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The Collected Complete Works of Lewis Carroll
A Tangled Tale
Alice in Wonderland
Eight or Nine Wise Words about Letter-Writingon
Feeding the Mind
Phantasmagoria and Other Poems
Rhyme And Reason
Sylvie and Bruno
The Game of Logic
The Hunting of the Snark
Three Sunsets and Other Poems
Through the Looking Glass
A Tangled Tale, by Lewis Carroll
A TANGLED TALE
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.
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.
"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.
"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, wegrows 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 we will take the room, and that her plan of growing her own cabbages is simply admirable!"
"Yes'm," said the girl, as she showed them out.
"One day-room and three bed-rooms," said Balbus, as they returned to the hotel. "We will take as our day-room the one that gives us the least walking to do to get to it."
"Must we walk from door to door, and count the steps?" said Lambert.
"No, no! Figure it out, my boys, figure it out!" Balbus gaily exclaimed, as he put pens, ink, and paper before his hapless pupils, and left the room.
"I say! It'll be a job!" said Hugh.
"Rather!" said Lambert.
"I waited for the train."
"Well, they call me so because I am a little mad, I suppose," she said, good-humouredly, in answer to Clara's cautiously-worded question as to how she came by so strange a nick-name. "You see, I never do what sane people are expected to do now-a-days. I never wear long trains, (talking of trains, that's the Charing Cross Metropolitan Station--I've something to tell you about that), and I never play lawn-tennis. I can't cook an omelette. I can't even set a broken limb! There's an ignoramus for you!"
Clara was her niece, and full twenty years her junior; in fact, she was still attending a High School--an institution of which Mad Mathesis spoke with undisguised aversion. "Let a woman be meek and lowly!" she would say. "None of your High Schools for me!" But it was vacation-time just now, and Clara was her guest, and Mad Mathesis was showing her the sights of that Eighth Wonder of the world--London.
"The Charing Cross Metropolitan Station!" she resumed, waving her hand towards the entrance as if she were introducing her niece to a friend. "The Bayswater and Birmingham Extension is just completed, and the trains now run round and round continuously--skirting the border of Wales, just touching at York, and so round by the east coast back to London. The way the trains run is most peculiar. The westerly ones go round in two hours; the easterly ones take three; but they always manage to start two trains from here, opposite ways, punctually every quarter-of-an-hour."
"They part to meet again," said Clara, her eyes filling with tears at the romantic thought.
"No need to cry about it!" her aunt grimly remarked. "They don't meet on the same line of rails, you know. Talking of meeting, an idea strikes me!" she added, changing the subject with her usual abruptness. "Let's go opposite ways round, and see which can meet most trains. No need for a chaperon--ladies' saloon, you know. You shall go whichever way you like, and we'll have a bet about it!"
"I never make bets," Clara said very gravely. "Our excellent preceptress has often warned us----"
"You'd be none the worse if you did!" Mad Mathesis interrupted. "In fact, you'd be the better, I'm certain!"
"Neither does our excellent preceptress approve of puns," said Clara. "But we'll have a match, if you like. Let me choose my train," she added after a brief mental calculation, "and I'll engage to meet exactly half as many again as you do."
"Not if you count fair," Mad Mathesis bluntly interrupted. "Remember, we only count the trains we meet on the way. You mustn't count the one that starts as you start, nor the one that arrives as you arrive."
"That will only make the difference of one train," said Clara, as they turned and entered the station. "But I never travelled alone before. There'll be no one to help me to alight. However, I don't mind. Let's have a match."
A ragged little boy overheard her remark, and came running after her. "Buy a box of cigar-lights, Miss!" he pleaded, pulling her shawl to attract her attention. Clara stopped to explain.
"I never smoke cigars," she said in a meekly apologetic tone. "Our excellent preceptress----," but Mad Mathesis impatiently hurried her on, and the little boy was left gazing after her with round eyes of amazement.
The two ladies bought their tickets and moved slowly down the central platform, Mad Mathesis prattling on as usual--Clara silent, anxiously reconsidering the calculation on which she rested her hopes of winning the match.
"Mind where you go, dear!" cried her aunt, checking her just in time. "One step more, and you'd have been in that pail of cold water!"
"I know, I know," Clara said, dreamily. "The pale, the cold, and the moony----"
"Take your places on the spring-boards!" shouted a porter.
"What are theyfor!" Clara asked in a terrified whisper.
"Merely to help us into the trains."The elder lady spoke with the nonchalance of one quite used to the process. "Very few people can get into a carriage without help in less than three seconds, and the trains only stop for one second." At this moment the whistle was heard, and two trains rushed into the station. A moment's pause, and they were gone again; but in that brief interval several hundred passengers had been shot into them, each flying straight to his place with the accuracy of a Minie bullet--while an equal number were showered out upon the side-platforms.
Three hours had passed away, and the two friends met again on the Charing Cross platform, and eagerly compared notes. Then Clara turned away with a sigh. To young impulsive hearts, like hers, disappointment is always a bitter pill. Mad Mathesis followed her, full of kindly sympathy.
"Try again, my love!" she said, cheerily. "Let us vary the experiment. We will start as we did before, but not to begin counting till our trains meet. When we see each other, we will say 'One!' and so count on till we come here again."
