" You must go
regularly
through
this," said his father, taking down a
book from the book-case.
this," said his father, taking down a
book from the book-case.
Childrens - Frank
hathitrust.
org/access_use#pd-google
? FRANK.
255
taking angles, she did not know what
that meant, or of what use it could be.
" Mary," said Frank, " you would
be more curious about it if you knew
what I know. "
" And what do you know, Frank,
my dear 1" said Mary.
At this question he felt his know-
ledge shrink into a small compass, and
he answered,
"I cannot say that 1 know much;
but, Mary, look out of the window at
that tower at a distance. You see it?
Well! / believe, mind I say / believe,
I do not say that I am sure -- but I
believe that he could, by taking angles,
tell you how high and how broad it is,
without going nearer to it than we are
now; and I think that he could tell
how far off it is from hence, and how
far from that tower to the mountain
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 256
FRANK.
opposite, or any other place that he
could see at ever so great a distance
with his telescope. "
" My dear Frank, do you believe
this? " said Mary.
" I do, for I was present," persisted
Frank, " when my father asked him
the height and distance of some moun-
tains, as far off as I could see through
the telescope ; and after looking through
his glass, and making some triangles and
calculations, he answered and told exactly
how high they were, and how far distant. "
Mary thought this was impossible;
but she said,
" There are many ways of doing
things, which I do not yet know ; and
this may be possible, though I cannot
conceive how it can be done. "
" We shall see when the good-
natured engineer comes," said Frank.
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
257
His father asked if he remembered
the definitions which he had learned
of an angle, and a right angle, and a
square, and a triangle. He told Frank,
that unless he had perfectly distinct
ideas of these, he would not be able to
understand what he wished to learn
from his good-natured engineer. Frank
took his father's advice, and first he
showed Mary what is meant by an
angle, or a corner; he drew a square
for Mary, and triangles of different
sorts, and he showed her which was a
right-angled triangle: teaching her,
he found, refreshed his own memory.
Mary copied the figures which he had
drawn for her, and then cut out similar
figures in paper, without looking at the
drawings, that she might be quite sure,
that she had a clear recollection of
what she had learned.
z3
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 258
FRANK.
The engineer arrived, while Frank's
drawings, and the bits of paper, which
Mary had cut into squares and triangles,
were lying on the table.
" I know what you have been doing
here, my little pupil," said he, smiling
at Frank; " you have been preparing
for me. "
" Yes, sir," said Frank, " and I
believe I know them all; ask me any
questions you please. "
"Show me an angle, then," said
the gentleman.
Frank touched the corner of the
square.
The gentleman desired him to
show him each of the angles in the
square and in the triangle; and Frank
did so.
Then, laying the square and the
triangle before Frank, he asked the
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
259
names of these figures, which Frank
answering rightly, he asked,
" What sort of triangle is this ?
Frank answered, " a right-angled tri-
angle. "
"Show me what you mean by a
right angle. "
Frank showed what he meant, first
in the triangle, and afterwards in the
square.
The engineer then took from his
pocket a flat-hinged rule, and asked
Frank if he could with that rule show
him a right angle.
Frank opened the rule, so as to form
with it two sides of a square, and
pointing to the corner where these two
sides met, he said this was a right
angle.
" Here is a pencil: try if you can
. draw a right angle. "
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 260
FRANK.
Frank drew a horizontal straight
line.
"Now," whispered Mary, "I know
what you are to do next; you will draw
a perpendicular line in the middle
of that, just as if you were going
to draw the wall of a house. Yes,"
said she, as he drew the line, " I knew
that. "
"Hush, little magpie," whispered
Frank's mother.
Frank pointed to the corner where
the perpendicular and horizontal line
joined, and said, that was a right angle.
" Can you show me another right
angle upon this horizontal line? " said
the engineer. " Do you see only one,
or do you see two 1"
" I see two," said Frank; and he
pointed to the corners on the right
hand and on the left hand of the per-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
261
pendicular line, where it joined the
horizontal line.
The engineer put his hand upon
Frank's head, and said, " Now I am
satisfied that you know what is meant
by an angle, a right angle, and a
triangle.
