in the
Preface to his Third book of the Systeme du
Monde, — " decrite par I'atome leger que les vents
semblent emporter au hasard est reglee d'une
maniere aussi certaine que les orbes planetaires."
Surely, for this branch of natural science may
be claimed precedence before all others. Euclid,
as we have said, is the first step on this intellectual
ladder, and, moreover, each successive step upon
it is so much clear gain.
There is no room here for Professor Seeley's
amusing simile: — "If a man is not quite up to
going to Cambridge, it is no use for him to go to
Eoyston and stop there ! "
Though we may never reach the heights of
41
celestial meclianics, Euclid is a clear gain. The
first principles of mechanics, the composition
and resolution of forces, are clear gains. So
is each successive step in advance, up to
Newton's giant step, — " The moon is retained in
her orbit by the force of gravity," (happy the
man who gets thus far,) and so on. The know-
ledge acquired and the mental training, no
matter where we stop, are both of the highest
benefit.
I ask, then, with an outline of physical science
so great, so pre-eminent before us, — Dr. Whewell
truly calls it classical, — why should we divert our
students' minds from it ; and propose in its place
something so shaky as experimental lectures on
branches of science not yet fixed ?
It is not very long ago that a chemical lecturer
told me that he had been obliged to modify his
printed programme in consequence of some modi-
fication of hypothesis which it had been found
necessary to introduce during the preceding
week ! Are branches of science which give, as yet,
such uncertain sounds, to be named as educational
studies, with those which are based on rigorously
established laws, and have acquired all the
firmness, authority, and permanence of classical
science ?
If boys have laid the sound foundation of
classics and mathematics, by all means let them
42
have scientific lectures* and teaching.* Their
intellectual training will prepare them to turn such
lectures to a profitable use. What I deprecate is
putting the scientific lectures in the place of
classics and mathematics. — {See Appendix C.)
To revert again to Euclid. All that I have been
* The following is a list of the Lectures given at Eton,
on scientific subjects, and on the discoveries of modern science,
which I furnished to the Public School Commissioners at their
request: — "I find thiit, during the last fourteen years, there
have been courses of Lectures on the following subjects : —
Natural Philosojihy ; Popular Astronomy ; Mechanical Philo-
sophy ; the Forces of Attraction ; Light ; Heat ; Frictionai
and Voltaic Electricity ; Chemistry (at various times and in
its various branches and applications). Organic and Inorganic ■
Chemistry of Gases, and of Metals ; Chemistry of Common
Things ; Water in its Three Conditions of Ice, Water, and
Steam ; the Chemical and Physical Properties of the Atmo-
sjihere ; Application of Scientific Discoveries to the Useful Arts
and Manufactures ; on Coal and Coal Mines ; the Manufacture
of Iron, &.C. Also X'emarkable discoveries or processes, which
have from time to time attracted attention, have been illus-
trated and explained by Lectures, such as the Electric Tele-
graph ; Photography ; Electro-Plating ; the Construction of
the Westminster Clock ; the Bessemer Process for Making
Steel ; Rifling Cannons, and the Science of the Armstrong and
Whitwortli Guns ; the Method of producing Brilliant Colours
from Coal Tar ; Professor Bunsen and KirchhoflTs Analysis of
the Spectrum, &c.
" The following courses have also been given : —
" Comi^arative Anatomy and Geology ; Physical Geography,
including the Theory of the Winds, Rain, and Climate ; Mo-
dern. History ; Ancient and Modern Assyria ; China and
Japan from Personal Observation." — Report of Commisdon
on Public Schools.
43
led on to say in these last paragraphs is based on
the assumption that EncHd may be made an
interesting, instead of a repulsive, study. I have
said that at Eton the boys like Euclid, and take
an interest in it. I ought to do more than this :
I ought to try to show how this is brought about.
Among the most charming pages of the essays
on a Liberal Education (second indeed in interest
only to the blunt and manly semi- autobiography
given by Mr. Johnson, which they who remember
his first coming to Eton Imow to be affectingly
true) are those in which Mr. Wilson gives his
graphic picture of the mode in which his colleague
initiated a class of boys into the study of botany.
One cannot help regretting that the poor boy who
made a mistake in spelling was not privately
corrected ; otherwise it is a beautiful picture,
valuable and suggestive in the highest degree.
I can well imagine that the French Commis-
sioner would have been charmed with the intelli-
gence and vivacity of a class which had been so
taught.
Now, I must confess to my readers that, to the
juxta position of the above graphic account of the
botanical lesson, and the note about the repulsive-
ness of Euclid, they owe the pleasure and profit,
such as they are, of this Narrative-Essay, which
they are reading ; for the thought occurred to me
that Euclid as well as botany may be made a
bright and pleasant lesson ; at least, I thought it
44
might bo useful to sliow how we try to make it so
at Eton.*
So now, as Mr. Wilson set his botanical
master face to face with his forty pupils, we will
suppose the mathematical master and his class are
assembled for the first time for a lesson of Euclid.
We wiU suppose them the weakest twenty of a
division which has lately been advanced to that
part of the school where the study of Euclid is
begun.
Some few may have had some lessons in Euclid
at the last school : only perhaps to hate it. These
are ready to ask the question, " What is the use
of Euclid ? " The master deprecates the question,
" Don't ask me now. We should not be talking
on fair terms. I should know what I was talking
about ; you would be talking about — you don't
know what. Wait one month. If at the end of
My readers must judge how far I have succeeded in my
sketch. It has grown very long — is necessarily, in some degree,
technical, and cannot be so interesting as the sketch of the lesson
on botany, to the general reader. Still I hope the perusal of it
will not be confined to those engaged in teaching Euclid, but that
the general reader will try if he can extract some profit or,
at any rate, some amusement from it. I ought also to premise
that I do not make my colleagues responsible for a mode of
expounding Euclid, which some grave teachers might think was
trifling with the subject. They have their own methods, and I
can add emphatically that some of them succeed equally with
myself in making boys take an interest in Euclid. The
St. Mark's Masters do teach it after my method. They learned
Euclid from me, and as they were taught it, so they teach it.
45
that time you are a /u-uo-t???, that is, if you under-
stand the meaning of EucHd — and then repeat your
question, I will answer it ; hut I never met an
instance of anyone asking the question after he
understood Euclid."
Now, open your books. Euclid begins with
definitions ; of course, every subject has its own
language, its technical words, as they are called.
We must be agreed about the words we are going
to use, and their meaning.
Look at the first definition, it is a curious one,
— "A point is that which hath no parts, no
magnitude." You will better see its meaning if
you consider how Euclid may have come to it.
Here is a wooden brick I have got in my hand.
You see that it has length, breadth, and thick-
ness. Each of these is called a dimension. The
brick, then, has three. Suppose I plane away
its thickness till it is all gone, then there will
remain two dimensions, length and breadth — that
is, the surface of one of the faces of the brick ;
again, in like manner, suppose the breadth be
taken away, then only one dimension remains ;
length — that is, the edge of one of the faces.
Now, suppose the length to shrivel up from one
end till all the length is gone, what would
remain ? — no dimension at all. We should have
just the dot of the corner of the brick.
This is Euclid's "point : " it is deprived of all
dimensions ; it has no parts, no magnitude.
From this he starts, and, travelling the opposite
way to that we have gone, he gets first to a line,
that which has one dimension, length ; then to sur-
face, that which has two, length and breadth.
By adding on thickness to the surface he would
come to the solid or full brick from which we
started. He does not do so, because he
treats, in the first six books of plane geometry only,
that part of the subject in which the lines are
drawn on a plane or flat surface.
And here let us pause for a minute. I wish to
say something to you, in a sort of parenthesis,
which I hope may help you hereafter to under-
stand two words that you will hear used to describe
two different ways of reasoning.
We began with the full brick, and went back
undoing it, taking it to pieces till we got to the
" point." Euclid, on the other hand, begins with a
point and goes forward, putting things together,
adding on length, &c., till he builds up the full
brick, that is, arrives where we started from.
Here you perceive are two different ways of
considering the same question — the way of
undoing, and the way of putting together. What
do you think would be a good name for the way
of undoing, of taking to pieces ? does dva-\u(o de-
scribe it ? and for the other way, the way of putting
together, do you think (rw-rlOrnML would be a good
word for that ?
Well, if hereafter you hear two rather long
47
words, which yon will easily trace to avaXvw and
a-vvrcOTjfMi for two jdnds of reasoning, think of the
brick; perhaps it will help you to understand
them.
Now, let us go back. Euchd wants a flat
surface to write on, and how does he find out if
his table is flat ? I will tell you. He takes a
straight line ; we all know what a straight line is : —
The edge of this ruler — carpenters call it a straight
edge — is meant to be a straight line. If wherever
this straight edge is placed along the table its edge
lies exactly in the surface of the table (if there is no
day-light between), then the table is flat, it is a
plane surface. Here is a bit of warped board. My
straight edge, though in some positions it may lie
in the surface of the board, in others it does
not do so ; so the face of this board is not a flat
surface, and therefore will not do for drawing
the lines oi plane geometry on.
' But supposing our table flat and our rulers
straight, draw now any two straight lines from
the same point, in any direction you like, and tell
me what have we got here ? — An angle. — Yes, a
flat straight lined, i. e., plane rectilineal, angle.
Now, what is the meaning of this word ''Angle?"
It is the inclination, the amount of opening be-
tween those lines. You will see plenty of angles
if you look round the room [an octogan roomj ;
all the different corners are angles ; some are blunt,
some are sharp ; in fact, an angle is a corner, the
48
opening at the corner. What does Horace say of
that cosy corner of his Tiburtine farm where he
hoped to sit in his old age, and drink his
Falernian ? — Angulus ille milii ridet.
