A TANGLED TALE
BY LEWIS CARROLL
A TANGLED TALE
BY
LEWIS CARROLL
_WITH SIX ILLUSTRATIONS_
BY
ARTHUR B. FROST
Hoc meum tale quale est accipe.
_SECOND THOUSAND._
London
MACMILLAN AND CO.
1885
[_All Rights Reserved_]
RICHARD CLAY & SONS,
BREAD STREET HILL, LONDON, E.C.
_And Bungay, Suffolk_.
To My Pupil.
Beloved pupil! Tamed by thee,
Addish-, Subtrac-, Multiplica-tion,
Division, Fractions, Rule of Three,
Attest thy deft manipulation!
Then onward! Let the voice of Fame
From Age to Age repeat thy story,
Till thou hast won thyself a name
Exceeding even Euclid's glory!
PREFACE.
This Tale originally appeared as a serial in _The Monthly Packet_,
beginning in April, 1880. The writer's intention was to embody in each
Knot (like the medicine so dexterously, but ineffectually, concealed in
the jam of our early childhood) one or more mathematical questions--in
Arithmetic, Algebra, or Geometry, as the case might be--for the
amusement, and possible edification, of the fair readers of that
Magazine.
L. C.
_October, 1885._
CONTENTS.
KNOT PAGE
I. EXCELSIOR 1
II. ELIGIBLE APARTMENTS 4
III. MAD MATHESIS 13
IV. THE DEAD RECKONING 19
V. OUGHTS AND CROSSES 27
VI. HER RADIANCY 34
VII. PETTY CASH 43
VIII. DE OMNIBUS REBUS 52
IX. A SERPENT WITH CORNERS 58
X. CHELSEA BUNS 66
ANSWERS TO KNOT I. 77
" " II. 84
" " III. 90
" " IV. 96
" " V. 102
" " VI. 106
" " VII. 112
" " VIII. 132
" " IX. 135
" " X. 142
A TANGLED TALE.
KNOT I.
EXCELSIOR.
"Goblin, lead them up and down."
The ruddy glow of sunset was already fading into the sombre shadows of
night, when two travellers might have been observed swiftly--at a pace
of six miles in the hour--descending the rugged side of a mountain; the
younger bounding from crag to crag with the agility of a fawn, while his
companion, whose aged limbs seemed ill at ease in the heavy chain armour
habitually worn by tourists in that district, toiled on painfully at his
side.
As is always the case under such circumstances, the younger knight was
the first to break the silence.
"A goodly pace, I trow!" he exclaimed. "We sped not thus in the ascent!"
"Goodly, indeed!" the other echoed with a groan. "We clomb it but at
three miles in the hour."
"And on the dead level our pace is----?" the younger suggested; for he
was weak in statistics, and left all such details to his aged companion.
"Four miles in the hour," the other wearily replied. "Not an ounce
more," he added, with that love of metaphor so common in old age, "and
not a farthing less!"
"'Twas three hours past high noon when we left our hostelry," the young
man said, musingly. "We shall scarce be back by supper-time. Perchance
mine host will roundly deny us all food!"
"He will chide our tardy return," was the grave reply, "and such a
rebuke will be meet."
"A brave conceit!" cried the other, with a merry laugh. "And should we
bid him bring us yet another course, I trow his answer will be tart!"
"We shall but get our deserts," sighed the elder knight, who had never
seen a joke in his life, and was somewhat displeased at his companion's
untimely levity. "'Twill be nine of the clock," he added in an
undertone, "by the time we regain our hostelry. Full many a mile shall
we have plodded this day!"
"How many? How many?" cried the eager youth, ever athirst for knowledge.
The old man was silent.
"Tell me," he answered, after a moment's thought, "what time it was when
we stood together on yonder peak. Not exact to the minute!" he added
hastily, reading a protest in the young man's face. "An' thy guess be
within one poor half-hour of the mark, 'tis all I ask of thy mother's
son! Then will I tell thee, true to the last inch, how far we shall have
trudged betwixt three and nine of the clock."
A groan was the young man's only reply; while his convulsed features and
the deep wrinkles that chased each other across his manly brow, revealed
the abyss of arithmetical agony into which one chance question had
plunged him.
KNOT II.
ELIGIBLE APARTMENTS.
"Straight down the crooked lane,
And all round the square."
"Let's ask Balbus about it," said Hugh.
"All right," said Lambert.
"_He_ can guess it," said Hugh.
"Rather," said Lambert.
No more words were needed: the two brothers understood each other
perfectly.
[Illustration: "BALBUS WAS ASSISTING HIS MOTHER-IN-LAW TO CONVINCE THE
DRAGON."]
Balbus was waiting for them at the hotel: the journey down had tired
him, he said: so his two pupils had been the round of the place, in
search of lodgings, without the old tutor who had been their inseparable
companion from their childhood. They had named him after the hero of
their Latin exercise-book, which overflowed with anecdotes of that
versatile genius--anecdotes whose vagueness in detail was more than
compensated by their sensational brilliance. "Balbus has overcome all
his enemies" had been marked by their tutor, in the margin of the book,
"Successful Bravery." In this way he had tried to extract a moral from
every anecdote about Balbus--sometimes one of warning, as in "Balbus had
borrowed a healthy dragon," against which he had written "Rashness in
Speculation"--sometimes of encouragement, as in the words "Influence of
Sympathy in United Action," which stood opposite to the anecdote "Balbus
was assisting his mother-in-law to convince the dragon"--and sometimes
it dwindled down to a single word, such as "Prudence," which was all he
could extract from the touching record that "Balbus, having scorched the
tail of the dragon, went away." His pupils liked the short morals best,
as it left them more room for marginal illustrations, and in this
instance they required all the space they could get to exhibit the
rapidity of the hero's departure.