Mary whispered something to Frank's
mother at this time, who smiled, and
said to the engineer, " Mary is surprised
that you ask Frank so often to show
you an angle in different things. "
"Yes," said Mary, "as if you could
not believe he knew it. "
" I am very careful on these sub-
jects," said the engineer, " for I know
children are sometimes taught very in-
accurately, and then they have such
confused ideas, that it is impossible to
make them understand what is meant.
A young lad was once sent to me to
be turned into a surveyor, who could
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 262 FRANK.
for some time understand nothing
that I endeavoured to explain to him;
because, though he talked of an angle,
and a right angle, he did not know
clearly what was meant by either; in
short, he mistook a triangle for an
angle. Had he confessed to me his
ignorance at once, I could have cor-
rected his error. "
" Poor boy, he had been ill taught,
I suppose," said Frank.
" You have been well taught, and
ought to be thankful for it," said the
engineer.
" Would you be so good as to come
to this window, sir," interrupted Frank.
" Do you see that tower at a distance?
Could you by taking angles, as you
stand here, find out its breadth and
height, without going to measure any
part of it, sir ? "
" I could," said the engineer.
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
263
" There, Mary! I was right," cried
Frank. " But now, sir, will you be
so very kind as to explain to me how
it is done ? "
" I would be so very kind, if I
could," answered the good-natured en-
gineer ; " but I cannot, I should only
puzzle you. If I were to attempt to
explain it, you could not understand
me.
" Oh, pray ! pray, sir, try ! " said
Mary, " I dare say Frank would un-
derstand you. "
" If you would only try," said
Frank, " I will tell you honestly, after-
wards, if I don't "
" I am sure you would," said the
engineer; " but I tell you beforehand,
that it is impossible. "
Frank looked at his father, hoping
that he knew him better; and that he
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 264 FRANK.
would say that it was possible. His
father shook his head, answering,
" It is impossible, my dear, till you
have learned a great deal more. "
" Oh, I am very much disappointed,"
said he, " for I expected that I should
have known all these things this morn-
ing. "
" But could you reasonably expect,
my young friend," said the engineer,
" to know in one morning, in one
hour, in one quarter of an hour, what
I have been many mornings, many
days, not to say years in learning? "
" Certainly not," said Frank, laugh-
ing, " that would be rather unrea-
sonable. "
" Then must Frank wait till he is
grown up quite, mamma? " said Mary.
" No, that is not necessary," said his
mother.
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
265
" How old must he be, mamma,
before he can understand them ? "
" How wise must he be, you should
ask, my dear," said his mother; " for
his being able to understand such
things will not depend upon the num-
ber of years he has lived, but upon
what he learns in those years. "
" True, madam, there is Mr. ,
What's his name ? the gentleman who
rode with us the other day, Mr. Rogers,
who has lived more years than I have,
but you saw that he did not understand
these things," said the engineer.
" Nor wish to understand them,"
said Frank: "that did surprise me. "
" And there is the gardener's boy,
Frank," said his father, " who is not
many years older than you are, and
he understands that which you want
to know. "
vol. i. 2 a
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 266
FRANK.
" Does he indeed ? " said Frank.
M Yes ; now I remember seeing in his
book drawings of triangles and circles,
and I could not guess of what use they
could be. "
" His father said, as you told me, that
he was learning mathematics," said
Mary, " and trig "
" Trigonometry, I suppose," said
the engineeer; " which, translating the
Greek word into English for you, my
little lady, means the measuring of
triangles. "
" Of triangles! " repeated Frank,
taking up one of the paper triangles
which lay upon the table, and looking
at it " Can measuring this have any
thing to do with the measuring that
tower ? "
" Yes; a great deal to do with it,"
answered the engineer. " I cannot ex-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK. 267
plain to you how; but I may, without
giving you any false ideas, tell you in
general, that the power we possess of
measuring that tower, and the most
distant objects that can be seen on
earth, and not those only on earth,
but those in the heavens, depends upon
our understanding the properties of a
triangle. "
" If the gardener's boy has learned
trigo-no-me-try," said Mary, " why can-
not Frank? "
" Is there any quick way of learn-
ing it ? " asked Frank.
