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YoungRichard G. BudynasAli M. SadeghEighth EditionNew York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney TorontoCopyright © 2012, 2002, 1989, 1975, 1965, 1954, 1943, 1938 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.ISBN: 978-0-07-174248-1MHID: 0-07-174248-4The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-174247-4, MHID: 0-07-174247-6.All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefi t of the trademark owner, with no intention of infringement of the trademark. 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Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.ContentsPreface to thecould write to her, andthank her for her letter. That was an attention which would pleaseher.Producing a small, morocco bound, memorandum tablet, which healways carried about with him, in his waistcoat pocket, the Kingmade a note to remind him to write to the Princess, in one of theintervals of his busy official day."Write to Betty."Then he resumed his attack on his eggs and bacon, and coffee. Hedid not notice that they were cold. This letter of his sister's hadturned his thoughts to—the Family!He was the Head of the Family now. Somehow, he had hardlyrealized the fact before. In the circumstances, it really behoved him,it would be absolutely necessary for him, to try to get to knowsomething about the various members of the Family. His earlydistaste for Court life, his absorption in his own chosen profession,his frequent absences at sea, had made him, of course, little betterthan a stranger to the rest of the Family. And, if they knew little ornothing about him, he knew less than nothing about them. ThePrince had been the only member of the Family with whom he hadhad any real intimacy, since the far off nursery days they had allshared together, the only link between him and the others. And nowthe Prince was dead.This fresh, unspoilt sister of his would probably be worth knowing.Any girl, who recalled Judith, must be well worth knowing. And therewas Lancaster! Lancaster was now, and was likely to remain, HeirApparent. And William? William had looked a very bright, andengaging youngster, in his naval cadet's uniform, the day before.The others? The others did not matter. But Lancaster, and William,and Betty, he must get to know. And now, at the outset of their newrelationship, he had a favourable opportunity to take steps in thematter, which would not recur. He could let them know that he wastheir brother, as well as—the King! No doubt, they had theirproblems, and difficulties, just as he had his. He would do what hecould, to make life easy for them. After all, it was quite enough thatone member of the Family, at a time, should be condemned to theintolerable isolation, and the dreary, treadmill round of the palace.Might he not usefully begin, at once, with Lancaster? He could senda message to Lancaster, asking him to join him, at his informallunch, at the palace, at noon. Lancaster had always seemed, to him,a dull, rather heavy, conventional, commonplace person; but theremight be something human in him, after all. Perhaps, at an informalintimate encounter, he might be able to establish some contact withhim, and get him to talk a little about himself. That would beinteresting, and useful. Yes. Lancaster should provide his firstexperiment in Family research.Picking up his memorandum tablet again, from where he haddropped it on the breakfast table, the King made another note, toremind him to send the necessary message to Lancaster during themorning."Send message to Lancaster."The fact that he was not sure whether Lancaster, or even William,would still be in town, emphasized, in his own mind, his ignorance ofthe Family.At this point, the gorgeously clad footmen approached the table.One of them removed the used dishes and plates. The other placeda stand of fresh fruit in front of the King.The King selected an apple, and proceeded to munch it like anyschoolboy.It was a good apple.After all, life had its compensations!And, he suddenly realized now, he was beginning to take hold of hisjob, at last. This decision of his to tackle the Family, to get to knowthem personally, was his own decision. It was an expression of hisown individuality, the exercise of his own will. The thought gave hima little thrill of pride, and pleasure. Perhaps, after all, there wasgoing to be some scope, some freedom, for his own personality, inhis place in the procession, more scope, more freedom than he hadbeen inclined to think. His own shoulders, directed by his own brain,might make a difference in the jostling in the market-place. If theopportunity arose, he would put his weight into the