 Chapter 1 of A Tangled Tale To My Pupil Beloved pupil, tamed by thee, adished, subtract, multiplication, 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. This Carol, October 1885. A Tangled Tale, not one. Excelsior. Goblin, lead them up and down. The ruddy glow of sunset was already fading into the somber 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 un-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 throw, he exclaimed. We sped not thus in the ascent. Goodly indeed, the other echoed with a groan. We clumped 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 virily replied. Not an ounce more, he added with that love of metaphors so common in old age, and not a far thing less. Tours three hours passed high noon when we left our hostelry, the young man said, musingly. We shall scarce be banked 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 meat. A brave concede, cried the other with a merry laugh. And should we bid him bring us yet another course, I'd trow his answer will be tart. We shall but get our desserts, sighed the elder knight, who had never seen a joke in his life, and was somewhat displeased at his companion's untimely levity. To a benign of the clock, he added in an undertone, by the time we regain our hostelry. Full many a mile shall we have plotted this day. How many? How many? cried the eager youth, ever a thirst 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. And I guess be within one poor half hour of the mark, this all I ask of their mother's son. Then will I tell thee, true to the last inch, how far we shall have trudged, between 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. End of chapter one Chapter two of A Tangled Tale This LibriVox recording is in the public domain. Recording by Avayee in October 2009. A Tangled Tale by Lewis Carroll. Chapter two. Not two, 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. 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 the 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 the moral from every anecdote about Balbus. Sometimes one of warning, as in, Balbus had borrowed a healthy dragon, against which he had written, rushness 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 he could get to exhibit the rapidity of the hero's departure. A very part of the state of things was discouraging. That most fashionable of watering places, little mendip, was chock-full, 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. There 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 his long, lanky creature would have been all the better with even shorter legs, but no such thought occurred to his loving pupils. One on each side did their best to keep up with his gigantic strides, while Hugh repeated a 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? Govtny, 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 are 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! Beautiful! Equilateral! And rectangular! The boys looked round with less enthusiasm. Number nine is the first with a card, said Prozac Lambert, but Balbus would not so soon awake from his dream of beauty. See, boys! he cried. Twenty doors on a side, what symmetry! He 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. There is one room, gentlemen, said the smiling landlady, and a sweet room too, a snug 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 was posed. Which indeed there is, gentlemen, the landlady indignantly protested as she drew up the blind and indicated the back garden. Cabbage, I perceive, Well, they're green at any rate. Which the greens at the shops, their hostess explained, are by no means dependable upon. Here he has them on the premises end 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 25. This landlady was grave and stern. I've no but one room left, she told him, and it gives on the back garden. 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 gross them ourselves. A singular advantage, said Balbus, and after the usual questions, they went on to 52. And I'd gladly accommodate you all if I could, was the greeting that met them. We are but mortal. You're relevant, muttered Balbus, and I've let all my rooms but one. Which one is the 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 gross 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 you 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 73, leaving the landlady curtsying 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 73 they found only a small shy girl to show the house, who said, Yes, hmm? 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, hmm? 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, hmm? said the girl as she showed them out. One day room and three bedrooms, 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. End of chapter 2 Chapter 3 of A Tangled Tale This LibriVox recording is in the public domain. Recording by Avayee in October 2009. A Tangled Tale by Lewis Carroll. Chapter 3. Not 3. Mad Mathesis. I waited for the train. Well, they call me so because I am a little mad, I suppose. She said, good-humidly, in answer to Clara's cautiously worded question as to how she came by so strange a nickname. You see, I never do what sane people are expected to do nowadays. I never wear long trains. Talking of trains, that's the Charing Cross Metropolitan Station. I have something to tell you about that. And I never play lawn tennis. I can't cook an omelet. I can't even set a broken limb. There's an ignamorous for you. Clara was her niece and full 20 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 you are 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 base water in 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 chaperone, 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 perceptress has often warned us. You'd be none the worse if you did, Matt Mathis is interrupted. In fact, you'd be the better, I'm certain. Neither does our excellent perceptress 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, Matt Mathis is 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 a light. 