Clara brightened up. "I shall win that," she exclaimed eagerly, "if I may choose my train!"
Another shriek of engine whistles, another upheaving of spring-boards, another living avalanche plunging into two trains as they flashed by: and the travellers were off again.
Each gazed eagerly from her carriage window, holding up her handkerchief as a signal to her friend. A rush and a roar. Two trains shot past each other in a tunnel, and two travellers leaned back in their corners with a sigh--or rather with two sighs--of relief. "One!" Clara murmured to herself. "Won! It's a word of good omen. This time, at any rate, the victory will be mine!"
But was it?
THE DEAD RECKONING.
"I did dream of money-bags to-night."
Noonday on the open sea within a few degrees of the Equator is apt to be oppressively warm; and our two travellers were now airily clad in suits of dazzling white linen, having laid aside the chain-armour which they had found not only endurable in the cold mountain air they had lately been breathing, but a necessary precaution against the daggers of the banditti who infested the heights. Their holiday-trip was over, and they were now on their way home, in the monthly packet which plied between the two great ports of the island they had been exploring.
Along with their armour, the tourists had laid aside the antiquated speech it had pleased them to affect while in knightly disguise, and had returned to the ordinary style of two country gentlemen of the Twentieth Century.
Stretched on a pile of cushions, under the shade of a huge umbrella, they were lazily watching some native fishermen, who had come on board at the last landing-place, each carrying over his shoulder a small but heavy sack. A large weighing-machine, that had been used for cargo at the last port, stood on the deck; and round this the fishermen had gathered, and, with much unintelligible jabber, seemed to be weighing their sacks.
"More like sparrows in a tree than human talk, isn't it?" the elder tourist remarked to his son, who smiled feebly, but would not exert himself so far as to speak. The old man tried another listener.
"What have they got in those sacks, Captain?" he inquired, as that great being passed them in his never ending parade to and fro on the deck.
The Captain paused in his march, and towered over the travellers--tall, grave, and serenely self-satisfied.
"Fishermen," he explained, "are often passengers in My ship. These five are from Mhruxi--the place we last touched at--and that's the way they carry their money. The money of this island is heavy, gentlemen, but it costs little, as you may guess. We buy it from them by weight--about five shillings a pound. I fancy a ten pound-note would buy all those sacks."
By this time the old man had closed his eyes--in order, no doubt, to concentrate his thoughts on these interesting facts; but the Captain failed to realise his motive, and with a grunt resumed his monotonous march.
Meanwhile the fishermen were getting so noisy over the weighing-machine that one of the sailors took the precaution of carrying off all the weights, leaving them to amuse themselves with such substitutes in the form of winch-handles, belaying-pins, &c., as they could find. This brought their excitement to a speedy end: they carefully hid their sacks in the folds of the jib that lay on the deck near the tourists, and strolled away.
When next the Captain's heavy footfall passed, the younger man roused himself to speak.
"What did you call the place those fellows came from, Captain?" he asked.
"And the one we are bound for?"
The Captain took a long breath, plunged into the word, and came out of it nobly. "They call it Kgovjni, sir."
"K--I give it up!" the young man faintly said.
He stretched out his hand for a glass of iced water which the compassionate steward had brought him a minute ago, and had set down, unluckily, just outside the shadow of the umbrella. It was scalding hot, and he decided not to drink it. The effort of making this resolution, coming close on the fatiguing conversation he had just gone through, was too much for him: he sank back among the cushions in silence.
His father courteously tried to make amends for his nonchalance.
"Whereabouts are we now, Captain?" said he, "Have you any idea?"
The Captain cast a pitying look on the ignorant landsman. "I could tell you that, sir," he said, in a tone of lofty condescension, "to an inch!"
"You don't say so!" the old man remarked, in a tone of languid surprise.
"And mean so," persisted the Captain. "Why, what do you suppose would become of My ship, if I were to lose My Longitude and My Latitude? Could you make anything of My Dead Reckoning?"
"Nobody could, I'm sure!" the other heartily rejoined.
But he had overdone it.
"It's perfectly intelligible," the Captain said, in an offended tone, "to any one that understands such things." With these words he moved away, and began giving orders to the men, who were preparing to hoist the jib.
Our tourists watched the operation with such interest that neither of them remembered the five money-bags, which in another moment, as the wind filled out the jib, were whirled overboard and fell heavily into the sea.
But the poor fishermen had not so easily forgotten their property. In a moment they had rushed to the spot, and stood uttering cries of fury, and pointing, now to the sea, and now to the sailors who had caused the disaster.
The old man explained it to the Captain.
"Let us make it up among us," he added in conclusion. "Ten pounds will do it, I think you said?"
But the Captain put aside the suggestion with a wave of the hand.
"No, sir!" he said, in his grandest manner. "You will excuse Me, I am sure; but these are My passengers. The accident has happened on board My ship, and under My orders. It is for Me to make compensation." He turned to the angry fishermen. "Come here, my men!" he said, in the Mhruxian dialect. "Tell me the weight of each sack. I saw you weighing them just now."
Then ensued a perfect Babel of noise, as the five natives explained, all screaming together, how the sailors had carried off the weights, and they had done what they could with whatever came handy.