Eemember, the size of an angle in no way
depends on the length of the lines containing it.
Here, as I open and close up the legs of my big
wooden compasses, I make angles greater or less
with the same straight lines ; and here, give me
one of your little brass compasses, — if I open it
equally, with the large compasses, the angles are
equal, though the legs are much shorter.
Plenty of time should be given to this matter —
the meaning of an angle ; and when the boys
have learned how, by means of three letters,
an angle is indicated in Euclid, a number of inter-
secting lines should be di'a's^Ti on the black board,
and while the Master puts his finger into the
angles, the boys should indicate them by naming
the letters ; and conversely he should name the
letters, and the boys should come up one by one
to the board and put their finger into the angle
named.
A Master will often be surprised how long it
will take before the whole of a class of weak boys
can do this ; but he will be greatly helped in
stimulating the slowest and weakest, by the hearty
and not ill-natured laugh elicited by their bad
attempts at hitting the angle named.
All teachers should assure themselves that
49
every individual boy has got over this difficulty.
I have met boys professedly reading the third
book of Euclid, who actually did not know the
angle they were naming. No wonder Euclid is
repulsive to such.
The same figure on the board will supply
another exercise which should not be omitted, —
the adding two contiguous angles, and pointing
out and naming the single angle which they make
when added together, also the taking one angle
from another, and naming the angle that remains.
This is a greater difficulty with many boys than
would be supposed, but it is a great gain when
they can do it promptly ; it helps them much
in the winding up of the fifth proposition, and
when they come to the seventh.
The three classes into which angles are divided,
according as they are acute, right, or obtuse, are
easily set before them, by the Master putting the
end of his long ruler to the edge of his table, and
making it slant more or less ; they soon get to
appreciate Euclid's test of a right angle.
Before drawing a circle with a pair of com-
passes, it is well to do it by the primitive mode
of a tack in the black board, and a bit of string
with a loop at one end to go round the tack, and
a piece of chalk tied to the other.
The rest of the definitions offer no difiiculty.
It is better to pass over ah reference to parallel
lines at present.
50
With regard to the Postulates, it may be
enough to observe you are allowed the use of a
straight niler and a pair of compasses. They are
allowed you only that you may draw, and pro-
duce, straight lines, and describe circles, and not
to mecmLre tcith. It is better at present not to
distract the boys by alluding to any deeper mean-
ing of the Postulates.
The Axioms are readily taken in. Let them
know that Euclid asks that they may be accepted
without proof, hccause he has no proof to offer, that
. he proves everything he can. Of course, they
will be told not to think about the twelfth axiom
at present.
And now we have arrived at the first pro-
position. Let the figures of the first three pro-
positions be drawn very carefully and deliberately ;
the boys will enjoy doing it. Let the equilateral
Fig. 1. triangle in the first proposition be drawn on each
side of the line. In the second proposition let
•^«'r/- 2. them join the point with each end of the given
line. Vary also the relative positions of the point
and the straight line, bring the point nearer and
nearer to the straight line, let them see that the
triangle thus becomes smaller and smaller, and
guide them to feel what it becomes when the
point actually coincides 'with an end of the line.
Also place the point in the given line.
Fifj. 3. In the third proposition, by all means let them
do all the figure of the second proposition re-
61
quired for drawing AD equal to C ; they had
better do it in j)€ncil, inking in the Hne AD ;
then let them efface all the pencil figure, and they
have the figure as given in their Euclid books,
and can proceed with the third proposition.
Boys like all this ; they take a great pleasure
and pride in it : they like to bring out neat and
good figures, and it is all very instructive.
The demonstrations of the first three propo-
sitions are very simple, and there is this good
about them, that the boys have the advantage
of going three times over the same argument,
with a little variety in details. But even here
boys think there is something mysterious about
lines, so that it is desirable to throw them
off the rut of Euclid's phraseology and ])ack on
their own common sense.
And on Horace's principle that FdcUculmn acri
fortius et melius, secat res, we proceed in some such
way as the following : —
At one side of the black board a few strokes
represent the Tower of London. Near it we draw
a soldier on guard, — soldier, musket, and all is
done in a few strokes. At the other side of the
board is drawn a round tower and a flag flying ;
this is Windsor Castle, and we place a sentry on
duty there too. Now tell them these are two
soldiers of the Grenadier Guards, one battalion
of which is stationed at Windsor, the other at
D 2
52
the Tower, and there is a bet pending between
these two men as to which is the taller. Un-
fortunately they are both on duty, one at Windsor,
the other in London, and cannot therefore settle
the question by the primitive method of standing
back to back and measuring. What shall they
do ? The Windsor man has a comrade who
measures with him ; they find they are exactly
of equal height. This comrade is not on guard,
and gets leave to go to London. Then, midway
between Windsor Castle and the Tower, a few
strokes exhibit the train and the '' comrade "
inside. By the time we have drawn the scare-
crow figure of the long-legged guardsman in the
train, all are in a roar of laughter. Well, he
gets to London, and measures back to back with
the man at the Tower, and they find they are
also of exactly equal height.
Now, the London man and the Windsor man
know, u-ithout measuring ivitli each other, that one is
exactly of equal height with the other.
By what axiom it is asked : they answer, doubt-
less rightly, the first.
Now, then, says the Master, who of you can pick
out, in each of the first three figures, the London
man and Windsor man, and, above all, the man
that went by the train ?
In the best humour they all turn to their
figures and look and think till, in a little while,
I
63
one after another, they all find out; and when
they have all caught the man that went by the
train, it is a great victory !
This done ; — turn, says the Master, to the thir-
teenth proposition. I tell you beforehand, that the
grand difficulty of that proposition is to see which
is the man that went by the train. You are con-
fused with the multitude of angles named, until
you have discovered the man that went by the
train, then it is all perfectly simple ; and I here
give you notice that when you come to that pro-
position, whoever finds out which is the man that
went by the train, may claim an exemption.
Make a note of that !
Now comes the tug of war : the fourth proposi-
tion, which is the key of Euclid. We tell them
that the first three propositions are put in first,
because in the fifth and sixth propositions we
have to cut off, from a greater line, a part equal
to the less ; but that the real beginning of Euclid
is the fourth proposition, the first theorem, and
that on this proposition the battle with Euclid is
to be fought, and the victory won.
From the beginning one cannot be too parti-
cular in pointing out the three distinct portions of
each proposition — the enunciation, construction,
and demonstration.
In drawing the figure of the fourth proposition. Fig. 4.
it is wise to be very deliberate, and make a great
to do about making the two given lines and the
64
iucludcd angle in each triangle equal, in order
that the fact of their equality may be strongly
impressed on the learners' minds.
Let each boy draw the AB and DE, and care-
fully, by his boxwood ruler, make them (say) two
inches long. [If any sharp boy retorts, *' You
told us we were not to use our rulers to measure
with," explain — this is only a datum; that it is
for the qucesita they are not to measure.]
For the included angle, if a boy has learned
the use of the protractor, and done a little practi-
cal geometry, (as he ought to,) he draws two lines
equally inclined to the lines AB and DE ; if not,
let him bend a bit of paper or cardboard to any
angle, and with its help draw the second lines AC
and BE equaUy inclined to the first ; and, by the
boxwood ruler, let him make them carefully (say)
two inches and a-half long.
Does this seem long and useless ? I think it is
highly important. It must be borne in mind that
I have supposed a set of very weak boys before the
Master. If he were to draw quickly the figures of
two triangles, and say (as he might if he had
more advanced pupils) we will suppose such lines
and angles equal in each, and expect them to take
in his words, he will be disappointed. I venture
to say, if he names different lines and angles, and
says was this and this given equal, or have they
to be proved equal, he will find the boys again
and again making bad shots ; but all this care-
55
fill deliberation which I advocate helps them
gradually to take in the idea, and till they know
accurately what is giveu, and what has to be
proved, they can make no progress.
It would be well at this point to take up the
eighth axiom, and dwell on it and elucidate it : let
them know that though in common parlance the
words '' same " and " equal " are used as if they
had the same meaning, (for instance, we speak of
two boys being of the same height, of two masses
being of the same weight, when we mean they are
of equal height and equal weight,) the words are
not confounded in Euclid : when he says the same,
he means the same identical.
He says, we know two magnitudes are equal, if we
know, if we can assure ourselves, that they fill the
very same identical space. Elucidate, by sup-
posing the boy you are addressing to be casting
bullets : he casts one out of the mould, then he
casts another out of the same mould ; there they
are lying side by side ; is he sure that they are
equal ? yes, why ? because he knows them to
ha.ve filled the same space, the same cavity of the
mould in which they were cast.
It is good, here, to get a promise from each boy
that they will not say that any two things which
they want to prove equal are so, until they have
first shown that they fill the same space.
We then begin with Euclid's ideal super-
position : place A on D and AB on DE. Where,
66
then, will B naturally and of necessity fall, and
why ? Some wall have difficulty in answering the
question ; they arc frightened at the phraseology
of geometry. Draw their minds, then, to some
homely illustration. Here are a couple of walking-
sticks, a long one and a short one. I lay them
alongside of each other. I bring the handles
together ; say, wdll the points come together ? No.
Why? Because one is longer than the other.
Quite right. Here are a couple of equal length ;
I do the same with them. Now, do the points
come together ? Yes. Why ? Because one stick
is as long as the other. Quite right again.
Now, says the Master, let us go back to the
lines ; consider them to represent walking-sticks ;
and remember, AB was given equal to DE.
Now, then, if you place A on D and AB along DE,
will B come on E ? Yes. Why ? Because they
are equal. Quite right, admirably said. You
have got over one-third of the difficulty of the
main part of the proposition.