" No, there is no quick way," said
the engineer.
" You must go regularly through
this," said his father, taking down a
book from the book-case.
" What is it? " cried Frank, seizing
and opening it. " The very thing I
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 268 FRANK.
saw with the gardener's son, Euclid's
Elements of Geometry. "
" A square is a figure that has
four "
" Oh, we know that," said Mary,
lookiug over his shoulder.
" But how shall I understand these
drawings of circles and triangles ? " said
Frank: " the line a b is equal to the
line c d ; proposition the 1 st, propo-
sition the 2d; and axiom the 1st,
axiom the 2d: almost as hard sound-
ing and difficult as the beginning of
the Latin grammar. "
" Yes," said his father, " in the be-
ginning of all sciences there are dif-
Acuities; a sort of grammar, which
must be learned, before you can get
on to the smooth and pleasant part. "
" But in this book, and in this
science, you will find," said the engi-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK. 269
neer, " that each step leads on securely
to another: not one will ever be lost. "
" That is a comfort," said Frank.
" But," said Mary, <<I hope we
may look through the telescope, and
see the men and mountains standing
on their heads. "
The engineer promised that she
should. But he had some business to
do, before he could comply with her
request; and, in the mean time, the
young people were desired to go out.
While Mary went to put on her
bonnet, Frank was left in the hall by
himself. Several of the engineer's
books and instruments, which had been
taken out of his carriage, were lying
on the hall table, and, among others,
one of the telescopes belonging to his
theodolite.
Frank ventured to take up this tele-
2a 3
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 270
FRANK.
scope, which he ought not to have
touched; he thought, however, that
he could not do it any harm by just
looking through it. He took off the
brass cover at one end, and slid back
the brass slide at the other end, and
looked through it at the tower, and at
some men who were at work in a distant
field.
" What can be the reason," said he
to himself, " that these men seem to
stand on their heads? This telescope
looks as if it were quite the same as
my father's. I wish I could find out
the reason. I should be so glad to
prove that I could understand it,
though they all say I cannot. "
He saw some very slight wires, as
he thought them, behind one of the
glasses ; and as there were none such in
his father's, he fancied that these i had
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
271
something to do with the secret, which
lie longed to discover.
" I know how to unscrew this
glass," said he, "I will not do it the
least harm. "
He unscrewed the glass, and, looking
into the tube, he could scarcely see
what had appeared to him to have been
wires. He put his hand in to feel for
them. There were no wires, there
was nothing that he could feel -- no-
thing ! except some very slight cob-
webs. These threw no light on his
difficulty; he blew them away, and,
despairing of making farther disco-
veries, and unconscious of the injury he
had done to the instrument, he screwed
on the glass, and left the telescope, as
he thought, in perfect safety, exactly
where he had found it on the table.
Frank, having no idea that he had
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 272
FRANK.
done any mischief, did not even men-
tion to Mary his having looked at
the telescope. She put it out of his
recollection by beginning to talk to
him, the moment she saw him, about
the parrot's cage, the door of which
had been broken; and Mrs. Catherine,
who was now standing with that broken
door in her hand, was anxious that it
should be mended immediately.
Mary had undertaken for Frank, that
he had both the power and the in-
clination quickly to accomplish her
wishes.
Frank instantly ran in search of the
osiers, that were necessary for the work.
As there was no one in the house-
keeper's room, except Mrs. Catherine,
his mother gave them leave to do the
job there, and to take the osiers to the
cage, instead of carrying the cage to
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
273
the osiers. She, moreover, was so
good as to promise, that she would call
them, as soon as the engineer had
finished writing his letters, if any thing
entertaining should be going on.
The repairs of Poll's habitation cost
Frank more trouble than he had ex-
pected ; as it often happens, he found,
that which he thought could be done in
five minutes, required five and twenty.
But the door at last turned easily
on its ozier hinges, and Poll was just
replaced in her cage, when their atten-
tion was suddenly roused by hearing
somebody sobbing in the passage.