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 smoked cigars, she said in a meagly apologetic tone. Our excellent perceptress, but Matt Mathis' 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. Matt Mathis' prattling on as usual. Clara silenced, 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 have been in that pail of cold water. I know, I know, said Clara dreamily. The pail, the cold and the moony. Take your places on the springboards! shouted the porter. What are they for? Clara asked in a terrified whisper. Merely to help us into the trains. The elder lady spoke with a 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 mini 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 chairing cross-platform and eagerly compared notes. Then Clara turned away with a sigh. Two young impulsive hearts like hers, disappointment is always a bitter pill. Mad Mathesys 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 springboards, 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 the tunnel and two travellers leaned back in the corners with a sigh or rather with two sighs of relief. One. Clara murmured to herself. One. It's a word of good omen. This time at any rate the victory will be mine. But was it? End of chapter three. Chapter four of A Tangled Tale. This LibriVox recording is in the public domain. Recording by Avayee in October 2009. A Tangled Tale by Lewis Carroll. Chapter four. Not four. The Dead Reckoning. I did dream of money bags tonight. Noonday on the open sea within a few degrees of the equator is apt to be oppressively warm and our two travellers were now eerily clad in suits of dazzling white linen having laid aside the chain armour which they had found not only indurable in the cold mountain air they had lately been breathing but a necessary precaution against the daggers of the Banditi 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 effect while in nightly disguise and had returned to the ordinary style of two country gentlemen of the 20th century. Stretched on a pile of cushions under the shade of huge umbrella they were lazily watching some native fisherman 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 fisherman 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. Fisherman, he explained are often passengers in my ship. These five are from Mruxy 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 realize his motive and with the 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, etc. as they could find. This brought their excitement to a speedy end they carefully hid their sacks in the fold of the jeep that lay on the deck near the tourists and strolled away. When next the captain's heavy foot form passed the young 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 called it 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 sat 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 come in close and a fatiguing conversation he had just gone through was too much for him. He sank back among the cushions in silence. His father courageously 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 landsmen. 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 anyone 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 which 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 fisherman 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 fisherman. Come here, my man, he said, in the Mruxy and 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 holy stones, 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 and 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 too 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 with the old man's more cautious remark. They did have five separate weighings, the captain said. But while it beats me entirely, he added in a sudden burst of candor. Here's the result. First and second sack weighed 12 pounds, second and third, 13 and a half, third and fourth, 11 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 16 pounds. Dear 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. It's such be your good pleasure. I contemplate myself. A Tangle Till by Lewis Carroll. Chapter five. Not five, aughts and crosses. Look here upon this picture and on this. And what made you choose the first train, Goosey? said Matt 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 perceptress always says when in doubt, my dears, take an extreme case. And I was in doubt. Does it always succeed? Her aunt inquired. 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 noise at tea, you know. The more noise you make, the less jam you will have and vice versa. And I thought they wouldn't know what vice versa 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 perceptress said it wasn't a good instance. Why wasn't it? She added plaintively. Her aunt evaded the question. She said, but how did you work it with the metropolitan trains? None of them go infinitely fast, I believe. I called them hairs and tortoises. Clara said, a little timidly, for she dreaded being laughed at. And I thought there couldn't be so many hairs as tortoises on the line. So I took an extreme case. One hair and an infinite number of tortoises. An extreme case indeed, 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 hair to meet. But if I went with the hair, 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 today. 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, Matt Mathesies 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 odds and crosses. Crosses for good marks for bad. The first column is for choice of subject. The second for arrangement. The third for coloring. 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. Anyone 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. But suppose we mark 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. One or two pictures, two odds to three or four, and one odd to eight or nine. I don't want you to be too hard on the arrays. 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 a broom enough for twenty. Mind what you say, my dear, her aunt into post. It's by an RA. 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 Matty 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 colored. The little old ladies glanced at each other in some alarm. Calm yourself, my dear, said the one who had spoken first and tried to remember which it was. What was the subject? Was it an elephant, for instance? The other sister suggested. They were still inside 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 called only the one word mad. They mean Aunt Matty, of course, she said to herself fancying in her innocence that London was like a native town where everybody knew everybody else. If you mean my aunt, she added aloud. She's there, just three pictures of Lieutenant Brown. Ah, well, then you better go to her, my dear, her new friend said soothingly. She'll find you the picture you want. Goodbye, dear. Goodbye, 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, I wonder why they pity me so. And she wanted on murmuring to herself it must have two good marks and end of Chapter 5. Chapter 6 of A Tangled Tale This LibriVox recording is in the public domain. Recording by Avayee in October 2009. A Tangled Tale by Lewis Carroll. Not Six Her Radiancy One PC Singh said may have got. Maskey said Singh might not can do. You talking you not say be what? Bamboo. Footnote Maskey in Pidgin English means without and footnote. 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 travelers whose guide could speak nothing but Kugofjnian. 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. 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 fella 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 vie it, for they are fat. This old man is thin and thankful to be so, muttered the elder traveler. Beaten we shall be without a doubt. It's a comfort to know it won't be beaten without the bee. 