Now, these lines AB and DE lying together,
where will AC naturally and of necessity lie, and
why ? Here it is well to have three triangles at
hand in cardboard, w^hich have two sides in each
respectively equal, the included angle being in two
cases equal, in the third case unequal. Place them
together as directed, bringing together alternately
the triangles which have unequal and equal in-
cluded angles. Thus the pupil will be brought to
57
feel the reason why AC will lie along DF. Two
pair of compasses will do as well.
And AC now lying along DF, will the point C
naturally and of necessity fall on F ? Yes. It is
hoped this time he will say firmly, " Because the
lines are equal."
He should now be called upon to give the three
consecutive steps of the reasoning. If he does it
correctly, he may deservedly be patted on the
back; for out of a hundred boys that come to
Eton professing to have read Euclid, not one can
do as much.
Now, take every boy consecutively, and make
him try to say the same three steps of the proof.
A Master will find comparatively few able to do
so, even after the foregoing explanation. He
must be ready to repeat and vary his illustrations ;
also by going round and round till each boy can
say it, one will teach the other, and the desire to
be classed with the successful will be a stimulus
that will help the poor weak fellows to fix their
thoughts. At last, we may suppose they have all
succeeded in saying this much, right.
Now, call a pupil up to the board, and ask him
where B now lies. It is ten chances to one that
he wiU point to the letter B on the board. No, the
Master cries energetically — and he dashes a couple
of chalk marks across the triangle ABC, saying,
ABC is not there ; it's lying on DEF. Now, try
again. Where is B '? He puts his finger on E ;
58
and Where is C ? He puts his finger on F.
Quite right now, observes the Master ; you have
shown that the two hues BC and EF begin to-
gether and end together. Now, answer me this.
Beginning together and ending together, as they
do, can they separate at all between the beginning
and the end '?
If they do not take in the meaning of this
question, and possibly they will not, they might
be helped thus : —
The Master might take up a couple of pens,
and bringing the points of the pens together with
one finger and thumb, and the feather ends to-
gether with the other, he might say. Here these
two pens begin and end together, but they don't
keep together ; they separate. In fact, they en-
close a space, don't they ? Put your finger into
the space they enclose. How is it that ' they en-
close a space ? Because they are not straight.
Exactly so, and if they w^ere straight lines, they
could not enclose a space. Is not that just wdiat
Euclid says ? Here are two straight pen-holders ;
if I bring the beginning and end of these together
as I did the quill pens just now, they do not enclose
a space, but keep together from beginning to end.
Now, these two lines BC and EF are sup-
posed to be straight lines, and you have shown
that they begin together and end together.
Say now, do they separate like the pens, or
keep together like the pen-holders ?
59
Tliey all answer promptly and rightly this time.
The Master now tells the boy whom he has called
up, to draw his finger along the space filled by EF;
he does so ; And again to draw his finger along
the space filled by BC ; he draws his finger along
the same space. Eight, and yon have discovered
(he adds) that the two lines fill the same space,
i. e., so much length, you need take no account of
their breadth because lines have not any.
Now, let us look back and see what we have
done. We have shown that if any two triangles
have two sides of the one equal to two sides of
the other, each to each, and have likewise the
included angles equal, — and that if one of the
triangles be applied to the other as a triangle of
any form ivhatever might he applied to any other, —
THE two BASES WILL OF NECESSITY FILL THE SAME
IDENTICAL SPACE.
Now, turn to your eighth axiom and read it.
" Magnitudes which coincide, that is, which
exactly ^/Z the same space, are equal."
What, then, can you now say of BC and EF ?
That they are equal. Quite right, well said.
After a minute or two's rest for breathing, the
lesson is resumed.
Now, tell me, where does AB lie ? On DE.
How do you know ? He hesitates. The Master
passes on the question. At last, one, a little
clearer or bolder than the rest, ventures to say,
" Because we put it there." Quite right. A very
60
good and sufficient reason, we put it there. Shake
hands for that. And where does BC He ? On
EF. How do you know ? If he is very bright
he will say, '' We have just proved that it must
come there," and the Master may well say,
"Capital." If he does not see the right answer,
he must be led on to it.
When he sees this, the Master says. Now put
your finge]' into the space filled by the angle ABC,
now into the space filled by DEF. He puts his
finger both times into the same space. So you
have discovered that the angles ABC and DEF
both fill the same space. And as they fill the
same space, what does the eighth axiom tell you ?
That they are equal. Eight again.
Now, once more. Where does AC lie ? On DF.
" How do you know ? Don't say because we put
it there." No, but we put AB on DE, and we
proved that, in that case, AC must come on DF.
A triumph ! you deserve exemption for that. Of
course, you know where BC lies, you have already
told me. Now put your finger into the space
filled by the angle ACB, and now into that filled
by DFE. Twice again he puts his finger into
the same space. So you have discovered for the
third time that the two things which you wish to
prove equal (that is, the second pair of remaining
angles) fill the same space.
How do you finish ? Therefore by the eighth
axiom The pupil finishes the sentence by say-
61
ing, "They are equal." Right agam. "You
are gomg ahead — one 'bout more, and you're safe
in port ! "
Once again, then, where was it you put AB ?
On DE. And where did you prove AC would
come ? On DF. And where did you show that
BO must lie ? On EF.
Now, then, put the flat of your hand into the
space filled by the triangle ABC, now into the
space filled by the triangle DEF ; twice he puts
the flat of his hand on the same space. So you
have for the fourth time made the discovery that
the two things you want to prove equal (now the
two triangles) fill the same space, and, therefore,
by the eighth axiom in tone of sympathetic
triumph, the pupil takes up the word, and adds,
the triangles are equal.
You have thus proved, in accordance with EucVuVs
eighth axiom, that if two triangles have two sides
of the one equal to two sides of the other, and
have the included angles also equal, thcg are equal
in every respect.
This is the grand fourth proposition. It is, as
I said, the key to Euclid. I congratulate you
on what you have done. Go now to your place,
read over the proposition, as it is written out in
Euclid, once or tv/ice, carefully, then close the
book and write it out, while I take another boy
in hand.
I have here imagined a very fair (a far too fair)
62
specimen of an average pupil. A Master must
not be disappointed if he has to lead a boy on and
encourage him many a time, before he wins the
victory. Many and many a time has a boy said
to me, *'AB lying along DE, AC will lie along
DF, because AC is equal to DF." And I have
had to answer, " My dear fellow, there is ex-
actly as much sense in what you have now said
to me, as if you were to tell me it is twenty-two
miles to London, because butter is eighteen-pence
a pound."
Boys are most apt to say words without attach-
ing a meaning to them. This is often found to
be the case where it would not be expected. They
must be shaken out of the habit, and this is
exactly one of those things that Euclid when
properly learnt does.
I remember once hearing a boy saying the pro-
position thus : —
Because AB is equal to DE, and the angle
BAC is equal to EDF, therefore the line AC lies
on DF. No, no, said I. What ought he to say ?
The next boy answered. Because AB lies on DE.
A little fellow sitting by the side of the speaker
(he is a post Captain in the Navy now) looked
up eagerly into my face and said. Will you tell
me why it is not as good to say it one way as the
other ? — " Do you wish to know why ? I'll tell
you willingly."
Look at those two triangles on the black board,
63
ABC and DEF. Remember AB and AC are
respectively equal to DE and DF, and the included
angles also. Yes.
Now, if I were to take a saw and cut down
through the board between the two triangles, and
were to send one-half of it, that on which the
triangle ABC is drawn, to Oxford, and the other,
that on which DEF is drawn, to Cambridge, the
lines and angles would still be equal, would they
not ? Of course. But if one of the triangles
was in Oxford and the other in Cambridge, could
the line AC lie oil DF ? Of course not.
But if the triangles are neither at Oxford nor
at Cambridge, but there on the board before us,
and I conceive the triangle ABC to be laid on
DEF, laying A on D, and AB along DE, then
indeed AC ti-ill lie along DF, because the included
angles are equal.
A rich, deep blush forthwith suffused the boy's
ingenuous countenance. "Thank you, sir," said he ;
" I see it perfectly now, — I never saw it before."
When the whole class have been thus set on the
right tack for appreciating the demonstration, and
by their own efforts have mastered it, and shown
themselves able to produce what they know by
writing it out correctly, then follows another exer-
cise most interesting and instructive. The aim
of it is to show the application of the fourth
proposition.
But it is high time the class should have a
64
little rest, and while they are resting, I should
like to have a little talk with my readers about
all this.
Will one of those friends who have been reading
these last pages feel ready to exclaim, "What
labour, what misdirected effort have we here ! all
this work to prove (in subjection to an artificial
test of equality) an axiom ! for the fourth pro-
position is nothing else ! " " My friend," I answer,
" let me speak as a Schoolmaster. Euclid is
the book which the traditions and the general con-
sent of the country put into our hands, and my
business as a Schoolmaster is to try and make it
do what it is put into our hands to effect. Now,
what do I find, by experience, is the result of this
mental ordeal I have been describing ? I reply,
confidently, the boys come out of it intellectually
changed. They are lifted into a higher mental
level from that in which they stood before, never
to descend again into it as long as they live."
After this badgering (it might be called, if there were
not a perfectly good understanding on both sides)
on the fourth proposition, there is comparatively
no more difficulty in Euclid. Henceforth they
take kindly to it ; they icill know the meaning of
what they are doing. They never think of learn-
ing a proposition by rote. It is too much trouble ;
there is no pleasure in it ; but there is very great
pleasure in understanding it.