Mrs. Catherine opened her room door,
and they saw a black boy, standing
in a corner, crying. Mrs. Catherine
asked what was the matter. The
boy began to stammer something in
broken English ; but before he could
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 274 FRANK.
get out any thing intelligible, a
man, whom Frank recollected to be one
of the engineer's assistants, came into
the passage, and told Mrs. Catherine
that she need not waste her pity upon
this boy.
" No use, ma'am, listening to
him, or asking him any questions,
for he is a sad liar--never can
speak a word of truth. His master,
who is the best of masters, has done
all he can to cure him, and so have I.
It was but last week he was guilty of
a falsehood, and his master said, and,
begging you pardon, ma'am, I swore,
he should be parted with the next
lie he told; and he has told a He
now, and he is to go; that is what
he is crying for, and nobody can help
him. "
" Nobody can help him to be sure,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
275
if he is a liar," said Mrs. Catherine,
who held liars in just abhorrence.
"But are they sure he is a liar? "
said Frank.
" He cannot deny it," said the man.
The Negro boy went on sobbing;
and when Mrs. Catherine asked if he
had any thing to say for himself, he
could only say,
" Me liar last week, ma'am, yes;
to-day, no liar--no lie! "
" Oh, if you were a liar last week,"
said Mrs. Catherine, "who can know
that you are not telling a lie this mi-
nute? "
The boy turned his face to the wall,
and cried more violently than before.
" I can't help it, nor nobody can
help it," said Mrs. Catherine : " I have
nothing to say for liars. Miss Mary,
master Frank, you had better go away,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 276
FRANK.
if you please; you have no farther
. business here. "
" But," said Mary, turning back, as
they reluctantly went up stairs, " I
think he is telling the truth now ; are
you sure, Catherine, that he has not
told the truth to-day? "
" Pray, good Catherine, find that
out, will you," said Frank.
Mrs. Catherine, whose countenance
now looked severe, as it always did
when she thought a liar stood near her,
said she must leave it to his master,
who knew his character, to settle the
business; it was not proper for her to
interfere. " When a boy was a liar, and
told a lie last week, who can know,"
said she, "that he is not telling a lie
this minute? "
"But, since he confessed that he
told a falsehood last week," said Frank,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
277
"perhaps--do, do, good Catherine
inquire into it. You know papa says
you are a just woman. "
" Well, well, go you both of you
out of the way, in the first and fore-
most place, for I am sure your papa
and mamma would not be pleased to
see you here, meddling with such things
-- so up stairs this moment. "
Up stairs that moment they went,
and Frank followed by Mary, who
could hardly keep pace with him,
ran to the library, where he had left
the engineer writing: but he was
gone.
" Well, Headlong ! " said his father,
when Frank threw open the door,
"What now? "
" And why do you look so terribly
disappointed, Mary," said Frank's
mother: " I told you that I would call
vol. i. 2b
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 278
FRANK.
you as soon as the engineer could show
you his telescope. "
" Oh, it is something of much more
consequence," said Mary.
Frank told all they had heard ; " and
though Catherine says it is not our
business, yet it is every body's busi-
ness to see justice done, especially to a
poor black boy, who cannot speak for
himself, is not it, papa ? " said Frank.
" I will go and find out that good-na-
tured master of his, and ask him to go
to the bottom of the affair this minute. "
Frank's father held his hand, how-
ever, and prevented him from going;
for though he liked his eagerness to
have justice done to the Negro boy, he
thought, he said, that this boy's master
must know his character better than
any stranger could; and that his master
would in all probability take care to
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
279
find out the truth, without Frank's in-
terference.
" But," said Frank, " they are going
to turn him out of the house directly.
Only just let me find the engineer,
and tell him this. "
Here he is, my dear," said Frank's
mother, " now do not be in a hurry.
Speak distinctly: for I could hardly
understand your story, you spoke so
very quickly. "
The engineer came into the room
with his telescope in his hand; that
telescope with which Frank had med-
dled. A sudden flash came across his
mind : a thrill came all over him.
" Miss Mary," said the engineer,
" I am sorry that I cannot keep my
promise to you, yet; but I must first
set to rights something which has been
broken in my telescope. The cross
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www.
? FRANK.
255
taking angles, she did not know what
that meant, or of what use it could be.