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 faulted one of his heroes. Come, come, don't lose heart, said the other. All this is full of charm for me. You are young, Norman, said his father, young and light-hearted. For me, it's charm without the sea. See, old one is sad, the governor remarked with some anxiety. He has without doubt defected 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 zoomed 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 we had 60,000 pounds between them. How did they do it? Norman eagerly exclaimed. Even the elder traveler looked excited. The governor handed him the open letter. Anybody can do it when once they know how surrender's oracular document. We borrowed not, we stole not. We began the year with only a thousand pounds apiece and last New Year's Day we had 60,000 pounds between us, 60,000 gold and sovereigns. Norman looked grave and thoughtful as he handed back the letter. His father hesitated one guess. Was it by gambling? A Cagovgenian never gambles, said the governor gravely as he ushered him through the palace gates. They followed him in silence down a long passage and soon found themselves in a lofty hall lined entirely with peacock's feathers. In the center was a pile of crimson cushions which almost concealed the figure of her radiancy. A plump little dimsel in a robe of green satin dotted with silver stars whose pale round face led up for a moment with a half smile as the traveler bowed before her and then relapsed into the exact expression of a wax doll while she languidly murmured a word or two in the Cagovgenian dialect. The governor interpreted. Her radiancy welcomes you. She notes the impenetrable purity of the old one and the imperceptible acuteness of the youth. Here the little potentate clapped her hands and the 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 the confectioners. Ask for a penny-bund, Norman. Not so loud, his son whispered. 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 man Avic, the governor interrupted angrily. Let's say you speak. Tell her, cried Norman, in a wild burst of eloquence, that like two grasshoppers in a volcano we are shriveled up in the presence of her spangled vehemence. Said the governor and translated this into Kugovgenian. 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 met 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, who is me, who can judge it? Three competitors are here and say 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 notebook and was calmly jotting down the particulars. Three day be, the governor proceeded. Lolo, Mimi and Zuzu. Lolo makes five scarves while Mimi makes two, but Zuzu makes four while Lolo makes three. Again, so far he likes Zuzu's handiwork. Five of her scarves were no more than one of Lolo's. Yet Mimi is lighter still. Five of hers will but balance three of Zuzu's. And for whams one of Mimi's is equal to four of Zuzu's. Yet one of Lolo's is as warm as three of Mimi's. Here the little lady once more clapped her hands. It's our sign of dismissal, the governor hastily said. Pay her radiancy your farewell compliments and walk out backwards. The walking part was all the elder tourists could manage. 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 Julie translating this. She casts on you a glance from her imperial eyes and is confident that you will catch it. That I warned we shall, the elder traveler moaned to himself distractedly. Once more they bowed low and then followed the governor down their case to the imperial dungeon, which they found to be lined with colored marble, lighted from the roof and splendidly dono 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 sing must and shall be done, and she has ordered up ten thousand additional bamboos. With these words he left them and they hurt him lock and barred the door on the outside. I told you how it would end, moaned the elder traveler ringing his hands and quite forgetting in his anguish that he had himself proposed the expedition and had never predicted anything of the sort, or that we were well out of this miserable business. Courage! cried the younger cheerily. Haq'olim memini se yuvabit. 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. End of Chapter 6 Chapter 7 of A Tangled Tale This LibriVox recording is in the public domain. Recording by Ava'i in October 2009. A Tangled Tale by Lewis Carroll Chapter 7 Not 7 Petty Cash Bass is the slave that pays. Aunt Matty My child 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 lunch and Julie entered. One glass lemonade Why can't you drink water like me? Three sandwiches they never put in half mustered enough. I told the young woman so to her face and tossed her head like her impudence and seven biscuits total one and two pence Well, now for two days One glass of lemonade Clara was beginning to say when suddenly the cab drew up and the courtyus 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 In 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 vouched safe 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 voice 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 humour of the two sisters. I tell you the cab tour 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 white for him. Growled the cab driver. 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 cab man touched his head 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 have 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 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 recognized 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 launching 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 are dear old things. Friends of yours, are they? said Matt 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 on the same bench waiting for the train, and chatting as if they had known one another for years. Now, this cycle 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 functioning life seemed to be to support a family opinion and who meekly responded, and me too, sister. Those are not independent coincidences. Matt 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. Too thick, 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 unequaled. Matt, 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 five pence. She handed the tablets to Clara, who gazed at them and told him 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 that 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 two larger 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 Myrma 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 arm 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. The omnibus rebus This little pig went to market. This little pig stayed at home. By her idiances expressed command, said the governor as he conducted the travelers 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 quota where the agony of parting if indeed nature can survive the shock must be endured. From said gate Grøm Stipps start every quarter of an hour both ways. Would you mind repeating that word? said Norman Grøm Grøm Stipps The