Two iron belaying-pins, three blocks, six holystones, four winch-handles, and a large hammer, were now carefully weighed, the Captain superintending and noting the results. But the matter did not seem to be settled, even then: an angry discussion followed, in which the sailors and the five natives all joined: and at last the Captain approached our tourists with a disconcerted look, which he tried to conceal under a laugh.
"It's an absurd difficulty," he said. "Perhaps one of you gentlemen can suggest something. It seems they weighed the sacks two at a time!"
"If they didn't have five separate weighings, of course you can't value them separately," the youth hastily decided.
"Let's hear all about it," was the old man's more cautious remark.
"They did have five separate weighings," the Captain said, "but--Well, it beats me entirely!" he added, in a sudden burst of candour. "Here's the result. First and second sack weighed twelve pounds; second and third, thirteen and a half; third and fourth, eleven and a half; fourth and fifth, eight: and then they say they had only the large hammer left, and it took three sacks to weigh it down--that's the first, third and fifth--and they weighed sixteen pounds. There, gentlemen! Did you ever hear anything like that?"
The old man muttered under his breath "If only my sister were here!" and looked helplessly at his son. His son looked at the five natives. The five natives looked at the Captain. The Captain looked at nobody: his eyes were cast down, and he seemed to be saying softly to himself "Contemplate one another, gentlemen, if such be your good pleasure. I contemplate Myself!"
OUGHTS AND CROSSES.
"Look here, upon this picture, and on this."
"And what made you choose the first train, Goosey?" said Mad Mathesis, as they got into the cab. "Couldn't you count better than that?"
"I took an extreme case," was the tearful reply. "Our excellent preceptress always says 'When in doubt, my dears, take an extreme case.' And I was in doubt."
"Does it always succeed?" her aunt enquired.
Clara sighed. "Not always," she reluctantly admitted. "And I can't make out why. One day she was telling the little girls--they make such a noise at tea, you know--'The more noise you make, the less jam you will have, and vice versâ.' And I thought they wouldn't know what 'vice versâ' meant: so I explained it to them. I said 'If you make an infinite noise, you'll get no jam: and if you make no noise, you'll get an infinite lot of jam.' But our excellent preceptress said that wasn't a good instance. Why wasn't it?" she added plaintively.
Her aunt evaded the question. "One sees certain objections to it," she said. "But how did you work it with the Metropolitan trains? None of them go infinitely fast, I believe."
"I called them hares and tortoises," Clara said--a little timidly, for she dreaded being laughed at. "And I thought there couldn't be so many hares as tortoises on the Line: so I took an extreme case--one hare and an infinite number of tortoises."
"An extreme case, indeed," her aunt remarked with admirable gravity: "and a most dangerous state of things!"
"And I thought, if I went with a tortoise, there would be only one hare to meet: but if I went with the hare--you know there were crowds of tortoises!"
"It wasn't a bad idea," said the elder lady, as they left the cab, at the entrance of Burlington House. "You shall have another chance to-day. We'll have a match in marking pictures."
Clara brightened up. "I should like to try again, very much," she said. "I'll take more care this time. How are we to play?"
To this question Mad Mathesis made no reply: she was busy drawing lines down the margins of the catalogue. "See," she said after a minute, "I've drawn three columns against the names of the pictures in the long room, and I want you to fill them with oughts and crosses--crosses for good marks and oughts for bad. The first column is for choice of subject, the second for arrangement, the third for colouring. And these are the conditions of the match. You must give three crosses to two or three pictures. You must give two crosses to four or five----"
"Do you mean only two crosses?" said Clara. "Or may I count the three-cross pictures among the two-cross pictures?"
"Of course you may," said her aunt. "Any one, that has three eyes, may be said to have two eyes, I suppose?"
Clara followed her aunt's dreamy gaze across the crowded gallery, half-dreading to find that there was a three-eyed person in sight.
"And you must give one cross to nine or ten."
"And which wins the match?" Clara asked, as she carefully entered these conditions on a blank leaf in her catalogue.
"Whichever marks fewest pictures."
"But suppose we marked the same number?"
"Then whichever uses most marks."
Clara considered. "I don't think it's much of a match," she said. "I shall mark nine pictures, and give three crosses to three of them, two crosses to two more, and one cross each to all the rest."
"Will you, indeed?" said her aunt. "Wait till you've heard all the conditions, my impetuous child. You must give three oughts to one or two pictures, two oughts to three or four, and one ought to eight or nine. I don't want you to be too hard on the R.A.'s."
Clara quite gasped as she wrote down all these fresh conditions. "It's a great deal worse than Circulating Decimals!" she said. "But I'm determined to win, all the same!"
Her aunt smiled grimly. "We can begin here," she said, as they paused before a gigantic picture, which the catalogue informed them was the "Portrait of Lieutenant Brown, mounted on his favorite elephant."
"He looks awfully conceited!" said Clara. "I don't think he was the elephant's favorite Lieutenant. What a hideous picture it is! And it takes up room enough for twenty!"
"Mind what you say, my dear!" her aunt interposed. "It's by an R.A.!"
But Clara was quite reckless. "I don't care who it's by!" she cried. "And I shall give it three bad marks!"