The sort of mental activity that is henceforth
65
evoked by Euclid, and the satisfaction of the
EucHd lesson, I can best illustrate by referring
to the actual facts of those weekly evening Euclid
lessons of last school-time with the class of
St. Mark's boys that I have alluded to. I can
speak more freely of them than I can of others.
When we had come to the third proposition of
Book III., I told them of a mistake which had
been made by some great men* in a mathe-
matical examination, who tried to prove the
second part of the proposition by the B.I. 4., and
I asked them to explain where their mistake lay.
They did so. One of them, however, observed,
'' But it might be proved by the fourth." " How
so?" "Because two of the angles of each
of the triangles are equal, so by the thirty-second
proposition the third must be, and that is
the included angle." Another of the lads here
interposed : "It might be proved by the forty-
seventh proposition."
* I am afraid tliese " great mea " here spoken of were
none other than the scholars of Trinity in their fellowship
examination. When I was trying for a fellowship, (which I did
not get,) one of the examiners told me that all the candidates
but two had made this mistake. Now, the story is so valuable
for making boys give an intellectual spring, for giving them
what the French would call elan, that I am afraid it often does
duty in my class-room. So I must here humbly apologize to that
most select and respected body of men the scholars of Trinity,
and ask them, " for a great good," to let me " do them a little
wron"; ? "
6G
There is not much in this ; but it shows mental
activity, and an appreciation of Euclid. The
study cannot be repulsive to boys who have this
kind of Imowledge of it, and can link on readily
one proposition to another ; and I can assure my
readers that as I led them on to discover for
themselves the different unexpected properties of
the circle, which Euclid brings out in admirable
continuity in the latter half of the third book, so
entirely interesting was the exercise, that they
could hardly refrain from a cheer of satisfaction at
the winding up of each proposition.
Come here, my friend, and stand by my side.
Look into those boys' faces. They are merry-
hearted boys ; they laugh like others, and sing
(that they do, and sing very well too !) Look at
them now. Mark the fixed eye — the rivetted
attention — the animated countenance — the smile
of satisfaction — they are not conscious of all this,
but you and I looking into their faces can see it.
What, I ask you, is all this the sign of ? The
interest and internal j^leasure felt in the exercise
of the mental faculties in the following out intel-
lectual truth.
Give me then your sjmapathy, my friend, and tell
me if you do not think that Euclid is doing them
a great good.
I could speak of others besides St. Mark's boys,
and say what pride I have in finding myself sur-
rounded by boys in whose minds has grown that
67
grand capacity which EucHd emphatically imparts,
*' the capacity to know when they know a thing,
and to hnow when they don't hioiv it.''
I rejoice to see them reject an explanation if
they do not see their way to link on all that is said,
from sentence to sentence, in a manner satisfactory
to themselves.
I rejoice to see their quickness at putting their
finger on the weak or obscure point of an expla-
nation. I rejoice to he pinned down by them by a
searching question. " Why is this ? You have
not explained that."
But we must leave this. It is time to go back
to the Euclid. We left the pupils resting ; but they
were only half through the battle.
To appreciate the fourth proposition the learner
must know, not only its demonstration, but its
application. Of course, the fifth and sixth pro-
positions are exercises on the fourth ; but it so
happens that they are particularly hard exercises.
There are a number of far easier ones scat-
tered about Euclid, if only it were permitted to
take a few things for granted, which they have no
difiiculty in doing; for instance, that an angle
may be bisected, and that a perpendicular may be
drawn from a point in a line. (If they have
done any practical geometry, they have learned
how to do such problems,) then very easy exer-
cises on the fourth proposition may be found Figs.5,Q.
in Euclid {e. g., the tenth prop.) — or framed.
E 2
68
Agaiu, if we assume that on opeiiiug a pair
of scissors the angle between the blades is equal
Fiij. 7. to the angle between the handles, then the six-
teenth proposition furnishes an exercise. If we
Fig. 8. write a figure like a Z on the black board, and
assume that the angles in the knees of the Z are
equal, then the thirty-third is an exercise. If we
Fi(i. 9. assume that a square may be described, the forty-
seventh furnishes a capital exercise.
And if they are told that all these things, which
they are asked to take for granted now, will be
regularly proved hereafter, no harm is done.
The two triangles to be proved equal being set
before the pupil, he examines them and finds out
for himself the two sides of the one that are equal
to the two sides of the other, observing that the
equal angles in each triangle must be those that are
contained by the respectively equal sides ; then he
writes formally out the exercise in five lines or
paragraphs : —
1. He names one side in each triangle that is
equal, giving the reason why.
2. He names a second side in each that is
equal, giving the reason why.
3. He recapitulates, — wherefore the two sides
named of the one triangle are respectively equal
to the two sides named of the other ?
4. He names the included angles, and gives the
reason why they are equal.
5. He concludes, therefore, hij the fourth pro-
69
position, the triangles are equal, in every respect,
naming the respects if necessary.
It is hitting a nail on the head that drives it
home, and that is just what these exercises do.
After doing two or three of them, they get quite
clear and hrisk. They enjoy the exercise. They
examine the triangles ; pick out the sides ; write
out the five formal paragraphs ; come up with it.
It is examined. Right. Off they are to do another.
One hears occasionally, in a tone of triumph,
" Therefore, hy the fourth proposition," &c.
The last exercise is always that crucial test,
the second part of the third proposition of Fiy. lo
the third book, and the scholars of Trinity do
duty again and again.
Now, among these exercises, we introduce the
following in an off-hand way, without letting
the class into the secret of what we are about.
Draw, says the Master, a couple of circles, with Fiy. 1 1.
the same centre one inside the other ; and draw
now a couple of radii (two spokes of the wheel) to
the rim of the outer circle ; call them AD, AE ;
put B and C where these lines cut the inner circles,
join BE and CD. Now take as an exercise to
prove that the triangles AEB and ADC are in
every respect equal, and name the respects. They
set to work ; in two or three minutes they bring
up the exercise, the five paragraphs written
correctly out. .
Then the Master says, Now join BC, and.
70
remembering what you have proved already, try
and prove that the triangles DBC and BCE
are also equal in eveiy respect, observing to them
that the bases of both triangles are the same line.
Down they go to work, and this exercise is
brought uj) in a few minutes.
Then the Master again quite casually says. Let
me see, we proved these big angles ACD and
ABE to be equal ? — Yes, say they, in the first
of the two exercises. And we have just now
proved that BCD is equalto CBE ? — Yes. Suppose
we take these little poky angles from the big ones.
Then ABC and ACB remain ; And if equals are
taken from equals, what do we know about the
remainders ? — They are equal. Exactly, then
what angles are equal ? ABC is equal to ACB.
The tutor's face, which has been solemn and
somewhat constrained all this time, now relaxes into
a serene smile of triumph and congratulation.
** Gentlemen," says he, "I have the pleasure to an-
nounce to you that you have done the fifth propo-
sition. The ' Bridge ' is passed." They are taken
aback. " Quite true. It's all over ! The tooth is
out ! It's all right ! " So, then, we are aU very
happy together.
In doing these exercises with the boys, I have
had reason to admire Euclid's judgment in speak-
ing of the two sides and the base of a triangle,
instead of talking, as we very commonly do, of
the three sides of a triangle. To observe which
dcoJ./^
<M4X^..I J 5
T.y.^
X^. 7.4-/
y^e^ /C^
s.
^
'3
t^.J.J^.
H- /'S--^ C-^' .^■F'c'i
71
lines are the bases of the triangles to be compared
is a great help to learners. One boy to whom I
gave the sixth proposition as an exercise on the
fourth, without, of course, telling him it was a
proposition of Euclid, came up a little baffled,
and scanning the figure, he said, "Which are
the bases of the triangles we have to compare ?"
" A capital question !" was my answer. " Shake
hands." I put him on the right tack to find out
for himself. He picked them out. " I see," he
said ; and he went down to his place, and wrote
out the exercise (really the proposition) at once
perfectly right.
After this we turn to our Euclids : they read
over the fifth and sixth* propositions, paragraph
by paragraph, and then write them out carefully.
These exercises are not intended to supersede the
careful writing out of Euclid. The appreciating
and falling in with Euclid's guarded choice diction
I hold to be a great intellectual benefit. It is a
help to those who wish their knowledge to be
clear and precise, and I cannot think it is lengthy.
Very often, when with a little oratory and
emphasis, suiting the action to the word and
the word to the action, I have gone over a pro-
position for a class at the black board, they have
said to me, '' Is that all ? we can understand that,
but there is such a lot of it in Euclid." Then I
* I do not find that they have any difficulty in taking in the
idea of the reductio ad absurdam proof, if dearly put.
72
take a Euclid in my hand, and say, " You tix
your eyes on the figure on the black board, while
I read the proposition in Euclid verbatim et lite-
ratim, and you will see if there is anything in it
that I have not said ; also, you will tell me if it
can be shortened, and where." At the end of
the reading they are always satisfied that the
wording of the proof is only what is needed for
completeness and precision.
They might go a-head now as P'Va-rat, but I gene-
rally take them by the hand, — keep the belt round
them, till they have reached the eighth. After
that they swim off by themselves.
So to complete my sketch, I will give a rapid
outline of our teaching the seventh and eighth.
We always teach them together ''without solution
of continuity."
The seventh, I frankly tell them, is a teaser.
I like to do so, it puts their courage up. I add,
it is a proposition introduced only to prove the
eighth, which is a most important proposition, as
valuable as the fourth, but the seventh is never
used again.
I tell them that some schools are afraid of the
seventh, and, explaining to them what is wanted
to be proved in the eighth, I guide them to show
me the proof that is given of the eighth (as a
simple deduction from the fifth), in schools where
they are afraid of the seventh. " But you are not
afraid of the seventh ? " No ! — Let us go at it then.