governor repeated. You call some 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 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 middles to the 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 to whisper 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 be the courteous farewell to the departing guests. The old one carried these three to the south corner and farewell to thee, so young one. Put this fat one on the top of the others in the western sky. May your shadows never be less. Who is me? It is wrongly done. Empty out all the skies and begin again. And the soldier lent 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 stye nearer to ten than the number in the last. Does she call ten nearer to ten the nineties, said Norman? Surely, said the governor. Her radiancy would admit that ten is nearer to ten the nineties 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. Sear only provisionally transferred, you know, said the governor. In most cases Sear immediately carried back again, so they did 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. All has no side there 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 bristly walking away. He might have waited to see us off, said the old man picturesly. 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 over takes 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 12 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 center of gravity beyond the base of support. Thus taken off his guard, the young man wildly staggered forwards about to plunge into space. But in another moment he had gracefully recovered himself. Problem in procession and notation, 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 over take us? When? When? The old man cried, growing more excited every moment. Norman looked gloomily. 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 stye to stye under the personal superintendence of the commander-in-chief. End of chapter 8 Chapter 9 of A Tangled Tale This LibriVox recording is in the public domain. Recording by Avayee in October 2009 A Tangled Tale by Lewis Carroll Chapter 9 Not 9, a serpent with corners. Water, water, everywhere nor any drop to drink. It'll just take one more pebble. Whatever are 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 too. 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 tea cup full. Do you mean to say that water is the same bulk as the little bucket? Of 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 you 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 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 a long in shape just half a yard longer than it's width and that a gravel walk one yard wide begins at one corner and runs all round it. It turns 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 center 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 seawater puzzle. You said it was a flower garden. Hugh inquired as Balbus was leaving the room. I did. said Balbus. Where did 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 side 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 four inches of it into the water so that the end of the cylinder comes down to the six inch mark. Well, that displaces two pints of water. What becomes of them? Why if there were no more cylinder they would lie comfortably on 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 Balbus's essay 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 equaling 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 6 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 a familiar instance of a man standing at the edge of the sea at Eptide 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 the philosophical truth and whose bodies the unraising wave cast sullenly upon our thankless shores have a truer claim to be called the martyrs of science than a Galileo or a Kepler to use Cotthas' eloquent phrase they are the unnamed demigods of the 19th century. Footnote Note by the writer for the above essay I am indebted to a dear friend now deceased and footnote There is a fallacy somewhere he murmured drowsily as he stretched his long legs upon the sofa I must think it over again He closed his eyes in order to concentrate his attention more perfectly and for the next hour or so his slow and regular breathing bore witness to the careful deliberation with which he was investigating this new and perplexing view of the subject. End of chapter Chapter 10 of A Tangled Tale This LibriVox recording is in the public domain recording by Avaí in October 2009 A Tangled Tale by Lewis Carroll Chapter 10 Not 10 Chelsea Buns Yeah, Buns and Buns and Buns Old Song How very, very sad exclaimed Clara in the eyes of the gentle girl filled with tears as she spoke Sad but very curious when he come to look at it arithmetically was her aunts less romantic reply Some of them have lost an arm in their country's service, some a leg some an ear, some an eye and some, perhaps, all Clara murmured dreamily as they passed the long rows of weather-beaten heroes basking in the sun. Did you notice that very old one with a red face who was drawing a map in the dust with his wooden leg and all the others watching? I think it was a plan of a battle The battle of Trafalgar, no doubt her aunts interrupted briskly Hardly that, I think Clara ventured to say You see, in that case he couldn't well be alive Couldn't well be alive the old lady contemptuously repeated He's as lively as you and me put together Why, if drawing a map in the dust with one's wooden leg doesn't prove one to be alive perhaps you'll kindly mention what does prove it Clara did not see her way out of it A logic had never been her forte To return to the arithmetic Mad Mathesis resumed The eccentric old lady never let slip an opportunity of driving her niece into a calculation What percentage do you suppose must have lost all four? A leg, an arm, an eye and an ear? How can I tell? Gasp the terrified girl She knew well what was coming You can't, of course, without data Her aunt replied But I'm just going to give you Give her a Chelsea bun, Miss That's what most young ladies likes best The voice was rich and musical and the speaker dexterously whipped back the snowy cloth that covered his basket and disclosed the tempting array of the familiar square buns joined together in rows richly egged and browned and glistening in the sun No, sir, I shall give her nothing so indigestible Be off! The pair are so threateningly but nothing seemed to disturb the good humour of the jolly old man who marched on chanting his melodious refrain Chelsea buns, Chelsea buns hot, Chelsea bun Chelsea buns hot, Chelsea buns Far too indigestible, my love said the old lady Percentages will agree with you ever so much better Claire aside, and there was a hungry look in her eyes as she watched a basket of pigeons but she meekly listened to the relentless old lady who at once proceeded to count off the data on her fingers Say that 70% have lost an eye 75% an ear 80% an arm 85% a leg that'll