Aunt and niece soon drifted away from each other in the crowd, and for the next half-hour Clara was hard at work, putting in marks and rubbing them out again, and hunting up and down for suitable pictures. This she found the hardest part of all. "I can't find the one I want!" she exclaimed at last, almost crying with vexation.
"What is it you want to find, my dear?" The voice was strange to Clara, but so sweet and gentle that she felt attracted to the owner of it, even before she had seen her; and when she turned, and met the smiling looks of two little old ladies, whose round dimpled faces, exactly alike, seemed never to have known a care, it was as much as she could do--as she confessed to Aunt Mattie afterwards--to keep herself from hugging them both.
"I was looking for a picture," she said, "that has a good subject--and that's well arranged--but badly coloured."
The little old ladies glanced at each other in some alarm. "Calm yourself, my dear," said the one who had spoken first, "and try to remember which it was. What was the subject?"
"Was it an elephant, for instance?" the other sister suggested. They were still in sight of Lieutenant Brown.
"I don't know, indeed!" Clara impetuously replied. "You know it doesn't matter a bit what the subject is, so long as it's a good one!"
Once more the sisters exchanged looks of alarm, and one of them whispered something to the other, of which Clara caught only the one word "mad."
"They mean Aunt Mattie, of course," she said to herself--fancying, in her innocence, that London was like her native town, where everybody knew everybody else. "If you mean my aunt," she added aloud, "she's there--just three pictures beyond Lieutenant Brown."
"Ah, well! Then you'd better go to her, my dear!" her new friend said, soothingly. "She'll find you the picture you want. Good-bye, dear!"
"Good-bye, dear!" echoed the other sister, "Mind you don't lose sight of your aunt!" And the pair trotted off into another room, leaving Clara rather perplexed at their manner.
"They're real darlings!" she soliloquised. "I wonder why they pity me so!" And she wandered on, murmuring to herself "It must have two good marks, and----"
"One piecee thing that my have got, Maskee[A] that thing my no can do. You talkee you no sabey what? Bamboo."
They landed, and were at once conducted to the Palace. About half way they were met by the Governor, who welcomed them in English--a great relief to our travellers, whose guide could speak nothing but Kgovjnian.
"I don't half like the way they grin at us as we go by!" the old man whispered to his son. "And why do they say 'Bamboo!' so often?"
"It alludes to a local custom," replied the Governor, who had overheard the question. "Such persons as happen in any way to displease Her Radiancy are usually beaten with rods."
[Illustration: "WHY DO THEY SAY 'BAMBOO!' SO OFTEN?"]
The old man shuddered. "A most objectional local custom!" he remarked with strong emphasis. "I wish we had never landed! Did you notice that black fellow, Norman, opening his great mouth at us? I verily believe he would like to eat us!"
Norman appealed to the Governor, who was walking at his other side. "Do they often eat distinguished strangers here?" he said, in as indifferent a tone as he could assume.
"Not often--not ever!" was the welcome reply. "They are not good for it. Pigs we eat, for they are fat. This old man is thin."
"And thankful to be so!" muttered the elder traveller. "Beaten we shall be without a doubt. It's a comfort to know it won't be Beaten without the B! My dear boy, just look at the peacocks!"
They were now walking between two unbroken lines of those gorgeous birds, each held in check, by means of a golden collar and chain, by a black slave, who stood well behind, so as not to interrupt the view of the glittering tail, with its network of rustling feathers and its hundred eyes.
The Governor smiled proudly. "In your honour," he said, "Her Radiancy has ordered up ten thousand additional peacocks. She will, no doubt, decorate you, before you go, with the usual Star and Feathers."
"It'll be Star without the S!" faltered one of his hearers.
"Come, come! Don't lose heart!" said the other. "All this is full of charm for me."
"You are young, Norman," sighed his father; "young and light-hearted. For me, it is Charm without the C."
"The old one is sad," the Governor remarked with some anxiety. "He has, without doubt, effected some fearful crime?"
"But I haven't!" the poor old gentleman hastily exclaimed. "Tell him I haven't, Norman!"
"He has not, as yet," Norman gently explained. And the Governor repeated, in a satisfied tone, "Not as yet."
"Yours is a wondrous country!" the Governor resumed, after a pause. "Now here is a letter from a friend of mine, a merchant, in London. He and his brother went there a year ago, with a thousand pounds apiece; and on New-Year's-day they had sixty thousand pounds between them!"
"How did they do it?" Norman eagerly exclaimed. Even the elder traveller looked excited.
The Governor handed him the open letter. "Anybody can do it, when once they know how," so ran this oracular document. "We borrowed nought: we stole nought. We began the year with only a thousand pounds apiece: and last New-Year's-day we had sixty thousand pounds between us--sixty thousand golden sovereigns!"
Norman looked grave and thoughtful as he handed back the letter. His father hazarded one guess. "Was it by gambling?"
"A Kgovjnian never gambles," said the Governor gravely, as he ushered them through the palace gates. They followed him in silence down a long passage, and soon found themselves in a lofty hall, lined entirely with peacocks' feathers. In the centre was a pile of crimson cushions, which almost concealed the figure of Her Radiancy--a plump little damsel, in a robe of green satin dotted with silver stars, whose pale round face lit up for a moment with a half-smile as the travellers bowed before her, and then relapsed into the exact expression of a wax doll, while she languidly murmured a word or two in the Kgovjnian dialect.