" Mary," said Frank, " you would
be more curious about it if you knew
what I know. "
" And what do you know, Frank,
my dear 1" said Mary.
At this question he felt his know-
ledge shrink into a small compass, and
he answered,
"I cannot say that 1 know much;
but, Mary, look out of the window at
that tower at a distance. You see it?
Well! / believe, mind I say / believe,
I do not say that I am sure -- but I
believe that he could, by taking angles,
tell you how high and how broad it is,
without going nearer to it than we are
now; and I think that he could tell
how far off it is from hence, and how
far from that tower to the mountain
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 256
FRANK.
opposite, or any other place that he
could see at ever so great a distance
with his telescope. "
" My dear Frank, do you believe
this? " said Mary.
" I do, for I was present," persisted
Frank, " when my father asked him
the height and distance of some moun-
tains, as far off as I could see through
the telescope ; and after looking through
his glass, and making some triangles and
calculations, he answered and told exactly
how high they were, and how far distant. "
Mary thought this was impossible;
but she said,
" There are many ways of doing
things, which I do not yet know ; and
this may be possible, though I cannot
conceive how it can be done. "
" We shall see when the good-
natured engineer comes," said Frank.
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
257
His father asked if he remembered
the definitions which he had learned
of an angle, and a right angle, and a
square, and a triangle. He told Frank,
that unless he had perfectly distinct
ideas of these, he would not be able to
understand what he wished to learn
from his good-natured engineer. Frank
took his father's advice, and first he
showed Mary what is meant by an
angle, or a corner; he drew a square
for Mary, and triangles of different
sorts, and he showed her which was a
right-angled triangle: teaching her,
he found, refreshed his own memory.
Mary copied the figures which he had
drawn for her, and then cut out similar
figures in paper, without looking at the
drawings, that she might be quite sure,
that she had a clear recollection of
what she had learned.
z3
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 258
FRANK.
The engineer arrived, while Frank's
drawings, and the bits of paper, which
Mary had cut into squares and triangles,
were lying on the table.
" I know what you have been doing
here, my little pupil," said he, smiling
at Frank; " you have been preparing
for me. "
" Yes, sir," said Frank, " and I
believe I know them all; ask me any
questions you please. "
"Show me an angle, then," said
the gentleman.
Frank touched the corner of the
square.
The gentleman desired him to
show him each of the angles in the
square and in the triangle; and Frank
did so.
Then, laying the square and the
triangle before Frank, he asked the
? ? Generated for (University of Chicago) on 2014-12-24 14:31 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
259
names of these figures, which Frank
answering rightly, he asked,
" What sort of triangle is this ?
Frank answered, " a right-angled tri-
angle. "
"Show me what you mean by a
right angle. "
Frank showed what he meant, first
in the triangle, and afterwards in the
square.
The engineer then took from his
pocket a flat-hinged rule, and asked
Frank if he could with that rule show
him a right angle.
Frank opened the rule, so as to form
with it two sides of a square, and
pointing to the corner where these two
sides met, he said this was a right
angle.
" Here is a pencil: try if you can
. draw a right angle. "
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 260
FRANK.
Frank drew a horizontal straight
line.
"Now," whispered Mary, "I know
what you are to do next; you will draw
a perpendicular line in the middle
of that, just as if you were going
to draw the wall of a house. Yes,"
said she, as he drew the line, " I knew
that. "
"Hush, little magpie," whispered
Frank's mother.
Frank pointed to the corner where
the perpendicular and horizontal line
joined, and said, that was a right angle.
" Can you show me another right
angle upon this horizontal line? " said
the engineer. " Do you see only one,
or do you see two 1"
" I see two," said Frank; and he
pointed to the corners on the right
hand and on the left hand of the per-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
261
pendicular line, where it joined the
horizontal line.
The engineer put his hand upon
Frank's head, and said, " Now I am
satisfied that you know what is meant
by an angle, a right angle, and a
triangle.