do it beautifully Now, my dear, what percentage at least must have lost all four? No more conversation occurred unless a smothered exclamation of piping hot which escaped from Claire's lips as the basket vanished round the corner could be counted as such until they reached the old Chelsea mansion where Claire's father was then staying with his three sons and their old tutor Balbus Lambert and Hugh had entered the house only a few minutes before them They had been out walking and Hugh had been propounding a difficulty which had reduced Lambert to the depths of gloom and had even puzzled Balbus It changes from Wednesday to Thursday at midnight, doesn't it? Hugh had begun Sometimes said Balbus cautiously Always said Lambert decisively Sometimes Balbus gently insisted Six midnight out of seven it changes to some other name I meant, of course, Hugh corrected himself When it does change from Wednesday to Thursday it does it at midnight and only at midnight Surely, said Balbus Lambert was silent Well, now suppose it's midnight here in Chelsea Then it's Wednesday west of Chelsea say in Ireland or America where midnight hasn't arrived yet and it's Thursday east of Chelsea say in Germany or Russia where midnight has just passed by Surely, Balbus said again Even Lambert noted this time But it isn't midnight anywhere else so it can't be changing from one day to another anywhere else And yet, if Ireland and America and so on call it Wednesday and Germany and Russia and so on call it Thursday there must be some place not Chelsea that has different days on the two sides of it And the worst of it is the people there get their days in the wrong order They've got Wednesday east of them and Thursday west just as if their day had changed from Thursday to Wednesday I've heard that puzzle before and I'll tell you the explanation When a ship goes around the world from east to west we know that it loses a day in its reckoning so that when it gets home and calls it's day Wednesday it finds people here calling it Thursday because we've had one more midnight than the ship has had and when you go the other way around you gain a day like you in reply to this not very lucid explanation but it doesn't help me because the ship hasn't proper days One way round you get more than 24 hours to the day and the other way you get less so of course the names get wrong but people that live on in one place always get 24 hours to the day I suppose there is such a place Balba said meditatively though I never heard of it and the people must find it very queer as you says to have the old day east of them and the new one west because when midnight comes round to them with a new day in front of it and the old one behind it one doesn't see exactly what happens I must think it over so they had entered the house in the state I have described Balba's puzzled and lambered buried in gloomy thought Master is at home said the stately old butler it is only a butler of experience who can manage a series of three M's together without any interjacent vowels and the old party is awaiting for you in the library I don't like his calling your father an old party Mad Mathesys whispered to her niece as they crossed the hall and Clara had only just time to whisper in reply he meant the whole party before they were ushered into the library and the side of the five solemn faces were assembled to chill her into silence her father sat at the head of the table and mutely signed to the ladies to take the two vacant chairs one on each side of him his three sons and Balba's completed the party writing materials had been arranged down to table after the fashion of a ghostly banquet the butler had evidently bestowed much thought on the grim device sheets of quarto paper each flanked by a pen on one side and the pencil on the other and the plates pen wipers did duty for rolls of bread while ink bottles stood in the places usually occupied by wine glasses the pièce de résistance was a large green base bag which gave forth as the old man restlessly lifted it from side to side a charming jingle as of innumerable golden guineas sister, daughter, sons and Balba's the old man began so nervously here, here while Hugh drummed on the table with his fists this disconcerted the unpracticed orator sister he began again then paused a moment moved the bag to the other side and went on with a rush I mean this being a critical occasion more or less being the year when one of my sons comes of age he paused again in some confusion having evidently got into the middle of his speech sooner than he intended but it was too late to go back here, here, cried Balba's quite so said the old gentleman recovering his self-possession a little when first I began this annual custom my friend Balba's will correct me if I am wrong Hugh whispered with a strap but nobody hurt him except Lambert who only frowned and shook his head at him this annual custom of giving each of my sons as many guineas as would represent his age it was a critical time so Balba's informed me as the ages of two of you were together equal to that of the third so on that occasion I made a speech he paused so long that Balba's thought it well to come to the rescue with the words it was at most but the old man checked him with a warning look yes, made a speech he repeated a few years after that Balba's pointed out I say pointed out cried Balba's quite so said the grateful old man that it was another critical occasion the ages of two of you were together double that of the third so I made another speech another speech and now again it's a critical occasion so Balba's says and I am making here Matt Mathes is pointedly referred to her watch all the haste I can the old man cried with wonderful presence of mind indeed sister, I'm coming to the point now the number of years that have passed since that first occasion is just two thirds of the number of guineas I then gave you now my boys, calculate your ages from the data and you shall have the money but we know our ages cried Hugh, silence sir thundered the old man rising to his full height he was exactly five foot five in his indignation he must use the data only you mustn't even assume which it is that comes of age he clutched the bag as he spoke and with tottering steps it was about as much as he could do to carry it he left the room and you shall have a similar cadeau the old lady whispered to her niece when you've calculated that percentage and she followed her brother nothing could exceed the solemnity with which the old couple had risen from the table and yet was it a grin with which the father turned away from his unhappy sons could it be could it be a wink with which the aunt abandoned her despairing niece and where those where those sounds of suppressed chuckling which floated into the room just before Balbus who had followed them out closed the door surely not and yet the butler told the cook but no that was merely idle gossip and I will not repeat it the shades of evening granted their unuttered petition and