The Governor interpreted. "Her Radiancy welcomes you. She notes the Impenetrable Placidity of the old one, and the Imperceptible Acuteness of the youth."
Here the little potentate clapped her hands, and a troop of slaves instantly appeared, carrying trays of coffee and sweetmeats, which they offered to the guests, who had, at a signal from the Governor, seated themselves on the carpet.
"Sugar-plums!" muttered the old man. "One might as well be at a confectioner's! Ask for a penny bun, Norman!"
"Not so loud!" his son whispered. "Say something complimentary!" For the Governor was evidently expecting a speech.
"We thank Her Exalted Potency," the old man timidly began. "We bask in the light of her smile, which----"
"The words of old men are weak!" the Governor interrupted angrily. "Let the youth speak!"
"Tell her," cried Norman, in a wild burst of eloquence, "that, like two grasshoppers in a volcano, we are shrivelled up in the presence of Her Spangled Vehemence!"
"It is well," said the Governor, and translated this into Kgovjnian. "I am now to tell you," he proceeded, "what Her Radiancy requires of you before you go. The yearly competition for the post of Imperial Scarf-maker is just ended; you are the judges. You will take account of the rate of work, the lightness of the scarves, and their warmth. Usually the competitors differ in one point only. Thus, last year, Fifi and Gogo made the same number of scarves in the trial-week, and they were equally light; but Fifi's were twice as warm as Gogo's and she was pronounced twice as good. But this year, woe is me, who can judge it? Three competitors are here, and they differ in all points! While you settle their claims, you shall be lodged, Her Radiancy bids me say, free of expense--in the best dungeon, and abundantly fed on the best bread and water."
The old man groaned. "All is lost!" he wildly exclaimed. But Norman heeded him not: he had taken out his note-book, and was calmly jotting down the particulars.
"Three they be," the Governor proceeded, "Lolo, Mimi, and Zuzu. Lolo makes 5 scarves while Mimi makes 2; but Zuzu makes 4 while Lolo makes 3! Again, so fairylike is Zuzu's handiwork, 5 of her scarves weigh no more than one of Lolo's; yet Mimi's is lighter still--5 of hers will but balance 3 of Zuzu's! And for warmth one of Mimi's is equal to 4 of Zuzu's; yet one of Lolo's is as warm as 3 of Mimi's!"
Here the little lady once more clapped her hands.
"It is our signal of dismissal!" the Governor hastily said. "Pay Her Radiancy your farewell compliments--and walk out backwards."
The walking part was all the elder tourist could manage. Norman simply said "Tell Her Radiancy we are transfixed by the spectacle of Her Serene Brilliance, and bid an agonized farewell to her Condensed Milkiness!"
"Her Radiancy is pleased," the Governor reported, after duly translating this. "She casts on you a glance from Her Imperial Eyes, and is confident that you will catch it!"
"That I warrant we shall!" the elder traveller moaned to himself distractedly.
Once more they bowed low, and then followed the Governor down a winding staircase to the Imperial Dungeon, which they found to be lined with coloured marble, lighted from the roof, and splendidly though not luxuriously furnished with a bench of polished malachite. "I trust you will not delay the calculation," the Governor said, ushering them in with much ceremony. "I have known great inconvenience--great and serious inconvenience--result to those unhappy ones who have delayed to execute the commands of Her Radiancy! And on this occasion she is resolute: she says the thing must and shall be done: and she has ordered up ten thousand additional bamboos!" With these words he left them, and they heard him lock and bar the door on the outside.
"I told you how it would end!" moaned the elder traveller, wringing his hands, and quite forgetting in his anguish that he had himself proposed the expedition, and had never predicted anything of the sort. "Oh that we were well out of this miserable business!"
"Courage!" cried the younger cheerily. "Hæc olim meminisse juvabit! The end of all this will be glory!"
"Glory without the L!" was all the poor old man could say, as he rocked himself to and fro on the malachite bench. "Glory without the L!"
[Footnote A: "Maskee," in Pigeon-English, means "without."]
"Base is the slave that pays."
"Would you mind writing it down at once? I shall be quite certain to forget it if you don't!"
"My dear, we really must wait till the cab stops. How can I possibly write anything in the midst of all this jolting?"
"But really I shall be forgetting it!"
Clara's voice took the plaintive tone that her aunt never knew how to resist, and with a sigh the old lady drew forth her ivory tablets and prepared to record the amount that Clara had just spent at the confectioner's shop. Her expenditure was always made out of her aunt's purse, but the poor girl knew, by bitter experience, that sooner or later "Mad Mathesis" would expect an exact account of every penny that had gone, and she waited, with ill-concealed impatience, while the old lady turned the tablets over and over, till she had found the one headed "PETTY CASH."
"Here's the place," she said at last, "and here we have yesterday's luncheon duly entered. One glass lemonade (Why can't you drink water, like me?) three sandwiches (They never put in half mustard enough. I told the young woman so, to her face; and she tossed her head--like her impudence!) and seven biscuits. Total one-and-two-pence. Well, now for to-day's?"