Mary whispered something to Frank's
mother at this time, who smiled, and
said to the engineer, " Mary is surprised
that you ask Frank so often to show
you an angle in different things. "
"Yes," said Mary, "as if you could
not believe he knew it. "
" I am very careful on these sub-
jects," said the engineer, " for I know
children are sometimes taught very in-
accurately, and then they have such
confused ideas, that it is impossible to
make them understand what is meant.
A young lad was once sent to me to
be turned into a surveyor, who could
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 262 FRANK.
for some time understand nothing
that I endeavoured to explain to him;
because, though he talked of an angle,
and a right angle, he did not know
clearly what was meant by either; in
short, he mistook a triangle for an
angle. Had he confessed to me his
ignorance at once, I could have cor-
rected his error. "
" Poor boy, he had been ill taught,
I suppose," said Frank.
" You have been well taught, and
ought to be thankful for it," said the
engineer.
" Would you be so good as to come
to this window, sir," interrupted Frank.
" Do you see that tower at a distance?
Could you by taking angles, as you
stand here, find out its breadth and
height, without going to measure any
part of it, sir ? "
" I could," said the engineer.
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
263
" There, Mary! I was right," cried
Frank. " But now, sir, will you be
so very kind as to explain to me how
it is done ? "
" I would be so very kind, if I
could," answered the good-natured en-
gineer ; " but I cannot, I should only
puzzle you. If I were to attempt to
explain it, you could not understand
me.
" Oh, pray ! pray, sir, try ! " said
Mary, " I dare say Frank would un-
derstand you. "
" If you would only try," said
Frank, " I will tell you honestly, after-
wards, if I don't "
" I am sure you would," said the
engineer; " but I tell you beforehand,
that it is impossible. "
Frank looked at his father, hoping
that he knew him better; and that he
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 264 FRANK.
would say that it was possible. His
father shook his head, answering,
" It is impossible, my dear, till you
have learned a great deal more. "
" Oh, I am very much disappointed,"
said he, " for I expected that I should
have known all these things this morn-
ing. "
" But could you reasonably expect,
my young friend," said the engineer,
" to know in one morning, in one
hour, in one quarter of an hour, what
I have been many mornings, many
days, not to say years in learning? "
" Certainly not," said Frank, laugh-
ing, " that would be rather unrea-
sonable. "
" Then must Frank wait till he is
grown up quite, mamma? " said Mary.
" No, that is not necessary," said his
mother.
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
265
" How old must he be, mamma,
before he can understand them ? "
" How wise must he be, you should
ask, my dear," said his mother; " for
his being able to understand such
things will not depend upon the num-
ber of years he has lived, but upon
what he learns in those years. "
" True, madam, there is Mr. ,
What's his name ? the gentleman who
rode with us the other day, Mr. Rogers,
who has lived more years than I have,
but you saw that he did not understand
these things," said the engineer.
" Nor wish to understand them,"
said Frank: "that did surprise me. "
" And there is the gardener's boy,
Frank," said his father, " who is not
many years older than you are, and
he understands that which you want
to know. "
vol. i. 2 a
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 266
FRANK.
" Does he indeed ? " said Frank.
M Yes ; now I remember seeing in his
book drawings of triangles and circles,
and I could not guess of what use they
could be. "
" His father said, as you told me, that
he was learning mathematics," said
Mary, " and trig "
" Trigonometry, I suppose," said
the engineeer; " which, translating the
Greek word into English for you, my
little lady, means the measuring of
triangles. "
" Of triangles! " repeated Frank,
taking up one of the paper triangles
which lay upon the table, and looking
at it " Can measuring this have any
thing to do with the measuring that
tower ? "
" Yes; a great deal to do with it,"
answered the engineer. " I cannot ex-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK. 267
plain to you how; but I may, without
giving you any false ideas, tell you in
general, that the power we possess of
measuring that tower, and the most
distant objects that can be seen on
earth, and not those only on earth,
but those in the heavens, depends upon
our understanding the properties of a
triangle. "
" If the gardener's boy has learned
trigo-no-me-try," said Mary, " why can-
not Frank? "
" Is there any quick way of learn-
ing it ? " asked Frank.
" No, there is no quick way," said
the engineer.
" You must go regularly through
this," said his father, taking down a
book from the book-case.