closed not over them for the butler brought in the lamp the same obliging shades left them a lonely bark the wail of a dog in the backyard baying the moon for a while but neither Morn alas nor any other epoch seemed likely to restore them to that peace of mind which had once been theirs ere ever these problems had swooped upon them and crushed them with a load of unfathomable mystery it's hardly fair muttered you to give us such a jumble as this to work out fair Clara echoed bitterly well and to all my readers I can but repeat the last words of gentle Clara farewell end of chapter 10 chapter 11 of a tangled tale this LibriVox recording is in the public domain recording by Avae in October 2009 a tangled tale by Lewis Carroll chapter 11 appendix a knot said Alice oh do let me help to undo it answers to not one problem two travelers spent from three o'clock till nine in walking along a level road to the hill and home again their pace on the level being four miles an hour uphill three and downhill six find distance walked also within half an hour time of reaching top of hill answer 24 miles half past six solution a level mile takes a quarter of an hour uphill third downhill one sixth hence to go and return over the same mile whether on the level or on the hill side takes half an hour hence in six hours they went 12 miles out and 12 back if the 12 miles out had been nearly all level they would have taken a little over three hours if nearly all uphill a little under four hence three and a half hours must be within one half an hour of the time taken in reaching the peak thus as they started at three they got there within half an hour of half past six 27 answers have come in of these nine are right 16 partially right and two wrong the 16 give the distance correctly but they have failed to grasp the fact that the top of the hill might have been reached at any moment between six o'clock and seven the two wrong answers are from Gertie Vernon and a nihilist the former makes the distance 23 miles while her revolutionary companion puts it at 27 Gertie Vernon says they had to go four miles along the plain and got to the foot of the hill at four o'clock they might have done so I grant but you have no ground for saying they did so it was seven and a half miles to the top of the hill and they reached that at a quarter before seven o'clock here you go wrong in your arithmetic and I must however reluctantly bid you farewell seven and a half miles at three miles an hour would not require two hours and three quarters a nihilist says let X denote a whole number of miles wide a number of hours to hill top therefore three Y equals the number of miles to hill top and X minus three Y equals the number of miles on the other side you bewilder me the other side of what of the hill you say but then how did they get home again however to accommodate your views we will build a new hostelry at the foot of the hill on the opposite side I also assume what I grant you is possible though it is not necessarily true that there was no level road at all even then you go wrong you say Y equals six minus the quantity X minus three Y divided by six two X over four and a half equals six I grant you one but I deny two it rests on the assumption that to go part of the time at three miles an hour and the rest at six miles an hour comes to the same result as going the whole time at four and a half miles an hour but this would only be true if the part were an exact half that is if they went uphill for three hours and downhill for the other three which they certainly did not do the sixteen who are partially right are Agnes Bailey F.K. Fifi G.E.B. H.P. Kit M.E.T. Mysee a mother's son Nairam a Redruthian a socialist Spearmaden TBC and this inertia do not attempt the second part at all F.K. and H.P. give no working the rest make particular assumptions such as that there was no level road that there were six miles of level road and so on all leading to particular times being fixed for reaching the hilltop the most curious assumption is that of Agnes Bailey who says let X equal the number of hours occupied in ascent then X and a half equals the hours occupied in descent and 4X over 3 equals the hours occupied on the level I suppose you were thinking of the relative rates uphill and on the level which we might express by saying that if they went X miles uphill in a certain time they would go 4X over 3 miles on the level in the same time you have in fact assumed that they took the same time on the level that they took in ascending the hill Fifi assumes that when the aged knight said they had gone 4 miles in the hour on the level he meant that 4 miles was the distance gone, not merely the rate this would have been if Fifi will excuse the slang expression a cell ill suited to the dignity of the hero and now descend your classic nine who have solved the whole problem and let me sing your praises your names are Blythe EW, LB Amalboro Boy OVL, Patney Walker Rose, Seabreeze Simple Susan and Money Spinner these last two I counters won as they sent a joint answer Rose and Simple Susan and Co do not actually state that the hilltop was reached some time between 6 and 7 but as they have clearly grasped the fact that a mile ascended and descended took the same time as two level miles I mark them as right Amalboro Boy and Patney Walker deserve honorable mention for their algebraical solutions being the only two who have perceived that the question leads to an indeterminate equation EW brings a charge of untruthfulness against the aged knight a serious charge for he was the very pinky of chivalry she says according to the data given the time at the summit affords no clue to the total distance it does not enable us to state precisely to an inch how much level and how much hill there was in the road fair damsel the aged knight replies if, as I surmise thy initials denote early womanhood be think thee that the word enable is thine, not mine I did but ask the time of reaching the hilltop as my condition for further parlay if now da wilt not grant that I am a truth loving man then will I affirm that those same initials denote evenum to wickedness Class list First Amalboro Boy Patney Walker Second Blythe EW LB OVL Rose Seabreeze Simple Susan and Money Spinner Blythe has made so ingenious in addition to the problem and Simple Susan and Co. have solved that in such tuneful verse that I record both their answers in full I have altered a word or two in Blythe's which I trust she will excuse Stay, said the youth as a gleam of inspiration lighted up the relaxing muscles of his quiescent features. Stay Me thinks it matters little when we reach that summit the crown of our toil for in the space of time wherein we clampered up one mile and bounded down the same on our return we could have trudged the twain on the level. We have plotted then four and twenty miles in these six mortal hours for never a moment did we stop for catching a fleeting breath or for gazing on the scene around very good said the old man