scrimmage.The King finished his apple, and then filled and lit his pipe.The footmen cleared away the breakfast things.Soothed by tobacco, and cheered by the bright morning sunlight, theKing leant back in his chair.It was another wonderful summer day. Overhead the sky was aluminous, cloudless blue. The sunlight lay golden on the green of thetrees, and on the more vivid green of the lawn. The garden flowerbeds were gay with masses of brilliant hued blossoms. One or twobirds whistled pleasantly from the neighbouring trees and bushes. Afat starling strutted about the lawn, digging for worms.A sense of general well-being stirred in the King, a sense of well-being which surprised him, for a moment, but only for a moment. Itwas always so, when he had been in Paradise, with Judith. Alwayshe returned to the palace refreshed, and strengthened, with a newzest for, with a new appreciation of, the joy of mere living.Somehow, he must see to it, that his—promotion—did not interferewith his visits to Judith, and to Uncle Bond. He must see to it—in theinterest of the State! He smiled as the words occurred to him. In theinterest of the State? What would his fellow victims of the State, ofthe people, the old Duke of Northborough, for example, say to that,if they knew? But the words were justified. It was to the interest ofthe State that he, the King, should obtain, from time to time, therefreshment, the renewed strength, the zest, the sense of generalwell-being, of which he was so pleasantly conscious now.But, meanwhile, in the interest of the State, he must not, he couldnot afford to, waste any more of these golden, summer morningmoments, idling here in the garden. The avalanche ofcorrespondence in the post bags, and the official documents, anddispatches, which had accumulated, during the last day or two,owing to the special demands on his time made by the Coronation,were awaiting him in the palace. Long hours of desk work lay beforehim. The thought did not displease him. He was in the mood forwork. Here was something he could put his weight into. Here was anopportunity for individual action, and self-expression, an opportunityfor the exercise of his own judgment, driving power, decision.Knocking out his pipe, the King stood up abruptly.Then, whistling gaily, an indication of cheerfulness which had grownvery rare with him, of late, he crossed the lawn, and re-entered thepalace, on his way back to duty.CHAPTER VIIIT was in the palace library, a large and lofty room on theground floor, with a row of tall windows overlooking thegarden, that the King spent his office hours. The library was strictlyreserved for his use alone. The secretaries, who served his personalneeds, were accommodated in a smaller room adjoining, whichcommunicated with the library by folding doors. Although he wascompelled to maintain, in this way, the isolation which was so littleto his taste, it was characteristic of the King, in his dealings with hisimmediate subordinates, that he should take some pains not toappear too patently the man apart. This was the way they hadtaught him in the Navy. On more than one "happy ship," on whichhe had served, the King had learnt that, to get good work out ofsubordinates, it was expedient to treat them as fellow workers, andequals, as men, although graded differently in rank, for the purposesof discipline, and pay. It was in more or less mechanical applicationof this principle, that, still whistling gaily, he chose now, to enter thelibrary, not directly, but through the secretaries' room adjoining.In the airy, sunny, secretaries' room, the low murmur of talk, and theclatter of typewriters, which seem inseparable from office work,ceased abruptly. There was a general, hurried, pushing back ofchairs. Then the half dozen men and women in the room rose,hastily, to their feet. They had not expected to see the King so early.After the exhausting Coronation ceremony of the day before, andthe heavy demands on his strength, which the day, as a whole, hadmade, they had expected him to rest. And here he was, a littlebefore his usual time, if anything, buoyant, and vigorous, andlaughing goodhumouredly at their surprise and confusion, readyapparently to attack the accumulation of papers which they hadwaiting for him.With a genial nod, which seemed to be directed to each man andwoman present, individually, the King passed quickly through theroom, into the library beyond, opening and shutting the interveningfolding doors for himself, with a sailor's energy.The secretaries, men and women alike, turned, and looked at eachother, and smiled.Although he was, of necessity, ignorant of the fact, the King had leftinterested, and very willing fellow workers behind him.The