" What is it? " cried Frank, seizing
and opening it. " The very thing I
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 268 FRANK.
saw with the gardener's son, Euclid's
Elements of Geometry. "
" A square is a figure that has
four "
" Oh, we know that," said Mary,
lookiug over his shoulder.
" But how shall I understand these
drawings of circles and triangles ? " said
Frank: " the line a b is equal to the
line c d ; proposition the 1 st, propo-
sition the 2d; and axiom the 1st,
axiom the 2d: almost as hard sound-
ing and difficult as the beginning of
the Latin grammar. "
" Yes," said his father, " in the be-
ginning of all sciences there are dif-
Acuities; a sort of grammar, which
must be learned, before you can get
on to the smooth and pleasant part. "
" But in this book, and in this
science, you will find," said the engi-
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK. 269
neer, " that each step leads on securely
to another: not one will ever be lost. "
" That is a comfort," said Frank.
" But," said Mary, <<I hope we
may look through the telescope, and
see the men and mountains standing
on their heads. "
The engineer promised that she
should. But he had some business to
do, before he could comply with her
request; and, in the mean time, the
young people were desired to go out.
While Mary went to put on her
bonnet, Frank was left in the hall by
himself. Several of the engineer's
books and instruments, which had been
taken out of his carriage, were lying
on the hall table, and, among others,
one of the telescopes belonging to his
theodolite.
Frank ventured to take up this tele-
2a 3
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 270
FRANK.
scope, which he ought not to have
touched; he thought, however, that
he could not do it any harm by just
looking through it. He took off the
brass cover at one end, and slid back
the brass slide at the other end, and
looked through it at the tower, and at
some men who were at work in a distant
field.
" What can be the reason," said he
to himself, " that these men seem to
stand on their heads? This telescope
looks as if it were quite the same as
my father's. I wish I could find out
the reason. I should be so glad to
prove that I could understand it,
though they all say I cannot. "
He saw some very slight wires, as
he thought them, behind one of the
glasses ; and as there were none such in
his father's, he fancied that these i had
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
271
something to do with the secret, which
lie longed to discover.
" I know how to unscrew this
glass," said he, "I will not do it the
least harm. "
He unscrewed the glass, and, looking
into the tube, he could scarcely see
what had appeared to him to have been
wires. He put his hand in to feel for
them. There were no wires, there
was nothing that he could feel -- no-
thing ! except some very slight cob-
webs. These threw no light on his
difficulty; he blew them away, and,
despairing of making farther disco-
veries, and unconscious of the injury he
had done to the instrument, he screwed
on the glass, and left the telescope, as
he thought, in perfect safety, exactly
where he had found it on the table.
Frank, having no idea that he had
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 272
FRANK.
done any mischief, did not even men-
tion to Mary his having looked at
the telescope. She put it out of his
recollection by beginning to talk to
him, the moment she saw him, about
the parrot's cage, the door of which
had been broken; and Mrs. Catherine,
who was now standing with that broken
door in her hand, was anxious that it
should be mended immediately.
Mary had undertaken for Frank, that
he had both the power and the in-
clination quickly to accomplish her
wishes.
Frank instantly ran in search of the
osiers, that were necessary for the work.
As there was no one in the house-
keeper's room, except Mrs. Catherine,
his mother gave them leave to do the
job there, and to take the osiers to the
cage, instead of carrying the cage to
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
273
the osiers. She, moreover, was so
good as to promise, that she would call
them, as soon as the engineer had
finished writing his letters, if any thing
entertaining should be going on.
The repairs of Poll's habitation cost
Frank more trouble than he had ex-
pected ; as it often happens, he found,
that which he thought could be done in
five minutes, required five and twenty.
But the door at last turned easily
on its ozier hinges, and Poll was just
replaced in her cage, when their atten-
tion was suddenly roused by hearing
somebody sobbing in the passage.
Mrs. Catherine opened her room door,
and they saw a black boy, standing
in a corner, crying. Mrs. Catherine
asked what was the matter. The
boy began to stammer something in
broken English ; but before he could
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 274 FRANK.
get out any thing intelligible, a
man, whom Frank recollected to be one
of the engineer's assistants, came into
the passage, and told Mrs. Catherine
that she need not waste her pity upon
this boy.