"One glass of lemonade----" Clara was beginning to say, when suddenly the cab drew up, and a courteous railway-porter was handing out the bewildered girl before she had had time to finish her sentence.
Her aunt pocketed the tablets instantly. "Business first," she said: "petty cash--which is a form of pleasure, whatever you may think--afterwards." And she proceeded to pay the driver, and to give voluminous orders about the luggage, quite deaf to the entreaties of her unhappy niece that she would enter the rest of the luncheon account.
"My dear, you really must cultivate a more capacious mind!" was all the consolation she vouchsafed to the poor girl. "Are not the tablets of your memory wide enough to contain the record of one single luncheon?"
"Not wide enough! Not half wide enough!" was the passionate reply.
The words came in aptly enough, but the voice was not that of Clara, and both ladies turned in some surprise to see who it was that had so suddenly struck into their conversation. A fat little old lady was standing at the door of a cab, helping the driver to extricate what seemed an exact duplicate of herself: it would have been no easy task to decide which was the fatter, or which looked the more good-humoured of the two sisters.
"I tell you the cab-door isn't half wide enough!" she repeated, as her sister finally emerged, somewhat after the fashion of a pellet from a pop-gun, and she turned to appeal to Clara. "Is it, dear?" she said, trying hard to bring a frown into a face that dimpled all over with smiles.
"Some folks is too wide for 'em," growled the cab-driver.
[Illustration: "I TELL YOU THE CAB-DOOR ISN'T HALF WIDE ENOUGH!"]
"Don't provoke me, man!" cried the little old lady, in what she meant for a tempest of fury. "Say another word and I'll put you into the County Court, and sue you for a Habeas Corpus!" The cabman touched his hat, and marched off, grinning.
"Nothing like a little Law to cow the ruffians, my dear!" she remarked confidentially to Clara. "You saw how he quailed when I mentioned the Habeas Corpus? Not that I've any idea what it means, but it sounds very grand, doesn't it?"
"It's very provoking," Clara replied, a little vaguely.
"Very!" the little old lady eagerly repeated. "And we're very much provoked indeed. Aren't we, sister?"
"I never was so provoked in all my life!" the fatter sister assented, radiantly.
By this time Clara had recognised her picture-gallery acquaintances, and, drawing her aunt aside, she hastily whispered her reminiscences. "I met them first in the Royal Academy--and they were very kind to me--and they were lunching at the next table to us, just now, you know--and they tried to help me to find the picture I wanted--and I'm sure they're dear old things!"
"Friends of yours, are they?" said Mad Mathesis. "Well, I like their looks. You can be civil to them, while I get the tickets. But do try and arrange your ideas a little more chronologically!"
And so it came to pass that the four ladies found themselves seated side by side on the same bench waiting for the train, and chatting as if they had known one another for years.
"Now this I call quite a remarkable coincidence!" exclaimed the smaller and more talkative of the two sisters--the one whose legal knowledge had annihilated the cab-driver. "Not only that we should be waiting for the same train, and at the same station--that would be curious enough--but actually on the same day, and the same hour of the day! That's what strikes me so forcibly!" She glanced at the fatter and more silent sister, whose chief function in life seemed to be to support the family opinion, and who meekly responded--
"And me too, sister!"
"Those are not independent coincidences----" Mad Mathesis was just beginning, when Clara ventured to interpose.
"There's no jolting here," she pleaded meekly. "Would you mind writing it down now?"
Out came the ivory tablets once more. "What was it, then?" said her aunt.
"One glass of lemonade, one sandwich, one biscuit--Oh dear me!" cried poor Clara, the historical tone suddenly changing to a wail of agony.
"Toothache?" said her aunt calmly, as she wrote down the items. The two sisters instantly opened their reticules and produced two different remedies for neuralgia, each marked "unequalled."
"It isn't that!" said poor Clara. "Thank you very much. It's only that I can't remember how much I paid!"
"Well, try and make it out, then," said her aunt. "You've got yesterday's luncheon to help you, you know. And here's the luncheon we had the day before--the first day we went to that shop--one glass lemonade, four sandwiches, ten biscuits. Total, one-and-fivepence." She handed the tablets to Clara, who gazed at them with eyes so dim with tears that she did not at first notice that she was holding them upside down.
The two sisters had been listening to all this with the deepest interest, and at this juncture the smaller one softly laid her hand on Clara's arm.
"Do you know, my dear," she said coaxingly, "my sister and I are in the very same predicament! Quite identically the very same predicament! Aren't we, sister?"
"Quite identically and absolutely the very----" began the fatter sister, but she was constructing her sentence on too large a scale, and the little one would not wait for her to finish it.
"Yes, my dear," she resumed; "we were lunching at the very same shop as you were--and we had two glasses of lemonade and three sandwiches and five biscuits--and neither of us has the least idea what we paid. Have we, sister?"
"Quite identically and absolutely----" murmured the other, who evidently considered that she was now a whole sentence in arrears, and that she ought to discharge one obligation before contracting any fresh liabilities; but the little lady broke in again, and she retired from the conversation a bankrupt.
"Would you make it out for us, my dear?" pleaded the little old lady.