library was almost too large, and too lofty a room to becomfortably habitable. Worse still, in spite of its south aspect, and itsrow of tall windows, the eight or nine thousand volumes, which filledthe wire fronted bookcases, which ran round two sides of the room,it always seemed to the King, gave it a dead and musty air. Thesebooks were for show, not for use. No one ever took them down fromthe shelves. No one ever read them. The erudite, silver-haired,palace librarian, himself, was more concerned with the raritiesamongst them, and with his catalogue, than with their contents. Butthe books, musty monuments of dead men's brains, as he regardedthem, were not the King's chief complaint. A number of Familyportraits, which usurped the place of the bookcases, here and there,on the lofty walls, were his real grievance. A queer feeling ofantagonism had grown up between him and these portraits. Theyalways seemed to be watching him, watching him, and disapprovingof him. The mere thought of them sufficed to check his good spirits,now, as he entered the library. As he sat down at his writing table,he turned, and looked round at them defiantly.The writing table stood as close up to the row of tall windows, onthe south side of the library, as was possible. The windows, withtheir pleasant view of the sunlit greenness of the garden, were onthe King's left, as he sat at the table. Straight in front of him werethe undecorated, black oak panels of the folding doors which led intothe secretaries' room. On his right on the north wall of the library,were many of the books, and three of the portraits.First of all, there, in the corner by the folding doors, was a portrait ofhis grandfather, in the Coronation robes, and full regalia, which hehimself had been compelled to wear, the day before; a strong,bearded man, with a masterful mouth, which was not hidden by hisbeard. A King. Further along, on the right, past several square yardsof books, hanging immediately above the ornate, carved, marblemantelpiece, in the centre of the north wall, was a portrait of hisfather, in Field Marshal's uniform, with his breast covered withdecorations; a man apart, isolated, lonely, remote, with a broodinglight in his eyes. A King, too. Then, past more books, in the furthestcorner of the room, by the door, came the portrait of his mother, astately, commanding figure, in a wonderful, ivory satin gown,marvellously painted. A Queen. And a hard woman, hard with herchildren, and harder still with herself, where what she had held to bea matter of Family duty had been concerned. And, last of all, in thecentre of yet more books, on the east wall, behind him, was theportrait of his brother, the dead Prince of Wales, a more humanportrait this, to see which, as he sat at the writing table, he had toswing right round in his revolving chair; the Prince, in the pink coat,white cord riding breeches, and top boots, of the hunting field,which had been his favourite recreation, leaning a little forward, itseemed, and smiling out of the canvas with the smile which had wonhim so much, and such well deserved popularity.All these had borne the Family burden, without complaint. All thesehad accepted the great responsibility of their position, withoutquestion, and even with a certain Royal pride. They had madeinnumerable, never ending sacrifices.And he? An unwilling King? A half-hearted King?No wonder they disapproved of him!The King swung round, impatiently, in his chair, back to the writingtable again.An unwilling King, a half-hearted King, he might be; but, at any rate,he could labour. He could put his full weight into his work. He couldshow, in his own way, even if it was not the Family way, even if theFamily disapproved of him, that he, too, was a man, that he, too,had individuality, force of character, driving power, decision—Portfolios, and files, of confidential State documents had beenarranged, in neat piles, and in a sequence which was a matter of acarefully organized routine, on the left of the writing table. On theright stood a number of shining, black japanned dispatch boxes, andone or two black leather dispatch cases, of the kind carried by theKing's Messengers. The "In" boxes for correspondence, in the centreof the table, were filled with a formidable accumulation of letters.The "Out" boxes, beside them, looked, at the moment, in thebrilliant, morning sunlight, emptier than emptiness.An almost bewildering array of labour saving devices, stamping,sealing, and filing machines, completed the furnishing of the table.These, the King swept, at once, contemptuously to one side. Thetelephone instrument, which stood on a special shelf at his elbow,was the only labour saving device he ever