twelve miles out and twelve miles in and we reached the top sometime between six and seven of the clock now mark me for every five minutes that had fled since six of the clock when we stood on Yonder Peak so many miles had we toiled upwards on the dreary mountain side the youth moaned and rushed into the hostel Blythe the elder and the younger night they sell it forth at three how far they went on level ground it matters not to me what time they reached a foot of hill when they began to mount are problems which are holds to be of very small account the moment that each waved his hat upon the top most peak to trivial query such as this no answer will I seek yet can I tell the distance well they must have traveled over on hill and plain tweaks three and nine the miles were 24 four miles an hour their steady pace along the level track three when they climbed but six when they came swiftly striding back down the hill and little skill it needs me things to show uphill and down together told four miles an hour they go for whether long or short the time upon the hill they spent two-thirds were passed in going up one-third in the descent two-thirds at three one-third at six if rightly reckoned over will make one hole at four the tail is tangled now no more simple Susan money spinner end of chapter 11 Chapter 12 of A Tangled Tail this LibriVox recording is in the public domain recording by Avae in October 2009 A Tangled Tail by Lewis Carroll Chapter 12 Answers to not two paragraph one the dinner party the governor of Kugovtni wants to give a very small dinner party and invites 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 find the number of guests answer one in this genealogy males are denoted by capitals and females by small letters the governor is capital E and his guest is capital C ten answers have been received of these one is wrong Galanthus Nivales major who insists on inviting two guests one being the governor's wife's brother's father if she had taken his sister's husband's father instead she would have found it possible to reduce the guests to one of the nine who sent right answers C. Breeze is the very faintest breath that ever bore the name she simply states that the governor's uncle might fulfill all the conditions by intermarriages wind of the western sea you have had a very narrow escape be thankful to appear in the class list at all Borg Oak and Brecho of the future use genealogies which require 16 people instead of 14 by inviting the governor's father's sister's husband instead of his father's wife's brother I cannot think it is so good a solution as one that requires only 14 Caius and Valentine deserve special mention as the only two who have supplied genealogies class list first B. Caius MM Mathematics Old Cat Borg Oak Brecho of the future Third C. Breeze Paragraph 2 The Loggings Problem A square has 20 doors on each side which contains 21 equal parts they are numbered all round beginning at one corner from which of the four numbers 9, 25, 52, 73 is the sum of the distance to the other three list answer from number 9 let A be number 9 B number 25 C number 52 and D number 73 then A B equals the square root of the quantity 12 squared plus 5 squared equals the square root of 169 equals 13 AC equals 21 AD equals the square root of the quantity 9 squared plus 8 squared equals the square root of 145 equals 12 plus notabene that is between 12 and 13 BC equals the square root of the quantity 16 squared plus 12 squared equals the square root of 400 equals 20 BD equals the square root of the quantity 3 squared plus 21 squared equals the square root of 450 equals 21 plus CD equals the square root of the quantity 9 squared plus 13 squared equals the square root of 250 equals 15 plus hence sum of distances from A is between 46 and 47 from B between 54 and 55 from C between 56 and 57 from D between 48 and 51 why not between 48 and 49 make this out for yourselves hence the sum is least for A 25 solutions have been received of these 15 must be marked 5 are partly right and 5 right of the 15 I may dismiss alphabetical phantom bog oak, dynamite, fifi garanthus nevalis major I fear the cold spring has blighted out snowdrop guy, HMS pinnafore, janet and valentine with the simple remark that they insist on the unfortunate lodges keeping to the pavement I use the words crossed to number 73 for the special purpose of showing that shortcuts were possible C breeze does the same and adds that the result would be the same even if they crossed the square but gives no proof of this MM draws a diagram and says that number 9 is the house as the diagram shows I cannot see how it does so old cat assumes that the house must be number 9 or number 73 she does not explain how she estimates the distances B's arithmetic is faulty she makes the square root of 169 plus the square root of 442 plus the square root of 130 equal 741 I suppose you mean the square root of 741 which would be a little nearer the truth but roots cannot be added in this manner do you think square root of 9 plus square root of 16 is 25 or even square root of 25 but Iris state is more perilous still she draws illogical conclusions with a frightful calmness after pointing out rightly that AC is less than BD she says therefore the nearest house to the other three must be A or C and again after pointing out rightly that B and D are both within the half square containing A she says therefore AB plus AD must be less than BC plus CD there is no logical force in either therefore for the first try numbers one 21, 60, 70 this will make your premise true and your conclusion false similarly for the second try numbers one 30 51, 71 of the five partly right solutions rags and tatters and mad hatter who send one answer between them make number 25 6 units from the corner instead of 5 CHIM ERDL and megipots leave openings at the corners of the square which are not in the data moreover CHIM gives values for the distances without any hint that they are only approximations CROFI and MOFI make the bold and unfounded assumption that there were really 21 houses on each side instead of 20 as stated by Bulbus we may assume they add that the doors of numbers 21, 42, 63, 84 are invisible from the center of the square what is it there I wonder that CROFI and MOFI would not assume of the five who are wholly right I think Brecho of the future, Caillous, Clifton C and Montrep deserve special praise for the full analytical solutions Mathematics picks out number 9 and proves it to be the right house in two ways very neatly and ingenuously but why he picks it out does not appear it is an excellent synthetical proof but lacks the analysis which the other four supply class list first Brecho of the future Caillous, Clifton C, Montrep second Mathematics third Chim, CROFI and MOFI ERDL Megipods, Rags and Hatters and Mad Hatter a remonstrance has reached me from screw tater on the subject of not one which he declares was no problem at all two questions he says are put to solve one there is no data the other