73
I find it simplest to put the enunciation in this
form. If the two sides terminating in one ex-
tremity of the base are equal, those terminating
in the other extremity must be unequal. Then
we proceed step by step, in the way of questions,
from the equal angles at the base of the isoceles
triangle to the "Much more then...." Some
boys have a great difficulty about the a fortiori
argument. We have a familiar illustration which
has often proved a great help to boys.— You agree
that a father is older than his son ? Yes. And
that a grandfather is older than the father ?
Yes. Much more must a grandfather be older
than his grandson. Now, then, in the seventh
proposition pick me out the father, the grand-
father, and the grandson. They do it after a
little, and the difficulty is got over, and they go
on at once to the eighth, see its connection and
take it in. In fact, the coinciding of the angles
is no difficulty to them after the drilling they
have had in the fourth proposition.
The work is done now. Those who have suc-
ceeded in mastering the eight propositions, and
have answered our questions* upon them, and
* One of our methods is to turn the eight propositions into
a series of questions (they make upwards of a hundred) ; to
these we get written answers. I had thought of putting our
questions into an Appendix to this Essay, but it is not worth
while. It" any teacher of Euclid who reads these pages would
like a copy of the questions, ho is heai'tily welcome to them.
74
liave written them out correctly, get their pass :
they are fivo-rat. And to them I say : " Now, if
you hke to ask, what is the use of EucHd ? I will
tell you." But, no ! they are too pleased and
proud to ask the question. Besides, they have felt
internal satisfaction in completing a geometrical
demonstration.
These are formed into a class of honour-men ;
they go on by themselves, learning their four
propositions, and writing them out each time
they come, wiiile the Master goes over the same
ground a second time with those who have not
conquered.
In this second going over the ground, with the
weakest boys, we find that the patent fact that
some of their companions have conquered, and the
exalted honours which they enjoy, are a great
stimulus to the less successful. Many a time I
hear a little tap at my door — "Come in," and the
face of one or other peeps in, asking for a little
private teaching in play-hours, that they may get
their "mystic " honours. When all have passed, we
can form ourselves into a class again, and sometimes
we lecture, sometimes write out Euclid, sometimes
do exercises. (And here I must say that School-
masters are under great obligation to the modern
editors of Euclid for the carefully graduated
exercises which they have appended to their
Euclids.) And the work is all pleasant.
I have now said my say on teaching Euclid, and
75
happy shall I be if any hint of mine in these pages
shall help any Schoolmaster to some of the bright-
ness and sunshine which teaching Euclid has been
to me for these many years back.
I must now bring my Essay or Narrative to a
close.
I have been reading over Mr. Wilson's essay
again. I do not think we are far apart in view.
I hope not. No reader of his essay can lay the
book down without feeling that Rugby is most
fortunate in having such a teacher of natural
science, and that, whatever can be made of it, he
will make of it ; if the study of natural science can
be prevented being cram, he will prevent it ; if its
votaries can be saved from sciolism, he is the man
to save them. But even he, I think, will say that
if Euclid can be made attractive instead of repul-
sive, and I have tried to show that it can, then
the boys who are imbued with geometrical concep-
tions and reasoning will pass on to mechanics,
which he judiciously places foremost in the course
of natural sciences, much more profitably than
those that are not. I do not speak as a novice. I
have before me papers on experimental mechanics,
hydrostatics, and explanatory astronomy, which
I set to my pupils at Eton in the year 1836-7
(and, I may add, the actual marks got in the
examination by the late Head Master of Eton,
Dr. Balston, then my pupil). Now, while the
Euclid and the non-Euclid boy will both enjoy
76
the models equally, the Euclid boy will be at
home iu the parallelogram of forces in a mauner
that the other will not be. The figure and its
properties are strange to this latter one ; you have
to be leading him on with hesitating steps, and
slow ; he does not see his way. The boy up in
his Euclid, on the contrary, when you put before
him the principle of the " parallelogram of forces,"
takes it in at a glance ; he sees directly what it
must lead to. This is not a fancy. In answer
to the question from one of my pupils, " What is
the meaning of the parallelogram of force?" I
drew a parallelogram on his paper, and, in a few
words, answered his question. "How jolly," said
he, rubbing his hands. " Oh, do teach us that ! "
And with a little knowledge of trigonometry,
founded on the second book of Euclid, how soon
is a boy at home in the triangle of force, and
the composition and resolution of forces. How
many easy, entertaining, and most instructive pro-
blems is he prepared to do. It is not to be
doubted that one who has read Euclid will bring
conceptions, and a mental training, and a know-
ledge to the subject that will make it far more
profitable to him than it will be to the other.
So, in explanatory astronomy, that most in-
structive and elevating subject, often have I tried
by paper triangles and models to make people,
untrained by Euclid, realize the greatness of
creation, and comparatively in vain. There is a
77
haziness of view, an indefiniteness in their con-
ception that one cannot get over ; the matter does
not seem to come home to such ; but take a set of
boys that are well up in their Euclid, who have a
clear understanding about the nature and proper-
ties of triangles, to whom the thirty- second
proposition is a truth known, felt, and easily
applied. Carry them gradually on from a base
measured on the earth's surface to find the dis-
tance of the moon, up to the fact that a base of
190 millions of miles shrivels to a point in com-
parison with the distance of the fixed stars, they
take in w^hat you say, and listen with wonder, and
(I can say so, for I have seen it) with breathless
awe.
I wonder and should very much like to know if
such charming books as " HerscheU's Astronomy,"
his " Familiar Lectures on Scientific Subjects," or
" Airy's Ipswich Lectures," are read to any extent
with interest and profit by any except those whose
minds are imbued with and trained by the con-
ceptions and reasoning of plane geometry.
Before I close, I would say a word about
Foreign Schools for the middle and lower classes ;
at least, as far as they have come before me.
Last summer, in Switzerland, I learned from my
Swiss Guide, that there was an excellent pensionat
at Sallenches, under the direction of the Freres
Chretiens ; that the numbers of the school had
78
doubled and more, within a year ; that, standing
on its own merits, it had gone far to empty the
Government College at Bonneville, which received
a large subvention from the State. My guide
had a son at the school ; he was going with his
wife the next day to the distrihution des Prix, and
to bring his boy home for the holidays. I asked
leave to go with him ; and the next day I ac-
companied him and his wife in their char-a-banc to
Sallenches. He introduced me to the principal,
clearly an able man. I had also much talk with
the Professors and the boys. I was present at the
closing ceremony of the year, heard their brass
band, listened to their glees and songs, heard
their pieces recited, saw their little plays acted,
and through the local knowledge of my guide, got
the names of those who appeared the most pro-
mising and successful pupils ; of those, at least,
who carried off the greatest number of that in-
exhaustible stock of chaplets and books, that are
distributed on such occasions at French Schools.
It was a very interesting meeting, and I greatly
enjoyed it, though Dr. Balston would have been
surprised and amused, if, in the course of his
Swiss rambles last summer, the local paper of
Sallenches had fallen into his hands, and he had
read as follows : —
"Nous devons mentionner un Suffrage non
moins precieux que ceux de I'assistance toute
entiere. Un stranger, venu du Village de St.
79
Gervais, montrait dans les rangs de 1' assemblee
sa tete venerable, et semblait ecouter avec plus
d'interet que tous ses voisins, ce qui se disait dans
la salle, ou sur le petit Theatre improvise. C'etait
le Eeverend Hewtrey, directeur du celebre College
d'Eton en Angleterre."
I found that some of the most promising pupils
were living up the valley of Mont Joye, where we
were staying, and as they were now dispersed for
the holidays, I found them out in their mountain
homes, and had most friendly and familiar com-
munication with them. They showed me their
cahiers, and explained the methods of instruction
pursued at their school. In fact, they gave me a
dozen or fifteen of their school cahiers filled dur-
ing the last year, and very neat and tidy they are.
Among them are books of drawing, both orna-
mental and geometrical, indeed, their geometrical
drawing is first rate ; their plans, sections, and
elevations, of all kinds of objects, even of com-
plicated pieces of machinery, are perfectly
astonishing ; so much so, that I went, when
passing through Paris, to the great depository of
the Freres Chretiens, in the Eue Oudinot, and got
a large case of their models and appliances for teach-
ing practical geometry and geometrical drawing, for
the use of St. Mark's. (They had carried off the
Gold Medal at the Great Exhibition.) Besides
their drawing books, there were cahiers of Book-
keeping, Arithmetic, the common working of
80
rules, aud rather complicated questions and
problems, Composition, Information about common
things, some facts of Natural History, a little
French grammar, and Physics.
The contents of the caliier on Physics seem to
have been given by dictation from a text-book.
They consist mainly of definitions in graceful
sonorous French phraseology of the properties of
matter : Molecular attraction, cohesion, affinity,
porosity, elasticity, vis-inertiae, specific gravity,
force, &c., &c.
Whether or not the boys took in what they
wrote down, I cannot say. My knowledge of boys'
minds would lead me to fear that it was all sound
to them and nothing more ; and I have high au-
thority for my doubts ; " ra fiev 6v irKnevovanv ol vioi
aX\a Xer/ovo-i," says Aristotlc,*
And if what they wrote down was not taken in,
digested, and assimilated, what was it to them ?
I fear that for one Rugby chef, who can lay before
his pupils an intellectual meal on physics really
nourishing and appctisant, there will be found a
hundred inferior artists who will give their pupils
nothing but — beans !