"You can do Arithmetic, I trust?" her aunt said, a little anxiously, as Clara turned from one tablet to another, vainly trying to collect her thoughts. Her mind was a blank, and all human expression was rapidly fading out of her face.
A gloomy silence ensued.
DE OMNIBUS REBUS.
"This little pig went to market: This little pig staid at home."
"By Her Radiancy's express command," said the Governor, as he conducted the travellers, for the last time, from the Imperial presence, "I shall now have the ecstasy of escorting you as far as the outer gate of the Military Quarter, where the agony of parting--if indeed Nature can survive the shock--must be endured! From that gate grurmstipths start every quarter of an hour, both ways----"
"Would you mind repeating that word?" said Norman. "Grurm----?"
"Grurmstipths," the Governor repeated. "You call them omnibuses in England. They run both ways, and you can travel by one of them all the way down to the harbour."
The old man breathed a sigh of relief; four hours of courtly ceremony had wearied him, and he had been in constant terror lest something should call into use the ten thousand additional bamboos.
In another minute they were crossing a large quadrangle, paved with marble, and tastefully decorated with a pigsty in each corner. Soldiers, carrying pigs, were marching in all directions: and in the middle stood a gigantic officer giving orders in a voice of thunder, which made itself heard above all the uproar of the pigs.
"It is the Commander-in-Chief!" the Governor hurriedly whispered to his companions, who at once followed his example in prostrating themselves before the great man. The Commander gravely bowed in return. He was covered with gold lace from head to foot: his face wore an expression of deep misery: and he had a little black pig under each arm. Still the gallant fellow did his best, in the midst of the orders he was every moment issuing to his men, to bid a courteous farewell to the departing guests.
"Farewell, oh old one--carry these three to the South corner--and farewell to thee, thou young one--put this fat one on the top of the others in the Western sty--may your shadows never be less--woe is me, it is wrongly done! Empty out all the sties, and begin again!" And the soldier leant upon his sword, and wiped away a tear.
"He is in distress," the Governor explained as they left the court. "Her Radiancy has commanded him to place twenty-four pigs in those four sties, so that, as she goes round the court, she may always find the number in each sty nearer to ten than the number in the last."
"Does she call ten nearer to ten than nine is?" said Norman.
"Surely," said the Governor. "Her Radiancy would admit that ten is nearer to ten than nine is--and also nearer than eleven is."
"Then I think it can be done," said Norman.
The Governor shook his head. "The Commander has been transferring them in vain for four months," he said. "What hope remains? And Her Radiancy has ordered up ten thousand additional----"
"The pigs don't seem to enjoy being transferred," the old man hastily interrupted. He did not like the subject of bamboos.
"They are only provisionally transferred, you know," said the Governor. "In most cases they are immediately carried back again: so they need not mind it. And all is done with the greatest care, under the personal superintendence of the Commander-in-Chief."
"Of course she would only go once round?" said Norman.
"Alas, no!" sighed their conductor. "Round and round. Round and round. These are Her Radiancy's own words. But oh, agony! Here is the outer gate, and we must part!" He sobbed as he shook hands with them, and the next moment was briskly walking away.
"He might have waited to see us off!" said the old man, piteously.
"And he needn't have begun whistling the very moment he left us!" said the young one, severely. "But look sharp--here are two what's-his-names in the act of starting!"
Unluckily, the sea-bound omnibus was full. "Never mind!" said Norman, cheerily. "We'll walk on till the next one overtakes us."
They trudged on in silence, both thinking over the military problem, till they met an omnibus coming from the sea. The elder traveller took out his watch. "Just twelve minutes and a half since we started," he remarked in an absent manner. Suddenly the vacant face brightened; the old man had an idea. "My boy!" he shouted, bringing his hand down upon Norman's shoulder so suddenly as for a moment to transfer his centre of gravity beyond the base of support.
Thus taken off his guard, the young man wildly staggered forwards, and seemed about to plunge into space: but in another moment he had gracefully recovered himself. "Problem in Precession and Nutation," he remarked--in tones where filial respect only just managed to conceal a shade of annoyance. "What is it?" he hastily added, fearing his father might have been taken ill. "Will you have some brandy?"
"When will the next omnibus overtake us? When? When?" the old man cried, growing more excited every moment.
Norman looked gloomy. "Give me time," he said. "I must think it over." And once more the travellers passed on in silence--a silence only broken by the distant squeals of the unfortunate little pigs, who were still being provisionally transferred from sty to sty, under the personal superintendence of the Commander-in-Chief.
A SERPENT WITH CORNERS.
"Water, water, every where, Nor any drop to drink."
"It'll just take one more pebble."
"What everare you doing with those buckets?"
The speakers were Hugh and Lambert. Place, the beach of Little Mendip. Time, 1.30, P.M. Hugh was floating a bucket in another a size larger, and trying how many pebbles it would carry without sinking. Lambert was lying on his back, doing nothing.
For the next minute or two Hugh was silent, evidently deep in thought. Suddenly he started. "I say, look here, Lambert!" he cried.
"If it's alive, and slimy, and with legs, I don't care to," said Lambert.
"Didn't Balbus say this morning that, if a body is immersed in liquid, it displaces as much liquid as is equal to its own bulk?" said Hugh.