used. A plain, and rathershabby fountain pen, and two or three stumps of coloured pencil,were the instruments with which he did his work. It was not until hehad found these favourite weapons of attack, and placed them readyto his hand, on his right, that he set himself to deal with theaccumulation of papers in front of him.The letters in the "In" boxes were his first concern. These he hadmerely to approve, by transferring them to the "Out" boxes, readyfor posting. It was a transfer which he could safely have made,which he very often did make, without reading a single letter. Hispersonal correspondence was in the capable hands of Lord Blaine,who had served his father, as private secretary, for many yearsbefore him. But this morning, in his new determination to find anoutlet for his own individuality, the King elected to read each of theletters through carefully. Lord Blaine had acquired a happy tact, inthe course of his long experience, in answering the letters, from allsorts and conditions of people, which found their way into the Royalpost bags, which was commonly considered beyond criticism.None the less, now, as he read the letters, a conviction grew uponthe King that not a few of the courtly old nobleman's phrases hadbecome altogether stereotyped.One letter, in particular, addressed to some humble old woman, in aprovincial almshouse, congratulating her on her attainment of acentenary birthday, seemed to him far too formal. The old womanhad written a quaint, and wonderfully clear letter, in her ownhandwriting to the King. Seizing his favourite stump of blue pencil,he added, on the spur of the moment, two or three unconventionalsentences of his own, to Lord Blaine's colourless reply—"I am writing this myself. I don't write as well as you do, do I?But I thought you might like to have my autograph as one ofyour hundredth birthday presents. This is how I write it—"ALFRED. R.I."Laughing softly to himself the King tossed the letter, thus amended,into one of the "Out" boxes.The little incident served to revive his previous good spirits.Lord Blaine would probably disapprove.But the old woman would be pleased!From the correspondence boxes, he turned, in due course, to theportfolios and files on the left of the table. These contained reports,and routine summaries from the various Government departments,copiesof official correspondence, one or two Governmentpublications, and certain minor Cabinet papers, and they requiredmore concentrated attention. He had to make himself familiar withthe contents of the various documents, and this involved carefulreading. An abstract, or a skilful précis, prepared by his secretaries,and attached to the papers, occasionally saved his time and labour;but even these had to be read, and the reading took time. Happily,here, as before, little or no writing, on his part, was necessary. Aninitial, and a date, to show that he had seen the document inquestion, a few words of comment, or a curt request for moreinformation, were the only demands made on his blue pencil.Documents, and copies of correspondence, from the Foreign andDominion Offices, held the King's attention longest. To him thesewere not "duty" papers, as were so many of the others. The placenames, the names of the foreign diplomats, and of the Dominionstatesmen, and administrators, which occurred in these papers, werefamiliar to him, thanks to the many ports, and countries, the manymen and cities, he had seen in his varied naval service. Here andthere, in these papers, a single word would shine out, at times, fromthe typewritten page in front of him, which conjured up, a vision,perhaps, of one of the world's most beautiful roadsteads, or amental picture of the strong and rugged features of some man, whowas a power, a living force, amongst his fellows, in the wilder placesof the earth, or a vivid memory of the cool and spacious rooms ofsome Eastern club house where men, who lived close to theelemental facts of life, gathered to make merry, and to showunstinted hospitality to the stranger. Here he was on sure ground.Here, he knew, his comments were often of real value. He had seenthe country. He had met, and talked with, the men on the spot.Frequently, his knowledge of the questions raised in these paperswas quite as comprehensive, and as intimate, as that of the oldestpermanent officials in Whitehall.At the end of an hour and a half of hard and methodical work, theKing became suddenly aware that he had made considerableprogress in his attack on the accumulation of papers in front of him.Leaning back in his chair he touched a bell which stood on the tablebeside him.The folding doors, leading into the secretaries' room, wereimmediately opened, and a