answers itself as to the first point screw tater is mistaken there are not ease data sufficient to answer the question as to the other it is interesting to know that the question answers itself and I am sure it does the question great credit still I fear I cannot enter it on the list of winners as this competition is only open to human beings end of chapter 12 chapter 13 of A Tangled Tale this LibriVox recording is in the public domain recording by Ava Yee in October 2009 A Tangled Tale by Lewis Carroll chapter 13 Answers to not three problem one two travellers starting at the same time went opposite ways round a circular railway trains start each way every 15 minutes the easterly ones going round in three hours the westerly in two how many trains did each meet on the way not counting trains met the determinists itself two they went round as before each traveller counting is one the train containing the other traveller how many did each meet Answers one nineteen two the easterly traveller met twelve the other eight the trains one way took 180 minutes the other way 120 let us take the least common multiple 360 and divide the railway into 360 units then one set of trains went at the rate of two units a minute and at intervals of 30 units the other at the rate of three units a minute and at intervals of 45 units an easterly train starting has 45 units between it and the first train it will meet it does two fifths of this while the other does three fifths and thus meets it at the end of 18 units and so all the way round a westerly train starting has 30 units between it and the first train it will meet it does three fifths of this while the other does two fifths and thus meets it at the end of 18 units and so all the way round hence if the railway be divided by 19 posts into 20 parts each containing 18 units trains meet at every post and in one each traveller passes 19 posts in going round and so meets 19 trains but in two the easterly traveller only begins to count after traversing two fifths of the journey that is on reaching the eighth post and so counts 12 posts similarly the other counts 8 they meet at the end of two fifths of three hours or three fifths of two hours that is 72 minutes 45 answers have been received of these 12 are beyond the reach of discussion as they give no working I can but enumerate their names Artmore, EA FAD, LD Mathematics, MET PooPoo and the Red Queen are all wrong Beta and Rowena have got one right and two wrong Cheeky Bob and Nairam give the right answers but it may perhaps make the one less cheeky and induce the other to take a less inverted view of things to be informed that if this had been a competition for a prize they would have got no marks Notabene, I have not ventured to put EA's name in full as she only gave it provisionally in case her answer should prove right Of the 33 answers for which the working is given 10 are wrong 11 half wrong and half right 3 right except that they cherished a delusion that it was Clara who travelled in the easterly train a point which the data do not enable us to settle and 9 holy right The 10 wrong answers are from Boupipe financier IWT MAH QYZ Siegall Thistledown Boupipe rightly says that the easterly traveller met all trains which started during the 3 hours of her trip as well as all which started during the previous 2 hours that is all which started at the commencements of 20 periods of 15 minutes each and she is right in striking out the one she met at the moment of starting but wrong in striking out the last train for she did not meet this at the terminus but 15 minutes before she got there she makes the same mistake in 2 financier thinks that any train met for the second time is not to be counted IWT finds by a process which is not stated that the travellers met at the end of 71 minutes and 26 and a half seconds Kate B thinks the trains which are met on starting and on arriving are never to be counted even when met elsewhere QYZ tries a rather complex algebraical solution and succeeds in finding the time of meeting correctly all else is wrong Siegall seems to think that in 1 the easterly train stood still for 3 hours and says that in 2 the travellers met at the end of 71 minutes 40 seconds Thistle down nobly confesses to having tried no calculation but merely having drawn a picture of the railway and counted the trains in 1 she counts wrong in 2 she makes the meet in 75 minutes Tom Quad omits 1 in 2 he makes Clara count the train she met on her arrival the unsigned one is also unintelligible it states that the travellers go 124th more than the total distance to be traversed the Clara theory already referred to is adopted by 5 of these that is Boupipe, financier Kate B, Tom Quad and the nameless writer the 11 half right answers are from Bog Oak, Bridget Castor, Cheshire Cat G.E.B, Guy Mary, M.A.H Old maid, R.W. and Vendredi all these adopt the Clara theory Castor omits 1 Vendredi gets 1 right but in 2 makes the same mistake as Boupipe I notice in your solution a marvellous proportion sum 300 miles to 2 hours proportional to 1 mile to 24 seconds May I venture to advise your acquiring as soon as possible utter disbelief in the possibility of a ratio existing between miles and hours do not be disheartened by your 2 friends sarcastic remarks on your roundabout ways their short method of adding 12 and 8 has the slight disadvantage of bringing the answer wrong even a roundabout method is better than that M.A.H in 2 makes the travellers count 1 after they met not even they met Cheshire Cat and Old maid get 20 as answer for 1 by forgetting to strike out the train met on arrival the others all get 18 in various ways B.O.K., Guy and R.W. divide the trains which the westerly traveller has to meet into 2 sets that is those already on the line which they rightly make 11 and those which started during her B.O.K. exclusive of train met on arrival which they wrongly make 7 and they make a similar mistake with the easterly train Bridget rightly says that the westerly traveller met a train every 6 minutes for 2 hours but wrongly makes the number 20 it should be 21 G.E.B. adopts Boo-Peeps method but wrongly strikes out for the easterly traveller the train which started the commencement of the previous 2 hours Mary thinks the train met on arrival must not be counted even when met on a previous occasion the 3 who are holy right but for the unfortunate clearer theory are F.Lee, G.S.C. and X.A.B. and now descend the classic 10 who have solved the whole problem your names are A.I.Leban Algernon Bray for a friendly remark which comes with a hard warmth that not even the Atlantic could chill Arvon Brecho of the future Fifi H.L.R. J.L.O. Omega S.S.G and waiting for the train several of these have put Clara provisionally into the easterly train but they seem to have understood that the data do not decide that point Class list first A.I.Leban Algernon Bray Brecho of the future Fifi H.L.R. Omega S.S.G waiting for the train second Arvon J.L.O. third F.Lee G.S.C. X.A.B. end of chapter