"He said things of that sort," Lambert vaguely replied.
"Well, just look here a minute. Here's the little bucket almost quite immersed: so the water displaced ought to be just about the same bulk. And now just look at it!" He took out the little bucket as he spoke, and handed the big one to Lambert. "Why, there's hardly a teacupful! Do you mean to say that water is the same bulk as the little bucket?"
"Course it is," said Lambert.
"Well, look here again!" cried Hugh, triumphantly, as he poured the water from the big bucket into the little one. "Why, it doesn't half fill it!"
"That's its business," said Lambert. "If Balbus says it's the same bulk, why, it is the same bulk, you know."
"Well, I don't believe it," said Hugh.
"You needn't," said Lambert. "Besides, it's dinner-time. Come along."
They found Balbus waiting dinner for them, and to him Hugh at once propounded his difficulty.
"Let's get you helped first," said Balbus, briskly cutting away at the joint. "You know the old proverb 'Mutton first, mechanics afterwards'?"
The boys did not know the proverb, but they accepted it in perfect good faith, as they did every piece of information, however startling, that came from so infallible an authority as their tutor. They ate on steadily in silence, and, when dinner was over, Hugh set out the usual array of pens, ink, and paper, while Balbus repeated to them the problem he had prepared for their afternoon's task.
"A friend of mine has a flower-garden--a very pretty one, though no great size--"
"How big is it?" said Hugh.
"That's what you have to find out!" Balbus gaily replied. "All I tell you is that it is oblong in shape--just half a yard longer than its width--and that a gravel-walk, one yard wide, begins at one corner and runs all round it."
"Joining into itself?" said Hugh.
"Not joining into itself, young man. Just before doing that, it turns a corner, and runs round the garden again, alongside of the first portion, and then inside that again, winding in and in, and each lap touching the last one, till it has used up the whole of the area."
"Like a serpent with corners?" said Lambert.
"Exactly so. And if you walk the whole length of it, to the last inch, keeping in the centre of the path, it's exactly two miles and half a furlong. Now, while you find out the length and breadth of the garden, I'll see if I can think out that sea-water puzzle."
"You said it was a flower-garden?" Hugh inquired, as Balbus was leaving the room.
"I did," said Balbus.
"Where do the flowers grow?" said Hugh. But Balbus thought it best not to hear the question. He left the boys to their problem, and, in the silence of his own room, set himself to unravel Hugh's mechanical paradox.
"To fix our thoughts," he murmured to himself, as, with hands deep-buried in his pockets, he paced up and down the room, "we will take a cylindrical glass jar, with a scale of inches marked up the side, and fill it with water up to the 10-inch mark: and we will assume that every inch depth of jar contains a pint of water. We will now take a solid cylinder, such that every inch of it is equal in bulk to half a pint of water, and plunge 4 inches of it into the water, so that the end of the cylinder comes down to the 6-inch mark. Well, that displaces 2 pints of water. What becomes of them? Why, if there were no more cylinder, they would lie comfortably on the top, and fill the jar up to the 12-inch mark. But unfortunately there is more cylinder, occupying half the space between the 10-inch and the 12-inch marks, so that only one pint of water can be accommodated there. What becomes of the other pint? Why, if there were no more cylinder, it would lie on the top, and fill the jar up to the 13-inch mark. But unfortunately----Shade of Newton!" he exclaimed, in sudden accents of terror. "When does the water stop rising?"
A bright idea struck him. "I'll write a little essay on it," he said.
* * * * *
"When a solid is immersed in a liquid, it is well known that it displaces a portion of the liquid equal to itself in bulk, and that the level of the liquid rises just so much as it would rise if a quantity of liquid had been added to it, equal in bulk to the solid. Lardner says, precisely the same process occurs when a solid is partially immersed: the quantity of liquid displaced, in this case, equalling the portion of the solid which is immersed, and the rise of the level being in proportion.
"Suppose a solid held above the surface of a liquid and partially immersed: a portion of the liquid is displaced, and the level of the liquid rises. But, by this rise of level, a little bit more of the solid is of course immersed, and so there is a new displacement of a second portion of the liquid, and a consequent rise of level. Again, this second rise of level causes a yet further immersion, and by consequence another displacement of liquid and another rise. It is self-evident that this process must continue till the entire solid is immersed, and that the liquid will then begin to immerse whatever holds the solid, which, being connected with it, must for the time be considered a part of it. If you hold a stick, six feet long, with its end in a tumbler of water, and wait long enough, you must eventually be immersed. The question as to the source from which the water is supplied--which belongs to a high branch of mathematics, and is therefore beyond our present scope--does not apply to the sea. Let us therefore take the familiar instance of a man standing at the edge of the sea, at ebb-tide, with a solid in his hand, which he partially immerses: he remains steadfast and unmoved, and we all know that he must be drowned. The multitudes who daily perish in this manner to attest a philosophical truth, and whose bodies the unreasoning wave casts sullenly upon our thankless shores, have a truer claim to be called the martyrs of science than a Galileo or a Kepler. To use Kossuth's eloquent phrase, they are the unnamed demigods of the nineteenth century."[B]
* * * * *
"There's a fallacy somewhere