■"■ The whole sentence from which the above few words are
taken is very worthy of attention in this day ; it occurs in the
Ethics vi. 8 : —
'Enii Kal tovt' av rig (TKt-^aiTO, Sid ti, /jiaOiJuariKOQ fiev ttoIq ykvoiT aV
ao(li6Q Se 7] (pvaiKOQ ov. "H on rd fiiv Si a(paiptatujg tcrrr rwv SI, at dpxai
i? iuntipiag ; Kal rd fxtv 6v TTidTtvovaiv o\ v'loi 'aWd X'tyovai' twv Si, to
Ti itjTiv ovK iiSijXoi'.
81
I liad much talk with the boys about their
school, and their work. They recited to me some
of their pieces, and translated into French the
patois, iu which some of them were written, and
explained the jokes, which had called forth the
hearty laughter of the audience on the speech-
day.
On the other hand, I talked to them of what
interested me. I told them of St. Mark's, and
when they were gathered round me, I told them
the affecting story of our little African boy (see
Appendix E). They were greatly interested in
his history, and asked how he was getting on.
I told them very well; and, though it was not
two years since he was living in a savage country
where he had never even heard of a white man,
he was now able to read and write. I showed
them a letter I had received from him ; they
scanned it with interest, and especially the signa-
ture, " James Chala Salfey," for so he had been
christened by the Bishop of Cape Town on his
way to England.
" Mais il n'ecrit pas aussi bien que vous, Henri,"
said I to an intelligent boy among them named
Henri Kevenaz. '* S'il eut appris aussi long-
temps peut-etre qu'il ecrirait beau coup mieux,"
was his answer. Another day the same little
fellow came to me, saying, " Le petit negre,
quel age a-t-il ? " I said we could not tell —
perhaps ten ; but I would send him his photograph.
82
I mention all these details to show that they
were not at all shy with me or constrained. We
had a good deal of very pleasant intercourse
during the ten days I remained in the valley, and
I got to feel a very great regard for them. — (See
Appendix F.)
To return now to the Sallenches School. Here
is a very favourable specimen of a French School,
with an able Director at its head, and with such
a character, that I found it drew scholars from so
great a distance as Lyons. On the other hand,
there is St. Mark's. The Schools are for about
the same classes of the community ; the French
School is, of the two, for the higher class.
The course of instruction at both Schools is much
the same, with one exception — that the French
School stops short of Latin and Geometry as a
science, and, of course, devotes more time to
other branches of Education, especially those im-
mediately bearing on the boys' future occupations.
The question for decision is this. Do the Latin
and Euclid of St. Mark's leave their seal — their
cachet — on the boys, so as to allow of no doubt
as to their being thoroughly worth the time and
effort which they demand ? I hope my readers
will give me credit for sufficient sincerity and
largeness of heart to be a fairly unprejudiced
judge when I answer, "Most decidedly they do."
There is a strength, a nerve, a development of
mind — a kind of completeness of mental training
83
— a difference of intellectual level in the St.
Mark's boys as compared with those of the
French School, which make me more than ever
sm-e that there is nothing like Latin and Euclid
if you want to produce "well-developed minds,
ready to turn with ease and vigour to any special
pursuits."
I trust that no one will think that in saying this,
I am bearing hard upon a poor school that cannot
speak for itself. Far be it from me to do so.
The school and the scholars greatly interested me.
But, if my readers will call to mind the struggle
with Euclid of a St. Mark's boy, and compare with
this the copying out definitions of the properties
of matter couched in language which a boy could
not, I think, understand, they will feel that it
must be as I have said.
I am not drawing invidious comparisons ; what
I say is prompted solely by the desire that my
fellow-countrymen may feel what is the more
excellent way, and take it.
Such are the thoughts that I have to offer on
the topic of the day.
It will be seen that, while giving in some detail
an account of the attempt to give a Liberal
Education to boys of the working class, I
have wandered at times into the history of my
Eton experiences, so that the two have become as
it were intertwined.
r 2
84
I am not sorry for this. Those who think
deepest will take it, I trust, as a sign of the truth
of the principles of Education advocated, that
they are found to suit equally the highest and the
lowest class ; and those who are now interested in
establishing schools for the middle class may con-
clude, d fortiori, that they will work beneficially
with that class also.
And so may w^e approach that happy time when
the healthiest of all bonds shall connect the whole
of the great English family ; that is, when the
same principles shall be at work through all the
gradations of society, from the highest to the
lowest, to reach the heart, enlighten the mind,
and form the character.
The cry that resounds at the present day is
this, — " The great extension of Political Power
renders the extension of Education necessary,"
I appeal to my readers whether the truer view
of the question, — whether the cry that should have
resounded years ago, — is not this ? " A great ex-
tension of political power is coming and must
come, and, therefore, our country must be pre-
pared for it by judicious Education."
This was the principle, I can safely say, on
which St. Mark's was founded, so much so, that
from fifteen to twenty years back, it has been
pleasantly called, within the sphere in which its
operations are known, the School of the coming
age.
85
In its principle and details, it was founded in
anticipation of a time coming, when in religious
matters the being imbued and formed by the
Gospels would be the stay and defence of the soul
amidst religious doubts and perplexities; and when,
in a political and social aspect, the strength and
well-being of the country would be best secured by
the more prosperous classes holding frankly out
the right hand of fellowship, and the less pros-
perous grasping it firmly and without suspicion ;
in order that, thus united and mutually supported,
all should stand together.
The writer cannot here forbear to adorn his page
with the description of this most happy time —
most blessed state of things, given by the gifted
editor in his preface to that Book — prized and
cherished by the country — in which Her Majesty
has been pleased to admit her people within the
sanctuary of her thoughts and feelings.
His words are as follows : —
" Nor does any wish more ardently than Her
Majesty, that there should be no abrupt severance
of class from class, but rather a gradual blending
together of all classes, caused by a full com-
munity of interests, a constant interchange of
good offices, and a kindly respect felt and ex-
pressed by each class to all its brethren in the
great brotherhood that forms the nation." — (See
Appendix G.)
The School in which it has been the writer's
86
aim to exemplify the working of these principles is
hefore the world. It has been long in action.
Many, far and wide, have evinced deep interest in
the success of the experiment. The men whom
the S3^stem has formed are scattered about the
country, doing their work in the different classes
of the community. " They are our epistle, known
and read of all men."
I do not say that none of them disappoint us.
I have, indeed, heard not long ago of an instance
which has given me sorrow. But by the general
character of the St. Mark's men, by the way in
which they are doing their duty in life, by the
specimens of Englishmen they form, I wish the
system I uphold — of giving a Liberal Education
to the working classes — to be judged.
And now, in closing, the writer would say one
word as to the character of the Liberal Education
advocated in this Essay.
It may not be according to the ideas of the
most advanced writers on the subject ; on the other
hand, readers of the foregoing pages will not
imagine that he wishes to throw any hindrance in
the way of the growth of Education, and of the
Social Progress of the country. All he wishes to
do is to w^rn those who are ready to give up the
old ways, and are somewhat nervously casting
about for new methods, to be careful that they
do not unawares throw aside engines of intel-
lectual and moral value, endangering thereby
87
some of the characteristics which we prize in
Enghshmen.
For himself, after being upwards of thirty years
in the work, he must feel that his time must be
approaching to its close, and he would as a last
word urge on those who will have in their hands
the charge of guiding the Education of the next
generation, " To prove all things, and to hold fast
that which is Goon ! "
Finis.
89
APPENDICES.
Appendix A.
I WAS exceedingly amused last school-time when hearing the
'' Gentil-homme bourgeois/'^ inimitably acted by Frank and
Henry Tarver, and their pupils, at being reminded that
Moliere ridicules as arrant pedantry what we have practised
in all seriousness. 1 mean the custom of analysing how the
different vowel sounds are produced, and how the consonants
are articulated. I think Moliere has here let his wit run
away with his good sense. We find it to be an admirable
exercise, and very amusing to little boys.
When you tell them how this or that articulation is pro-
duced, you see each boy testing the rule with his own tongue,
lips, and teeth. It is also the best corrective I know for
provincial mispronunciation. And how often have I seen
a non-scientific teacher teasing a young child by telling it to
say cat, not tat ; how much better, and more instructive, to
tell the class that the hard C is produced by raising the
middle of the tongue towards the roof of the mouth. That
the child's mistake is, that, instead of doing so, he puts the
tip of his tongue to the roof of his mouth, which is the way
to pronounce t. To prove the truth of the rule, you call for
a spoon, and, gently holding down the tip of the tongue with
the spoon, you tell the child to say cat, and he says it to his
own surprise, and \h.Q delight of the others who are watching
the experiment.
90
Appendix B.
My Eton experience enables me to give a few useful hints
in the matter of writing. To superintend the lower school
writino" is an occupation in which I take great delight.
A most important element of success in every branch of
instruction is this — to make a boy respect what he is doing.
No one, in my time, has been a better friend to writing-
masters than Lord Palmerston. It may be remembered that
some years ago, in the House of Commons, he extolled the
old and distinct writing of some eighty years back, in whicli
each letter might be distinguished when deprived of its sup-
porters. The authority and countenance of Lord Palmerston
have contributed greatly to our success in teaching writing in
the Lower School at Eton. What Lord Palmerston thought
important is entitled to respect in the eyes of an Eton
Lower School-boy. Many a one has taught himself very
good and distinct handwriting in consequence.
I sent one of the Lower School copy-books (that of a little
fellow of nine years of age) with his photograph to Lord
Palmerston, and received a speedy answer from his Private
Secretary, saying that he was desired to say that " Lord
Palmerston thought B 's handwriting remarkably good,
and especially on the page which Lord Palmerston had
doubled down, the letters being well and distinctly formed,
and there being none of those fine strokes which prevent the
eye from catcliing the form of the letter." This book, along
with Mr. Evelyn Ashley's letter, itself a model of good writing,
is preserved in a glass-case, and is shown to successive gene-
rations of Lower school-boys. " This is the writing that
Lord Palmerston admired !" " This is the page which Lord
Palmerston doubled down ! " The book has been a treasure
to us.