" No use, ma'am, listening to
him, or asking him any questions,
for he is a sad liar--never can
speak a word of truth. His master,
who is the best of masters, has done
all he can to cure him, and so have I.
It was but last week he was guilty of
a falsehood, and his master said, and,
begging you pardon, ma'am, I swore,
he should be parted with the next
lie he told; and he has told a He
now, and he is to go; that is what
he is crying for, and nobody can help
him. "
" Nobody can help him to be sure,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
275
if he is a liar," said Mrs. Catherine,
who held liars in just abhorrence.
"But are they sure he is a liar? "
said Frank.
" He cannot deny it," said the man.
The Negro boy went on sobbing;
and when Mrs. Catherine asked if he
had any thing to say for himself, he
could only say,
" Me liar last week, ma'am, yes;
to-day, no liar--no lie! "
" Oh, if you were a liar last week,"
said Mrs. Catherine, "who can know
that you are not telling a lie this mi-
nute? "
The boy turned his face to the wall,
and cried more violently than before.
" I can't help it, nor nobody can
help it," said Mrs. Catherine : " I have
nothing to say for liars. Miss Mary,
master Frank, you had better go away,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 276
FRANK.
if you please; you have no farther
. business here. "
" But," said Mary, turning back, as
they reluctantly went up stairs, " I
think he is telling the truth now ; are
you sure, Catherine, that he has not
told the truth to-day? "
" Pray, good Catherine, find that
out, will you," said Frank.
Mrs. Catherine, whose countenance
now looked severe, as it always did
when she thought a liar stood near her,
said she must leave it to his master,
who knew his character, to settle the
business; it was not proper for her to
interfere. " When a boy was a liar, and
told a lie last week, who can know,"
said she, "that he is not telling a lie
this minute? "
"But, since he confessed that he
told a falsehood last week," said Frank,
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
277
"perhaps--do, do, good Catherine
inquire into it. You know papa says
you are a just woman. "
" Well, well, go you both of you
out of the way, in the first and fore-
most place, for I am sure your papa
and mamma would not be pleased to
see you here, meddling with such things
-- so up stairs this moment. "
Up stairs that moment they went,
and Frank followed by Mary, who
could hardly keep pace with him,
ran to the library, where he had left
the engineer writing: but he was
gone.
" Well, Headlong ! " said his father,
when Frank threw open the door,
"What now? "
" And why do you look so terribly
disappointed, Mary," said Frank's
mother: " I told you that I would call
vol. i. 2b
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? 278
FRANK.
you as soon as the engineer could show
you his telescope. "
" Oh, it is something of much more
consequence," said Mary.
Frank told all they had heard ; " and
though Catherine says it is not our
business, yet it is every body's busi-
ness to see justice done, especially to a
poor black boy, who cannot speak for
himself, is not it, papa ? " said Frank.
" I will go and find out that good-na-
tured master of his, and ask him to go
to the bottom of the affair this minute. "
Frank's father held his hand, how-
ever, and prevented him from going;
for though he liked his eagerness to
have justice done to the Negro boy, he
thought, he said, that this boy's master
must know his character better than
any stranger could; and that his master
would in all probability take care to
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www. hathitrust. org/access_use#pd-google
? FRANK.
279
find out the truth, without Frank's in-
terference.
" But," said Frank, " they are going
to turn him out of the house directly.
Only just let me find the engineer,
and tell him this. "
Here he is, my dear," said Frank's
mother, " now do not be in a hurry.
Speak distinctly: for I could hardly
understand your story, you spoke so
very quickly. "
The engineer came into the room
with his telescope in his hand; that
telescope with which Frank had med-
dled. A sudden flash came across his
mind : a thrill came all over him.
" Miss Mary," said the engineer,
" I am sorry that I cannot keep my
promise to you, yet; but I must first
set to rights something which has been
broken in my telescope. The cross
? ? Generated for (University of Chicago) on 2014-12-24 14:32 GMT / http://hdl. handle. net/2027/hvd. hn2gwl Public Domain, Google-digitized / http://www.