Their report of the state of things was discouraging. That most
fashionable of watering-places, Little Mendip, was "chockfull" (as the
boys expressed it) from end to end. But in one Square they had seen no
less than four cards, in different houses, all announcing in flaming
capitals "ELIGIBLE APARTMENTS." "So there's plenty of choice, after all,
you see," said spokesman Hugh in conclusion.
"That doesn't follow from the data," said Balbus, as he rose from the
easy chair, where he had been dozing over _The Little Mendip Gazette_.
"They may be all single rooms. However, we may as well see them. I shall
be glad to stretch my legs a bit."
An unprejudiced bystander might have objected that the operation was
needless, and that this long, lank creature would have been all the
better with even shorter legs: but no such thought occurred to his
loving pupils. One on each side, they did their best to keep up with his
gigantic strides, while Hugh repeated the sentence in their father's
letter, just received from abroad, over which he and Lambert had been
puzzling. "He says a friend of his, the Governor of----_what_ was that
name again, Lambert?" ("Kgovjni," said Lambert.) "Well, yes. The
Governor of----what-you-may-call-it----wants to give a _very_ small
dinner-party, and he means to ask his father's brother-in-law, his
brother's father-in-law, his father-in-law's brother, and his
brother-in-law's father: and we're to guess how many guests there will
be."
There was an anxious pause. "_How_ large did he say the pudding was to
be?" Balbus said at last. "Take its cubical contents, divide by the
cubical contents of what each man can eat, and the quotient----"
"He didn't say anything about pudding," said Hugh, "--and here's the
Square," as they turned a corner and came into sight of the "eligible
apartments."
"It _is_ a Square!" was Balbus' first cry of delight, as he gazed around
him. "Beautiful! Beau-ti-ful! Equilateral! _And_ rectangular!"
The boys looked round with less enthusiasm. "Number nine is the first
with a card," said prosaic Lambert; but Balbus would not so soon awake
from his dream of beauty.
"See, boys!" he cried. "Twenty doors on a side! What symmetry! Each side
divided into twenty-one equal parts! It's delicious!"
"Shall I knock, or ring?" said Hugh, looking in some perplexity at a
square brass plate which bore the simple inscription "RING ALSO."
"Both," said Balbus. "That's an Ellipsis, my boy. Did you never see an
Ellipsis before?"
"I couldn't hardly read it," said Hugh, evasively. "It's no good having
an Ellipsis, if they don't keep it clean."
"Which there is _one_ room, gentlemen," said the smiling landlady. "And
a sweet room too! As snug a little back-room----"
"We will see it," said Balbus gloomily, as they followed her in. "I knew
how it would be! One room in each house! No view, I suppose?"
"Which indeed there _is_, gentlemen!" the landlady indignantly
protested, as she drew up the blind, and indicated the back garden.
"Cabbages, I perceive," said Balbus. "Well, they're green, at any rate."
"Which the greens at the shops," their hostess explained, "are by no
means dependable upon. Here you has them on the premises, _and_ of the
best."
"Does the window open?" was always Balbus' first question in testing a
lodging: and "Does the chimney smoke?" his second. Satisfied on all
points, he secured the refusal of the room, and they moved on to Number
Twenty-five.
This landlady was grave and stern. "I've nobbut one room left," she
told them: "and it gives on the back-gyardin."
"But there are cabbages?" Balbus suggested.
The landlady visibly relented. "There is, sir," she said: "and good
ones, though I say it as shouldn't. We can't rely on the shops for
greens. So we grows them ourselves."
"A singular advantage," said Balbus: and, after the usual questions,
they went on to Fifty-two.
"And I'd gladly accommodate you all, if I could," was the greeting that
met them. "We are but mortal," ("Irrelevant!" muttered Balbus) "and I've
let all my rooms but one."
"Which one is a back-room, I perceive," said Balbus: "and looking out
on--on cabbages, I presume?"
"Yes, indeed, sir!" said their hostess. "Whatever _other_ folks may do,
_we_ grows our own. For the shops----"
"An excellent arrangement!" Balbus interrupted. "Then one can really
depend on their being good. Does the window open?"
The usual questions were answered satisfactorily: but this time Hugh
added one of his own invention--"Does the cat scratch?"
The landlady looked round suspiciously, as if to make sure the cat was
not listening, "I will not deceive you, gentlemen," she said. "It _do_
scratch, but not without you pulls its whiskers! It'll never do it," she
repeated slowly, with a visible effort to recall the exact words of some
written agreement between herself and the cat, "without you pulls its
whiskers!"
"Much may be excused in a cat so treated," said Balbus, as they left the
house and crossed to Number Seventy-three, leaving the landlady
curtseying on the doorstep, and still murmuring to herself her parting
words, as if they were a form of blessing, "---- not without you pulls
its whiskers!"
At Number Seventy-three they found only a small shy girl to show the
house, who said "yes'm" in answer to all questions.
"The usual room," said Balbus, as they marched in: "the usual
back-garden, the usual cabbages. I suppose you can't get them good at
the shops?"
"Yes'm," said the girl.
"Well, you may tell your mistress