If the boys are sitting in a good attitude, and pressing
equally on both nibs of the pen, (Mr. Harris's rule ensures
91
this,) a single Master's eye can superintend a large class. I
read a story-book out to them while they are ■writing under
the eye of their writing-masters^ and make the story do duty
in insuring attention by simply leaving off when any one is
sitting improperly or looking about. " I leave off because
is not writing." That is quite enough to brace the
whole class up to attention.
In writing, as in all branches of instruction, individualize
and classify. We divide the boys periodically into Classes 1 ,
2, 3. We let Class ]. go when they have had half-an-hour's
writing. Class 2 goes at the end of three-quarters of an
hour, and Class 3 at the end of the full hour. Any other
encouragement that may suit the discipline of the school
could be adopted ; but inspect periodically, and classify.
I got some useful hints and appliances for teaching writing
from the Paris Exhibition. In the Educational Department
I saw some curious copy slips of indented metal. I made the
acquaintance of the inventor, Mr. Sinet, and got a supply
of his indented metal plates. His theory is, that a learner
by following the indented letters with his pen is obliged to
form them right ; a sponge prepares the plate for another
writing lesson.
I also got a model hand in the right pose for writing, and
some inventions of his for keeping the hand in a proper
position. They have been of service to some of the younger
boys, and are very popular. We call them " Sinef s Yokes."
I called on the old man again last Christmas when in
Paris. He was delighted at the popularity of his inventions.
When I said to him, " Void I'ecriture de mon eleve avant
qu'il ne se soit servl de la machine Sinet, void sou ecriture
apres qu'il en a fait usage," it was almost too much for him.
I got more " Yokes," and some hints : —
One of these was to practise what he called '' la gtjmnas-
tique des doigts." This consists in doubling up the last
two fingers of the hand, and straightening the two writing
fingers and the thumb, so as to bring their points together, —
92
to place their points against the palm of the left hand, and
squash them, letting the knuckles give way ; this was to be
repeated frequently. The wrist is not to be bent in writing,
that the muscles of the fingers and thumb may have their full
play ; to this end the right arm should rest on the table mid-
way between the elbow and the point of the fingers that are
supporting the hand on the paper, and the root of the hand
should not rest on the table, but be raised just sufficiently
"pour quun petit souris hlanc puisse passer dessom ! "
Appendix C.
I will add one word to what I have said about arithmetic,
in memory of our celebrated visit to Her Majesty's ship
" Pembroke." We met an old Naval Instructor on board ;
he told me he owed all his success as a Teacher to one kind
of sum, which he named, from the inventor, " Ranklin."
It was to put down a sum of money, £ s. d., and multiply
it by the odd figures 3, 5, 7, 9, 11 ; and then, by the same
figures, in an inverse order, 11, 9, 1, 5, 3. If the final
results agreed, the sum was right. The odd figures, of course,
to preserve the farthings to the end. Examples of weights
and measures may be dealt with in the same way.
I am disposed to think, and the St. Mark's Masters agree
with me, that this kind of exercise, worked off quickly at odd
minutes, has been of use to the School, that it has taught the
boys quickness and accuracy.
It has this to recommend it, that it is so easily set ; any
boy can set himself a " Rauklin," and the consciousness that
if there is one error it all goes for nothing, and that he will
have to do it all over again, helps, we think, to give that
earnest and sustained attention which is requisite for ensuring
correctness.
Appendix D.
And here I would put in an admission that, in addition to
(not instead of) those mental habits which are formed by the
study of language and geometry, the habit of exact observation
93
might be cultivated witli great advantage. This, no doubt,
is what the advocates of Botany aim at, and I think they are
quite right in choosing that particular science. The objects
of observation are accessible without expense or difficulty, are
infinitely various, beautiful, and interesting ; and the obser-
vations admit of perfect precision with the simplest possible
apparatus. Also the pupils incidentally learn something of
the principles of classification, besides acquiring information
which may turn out to be very useful. In the same way, in
suitable localities, I should think Geology might be taught
with great advantage. Whereas Chemistry, Electricity, &c.,
can hardly be taught to boys otherwise than in the way of
superficial information.
I think, also, a great deal might be said in fiivour of
elementary Physiology, even icitJiout rats, for the higher classes
of middle schools. Such a book as Huxley's Lessons on
Physiology (which is suitable for either boys' or girls' schools),
in the hands of an intelligent teacher, might be very useful.
And here is a case where a knowledge of facts as such is of
real importance ; besides, we have got in us the natural
faculties of wonder and admiration ; and no one who is totally
ignorant of the structure of his own bodily organs can have
experienced the full exercise of these faculties.
Only let it be always remembered that nothing ought to
supersede the solid foundation laid by the old studies, and
that in all studies, old or new, it is the training of our facul-
ties which should.be the primary object, though, when useful
information can be also acquired by the process, so much the
better.
Appendix E.
It may not be uninteresting to my readers if I refer to the
incidents of this little boy's story ; nor is it quite out of
place, for it bears on the main subject of my Essay, the value
of a Liberal Education to every class. And I am unwilling to
lose any opportunity I have of showing how such Education
94
nets on those whose circumstances and condition would point
them out as extreme cases.
This made me, in a former tract, refer to tlie little Russian
boy taken prisoner after the battle of the Alma, and brought
to this country by Col. Brovvnrigg, and put to St. ]\Iark's
School. What is he now ? An apprentice in the Mercantile
Navy, nearly out of his time, who brings home the highest
character from his captain and the shipowners for being a
smart and active seaman, and " being free from those vices
which that class of men are much addicted to." He has every
prospect of rising in his calling.
And not only is he an able seaman, who does his duty in a
gale of wind, but he can sit beside the bunk of a sick messmate
and read a chapter in the Bible to him, and tell or read to him
stories of his school-boy days, till the tear gathers in the sick
man's eye, and he says, " Oh, that I had been brought up
so!"
Whenever his ship comes into port from China, Singapore
Calcutta, &c., as soon as he gets leave, down he comes rushing
to the old School, to re-visit the old scenes, and renew his
acquaintance with his former schoolfellows. Our worthy
Russian seems to enjoy nothing much more than to sit beside
his old and well-loved Schoolmaster, ]\Ir. Blythe, and listen to
him giving a lesson to the new generation of St. Mark's boys.
And now for the story of our little African. He belongs to
the Galla tribe, who may be found on the south-west of
Abyssinia : they are a very beautiful race, and, in consequence,
fetch an immensely high price in the Turkish slave market.
The men of the tribe are great warriors, and during his
father's absence on some expedition, the Turks kidnapped
our little boy, and. carried him oflF to the coast some six or
seven hundred miles distant I believe. Here he was shipped
for the port of Muscat. Before they landed, by God's good
providence, an English cruiser (the "Pantalon") caught sight of
the slaver. The Turks (our little fellow tells us) put their
money into their turbans and took to their boat ; and the slaves,
95
consisting of women and children, were rescued. Captain
\V. F. Hastings (then First Lieutenant of the " Pantalon ")
undertook the whole charge of one of the boys thus saved.
He has taken the greatest care of him, and brought him to
England, and has put him to St. Mark's School. Here, then,
is a new and unexpected case upon which to try the effect of
a Liberal Education. Two years ago the boy was an untutored
savage in the interior of Africa ; he has been about one year
under training at St. Mark's, and is now a thorough English
boy, and takes rank among his compeers. The school has
got hold of his affections, and is moulding his character. He
is an intelligent boy, with a sweet disposition and reverent
spirit. He is as much interested about getting on in school,
doing his evening lessons well, and getting good reports, as
any boy in the School. His instincts are gentlemanly ; he
cannot bear to be taken out from among his companions for
any special notice or attention. To be seen to advantage, he
should be seen at school, or in the play-ground with his school-
fellows. He is a great favourite with them all, and, indeed,
with everyone who knows him. His natural disposition is so
sweet, that he must have been greatly beloved at home. His
own sentiments, and little incidents of his former life which
he has told me, prove it. His parents have not the remotest
conception where he is. They must have known that he was
carried away by the Turks, so that slavery would be the
natural consequence ; and when I look at him in church,
amongst the other boys, with his surplice on — for he is one of
our choristers — and observe his reverent demeanour in chanting
the Psalms, or following the lessons in his Bible, I cannot but
feel an indescribable emotion of gratitude that the dear little
fellow is not now in a Turkish seraglio, but that we have him
safe in the bosom of St. Mark's School, to bring him up as a
Christian boy.
When I saw in the telegram from Abyssinia a few weeks
since that the " Gallas " were one of the hostile tribes that
were leagued on the south side against the unfortunate and
96
absurdly mcomprehensible Theodore, the idea occurred to me
of printing an account of our " Jem/' and sending it, with his
photograph, to our young St. Clark's Serjeants and corporaJs
in the army in Ahysr^inia ; for many of our boys take to the
army. I hear of them as young Serjeants in a very short
time after their enlisting. Their education makes them be
picked out ; and they all seem very ready to volunteer for
foreign or special service.
Now, if in the course of events they should come in contact
with the Galla tribe, I know that they would do their utmost
by means of the photograph, and of his name Chala, and his
father's name Salfey, to bring him, if possible, to the knowledge
of some of his kindred ; but this may be a wild idea.
Captain Hastings' hope is that the boy may grow up to be a
well-educated and good man, and ciualified for Holy Orders
that so he may be ordained as a Missionary. In which case
Captain Hastings hopes to return with him to his own country,
and go with him into the interior of Africa to search for his
tribe and parents ; that our boy may, according to his own
great wish, hope, and prayer, " tell his father and mother
about Jesus Christ."
Morally and intellectually, I see no reason to doubt about
the fulfilment of the desire of both ; nor do I at all see why
we should not hope to rear our Jemmy to man's estate. He
has passed through two English winters, and is in excellent
health. God grant this blessed conclusion to the dear boy's
romantic history, and may St. Mark's do its part towards
bringing about the fulfilment of the pious hope of his
protector and friend.
Appendix F.
Nor, indeed, has this intercourse ceased. The cahiers given
to me by the Sallenches' school-boys have been handed round
St. Mark's School, and are greatly admired. Their neatness I
hope will be imitated.
I have before me at this moment letters which " Le petit
negre" and one of his school-fellows, have written to Henri
Revenaz, to accompany their photograph which they have
had taken for him. These I am to translate, (for our African
has not, of course, begun French, nor has the other, though
learning it, yet attempted a French letter,) and under the
two figures in the photograph 1 am to write in French,
" White," " Black," so says our little negro.
It enters very largely into my idea of a Liberal Education
to draw the boys out of themselves, and to give them
external sympathies and wide-spread interests. With
this view I have encouraged intercourse and correspondence
between them and Bishop Patteson's Melanesian boys. Our
boys know his by name, have sent photographs and presents
to them, and have received letters from them.
And now, while on this subject, I may add, that not only
do our boys know about and correspond with lads living
in the mountains of Savoy, but I hope, before two years are
over, that the acquaintance will be a, personal one, and that
the Savoyards of the Pensionuat of Sallenches will accom-
pany the St. Mark's boys in their mountain excursions.
Poor untravelled English boys living in a flat country, who
have seen but flat maps with a little shade for mountains,
what can they know of Physical Geography except in words ?
But when I have taken them up the enchanting valley of
Montjoye, and have led them up its wilder and wilder fast-
nesses till they have stood on the rugged " neck of the Bon-
homme," henceforth, indeed, the chain of the Pennine
Alps will have a different meaning for them than it has
hitherto had.
This most pleasant prospect we have, for the offer of the
free use of three large " Granges " for the St. Mark's boys
has been made me in three choice localities in Swizerland,
St. Gervais, Chamonix, and Comballaz, by prbprietaircs who
wish to send their sons to St. Mark's.
Indeed, I may here say what I think will interest many an
English family, that the motherless grandchildren of one
G
98
who is known to many as a much esteemed guide, " Michel
Alphonse Couttet," are coming to St. Mark's as soon as tliey
are old enough. I am told that the thought of this was the
comfort of their poor mother on her death-bed.
I need hardly apologize for wandering into these details. I
am giving the account of an attempt to give a Liberal Educa-
tion to boys of the working class, and these summer ex-
cursions are, as my friends know, a very prominent feature of
my system. I have only to tell those friends who have read
with kindness the visits of St. j\Iark's to the '' Pembroke,"
&c., that, if this excursion takes place, they may count
upon having a new St. Mark's Story, — "St. Mark's in
Switzerland,"
Appendix G.
The idea of the various classes of the Nation being
drawn into one great English brotherhood is on e that has
been long uppermost in the writer's mind. Th is will be seen
in the following Address, which he circula ted in the year
185.9, along with copies of the account of St. jNIark's School,
araono; the Parochial Schoolmasters of Enicland, throu2;h the
hands of their Clergymen. It is reprinted here in the hope
that it may do good : —
An Address to Parochial Schoolmasters, circulated in
1859. — This paper will probably be put into your hands with
a pamphlet, called " An Account of St. Mark's School,
Windsor." I hope that you will not think I am taking a
liberty if I ask you to peruse tlie tract ; and, in connection
with it, point out to you, that it is in your power to help
forward a great social movement — full of hope for the future
— which may be called the distinctive feature of our day.
I mean the increasing community of feeling and interest
99
amono;st the different classes of society, which is gradually
drawins; them to2;ether, and is o-ivino; to Ensjland more and
more the character of one large family.
About the fact, thank God, there can be no doubt. And
of the causes which conspii-e to bring about this result, none
certainly is more influential than the personal character of the
Queen of England, considered both as a Sovereign and a
Mother.
There are Physical causes, no doubt, which it is impossible
to overlook. The great moral engine^ however, is doubtless
the thought and care which very many of those who occupy a
position in the country, corresponding to that of parent in the
family, bestow in furthering the well-being of their de-
pendents. The great Landed Proprietors of the country,
beginning; with the Highest Personao;es in the realm,^Q;ive
constant proofs of this feeling. So also do the great Manu-
facturers and Tradesmen of the country : tlic ]r.-. vision which
many amongst them have made for the social improvement of
their dependents is proverbial. A similar kindly and parental
feeling is also widely extending itself between Merchants'and
Professional men and their Clerks ; and instances have come
within the writer's knowledge of its exercise in public offices,
between the heads of departments and their subordinates in
the office.
The friendly relation which has long existed between the
Clergy of the country and their people is too obvious to
allude to. But I may mention another phase of English life
which has been revolutionized by the action of friendly sym-
pathy between classes — I mean the English Army. Thirty
years ago, a regiment was little more' than a great machine
organized to produce a certain result : from a great machine
it is now transformed into a large family. The officers know
their men individually. Their moral and religious well-being,
— their health — their social recreations — their manly sports
—their families — all occupy much considerate thought on
their part. The men can see this, and meet it' with a feeling
G 2
100
of loyal attachment to their officers. The existence of this
friendly relation between officers and men is well known to
those who have the opportunity of observing the inner life
of a regiment ; and its effect was abundantly evidenced in the
endurance, gallantry, and devotion exhibited in the last two
wars in which this country has been engaged.
In the Navy, with the rough materials of which a man-of-
war's crew is made up, it might be supposed that this kindly
regard and fellow-feeling must give way to a sterner rule ;
but the contrary is the fact. The martinet-rule is fast dying
out, or has died out, of the service ; and those vessels will be
found in the highest state of discipline where the friendliest
feelinss exist between the officers and men.
You will see this statement exemplified in a little pamphlet
(which will possibly be put into your hands along with the
account of the School), giving the history of a week which
some of the boys of St. ]\I ark's School were privileged to
spend on board a man-of-war. The story has not only been
read with pleasure in this country, as an illustration of the
foregoing statement, but has excited a lively interest wherever
it has been read on the Continent — as giving an agreeable
peip into an English man of-war, and as detailing occur-
rences which (it has been frankly observed) could not have
happened on board a ship of war belonging to any nation in
the world but England.
This testimony is important as showing that the bond of
family feeling, which rendered the occurrences of the narrative
possible, is thoroughly English.
it will be seen from these various instances that there is
hardly a ramification of English life into which the working
of this principle has not in some measure penetrated. It is
the bond which keeps the whole machinery of English society
together and in good working order. If there is any part
that does not work well, if any hitch occurs that throws any
part of the machine out of gear, or brings it to a standstill,
it is because this bond is displaced, or wants tightening.
101
My object, however, in addressing you is mainly to trace
the working of this principle in the economy of schools.
There has been for several years, in the great schools of
the country, and those private schools which have the largest
share of the confidence of parents, an increasing cordiality
of feeling, and friendliness of intercourse, between tutor and
pupil, which has been followed with the happiest effects.
The very great confidence which the public schools of
England enjoy at the present time, and the high esteem in
which they are held on the Continent, arises mainly from the
influence on the formation of character of this mutual good
understanding, confidence, and sympathy existing between the
tutor and the pupil.
It is evident that not only is the freedom of mind and
happiness of the boy at school justly attributable to a good
understanding with his tutor ; this must also be the main-
spring of the happiness and comfort which the tutor himself
has in his work. Certain I am, that this friendliness of
feeling between tutor and pupil is what parents most desire ;
and those tutors are the most valued in our public schools and
elsewhere who sympathize most heartly with their pupils.
Will it be said that this kind of parental relation between
tutor and pupil is very possible with those who have been
well brought up at home, who are well toned, and responsive ;
but that such a relation could not exist between the Master
of a National School and the kind of children which he has
to educate ?
Let me say in reply, that it is now about eighteen years
since, observing the happiness and unaffected manliness of boys
brought up under the culture I describe, I first asked myself,
Must this be confined to the rich ? What would be the efiect
if a similar relation were established between the teacher
and the taught, at schools for the children of the poor?
What if their boyhood were also made a joyous one, by kind
usage and friendly confidence on the part of the Master ?
Would it unfit them for the life of toil in prospect for them ?
102
I resolved to try the experiment. The history of St. Mark's
School is the history of that experiment ; and an experience
of above thirteen years warrants me, I think, in saying,
that the same principles of treatment which are pursued at
the great schools of the country, with the sons of the gentry
of the land, (viz., vigorous mental cultivation, joined with
trustfulness and cordiality in intercourse with them,) may be
safely pursued with the children of the poor ; and that, far
from unfitting them for their position in life, such training
will, under the Divine blessing, make them useful, simple-
minded, well-conditioned, and pleasant to deal with ; in a
word, valuable men in all the relations of life.
It is a strong confidence in the truth of the above, which
leads me to invite you to read the tract on St. Mark's School.
If you have established such a relation with your scholars as
is there described, you will learn with satisfaction that others
are pursuing the same plan, with comfort to themselves. If
you have not hitherto contemplated the possibility of being
on such terms with your boys, I trust you will be encouraged
to try this method of dealing with them ; and be assured,
that it will prove not less full of happiness to yourself than
of benefit to your scholars.
S. HAWTREY.
Mab7 S. Rickebbt, Printer, 4a, Walbrook, Mansion House. E. C.
5 2 4: Q
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