tall, fair, good looking young man, whowas chiefly remarkable for the extreme nicety of his immaculatemorning dress, entered the library, in answer to the summons.The King indicated the now full "Out" boxes, with a gesture, whichbetrayed his satisfaction, and even suggested a certain boyish pride,in the visible result of his labour."Anything more coming in?" he enquired."Not at the moment, I think, sir. The Government Circulations are allunusually late this morning, sir," the tall young man replied,approaching the table, and picking up the "Out" boxes for removal tothe secretaries' room.The King was filling his pipe now. He felt that he had earned asmoke."Bought any cars, lately, Blunt?" he enquired, with a merry twinkle inhis eyes.He had suddenly realized that this was Geoffrey Blunt, the nominaltenant of the garage in Lower Grosvenor Place, and the nominalpurchaser of the car housed there.Geoffrey Blunt laughed, and then blushed, as he became consciousof the liberty into which the King had betrayed him."We must organize one of our little incognito excursions, in the nearfuture, Blunt, I think," the King murmured, looking out through thetall windows, on his left, at the sunny, morning glory of the garden."We will run out into the country."At the moment, his thoughts were in Paradise. Judith and the Imps,in all probability, would be in the hayfields—"You must be ready for a holiday, sir," Geoffrey Blunt ventured toremark. "You took us all by surprise, this morning, sir. Afteryesterday, we did not expect to see you, so early, this morning, sir.""No. And that reminds me of something I wanted to say," the Kingreplied, looking round from the windows, and speaking with asudden, marked change of manner. "I can see by the papers whichyou had waiting for me, this morning, that you people have all beenkeeping hard at it during the last day or two. I appreciate that. Tellyour colleagues, in the next room, that I expressed my appreciation.That is all now. Let me see today's Circulations, when they do arrive.I do not want to be faced with an accumulation of papers, like thismorning's, again."Flushing with pleasure at this praise, Geoffrey Blunt bowed, andwithdrew, taking the "Out" boxes with him.The King smiled to himself as he lit his pipe."But who is there to praise me?" he muttered.Leaning back in his chair, for a moment or two, he gave himself upto the luxury of the true smoker's idleness.But had there not been something that he had meant to do, in anyinterval of rest, like this, which might occur during the morning?The morocco bound memorandum tablet, which he produced fromhis waistcoat pocket, answered the question—"Write to Betty.""Send message to Lancaster."It was too late to send any message to Lancaster now. A couple ofhours was not sufficient notice to give him of an invitation to lunch.He was not intimate enough with Lancaster to treat him in sooffhand a manner. It would be an abuse of his new position, atactical mistake. The lunch must be arranged for tomorrow. Crossingoff his original note, he scribbled another—Lancaster to lunch tomorrow. See him, personally, thisafternoon, or this evening.But he could write to Betty!Clearing a space on the writing table, by pushing to one side the lessurgent documents and papers, which he had retained forsubsequent attention, he picked up his fountain pen; then, when hehad found, after some search, a sheet of note paper sufficiently plainand unostentatious, to suit his taste, he began to write—Dear Betty,Your letter this morning gave me great pleasure. I do not knowthat there is very much pleasure in this business of being King—But he got no further.The folding doors facing him were suddenly reopened.Then there entered, not Geoffrey Blunt, nor any other member ofthe secretarial staff, but—the old Duke of Northborough.The King looked up with a surprise which at once gave place to asmile of welcome. This was contrary to all etiquette. But he was gladto see the old Duke. And it was in deference to his own repeatedrequests on the subject that the veteran Prime Minister had latelyconsented to make his visits to the palace, in working hours, asinformal as possible.Putting down his pipe, and his pen, the King stood up to receive theold statesman.The Duke, as if to atone for the abruptness of his entry, paused for amoment on the threshold of the large and lofty room, and bowed,with a slightly accentuated formality.The folding doors behind him were closed by unseen hands.Then he advanced, into the room, towards the King.CHAPTER IXN unusually tall man, and a big man, with a breadth of chest,and a pair of shoulders, which had made him conspicuous, inevery assembly, from his youth up, the Duke still held himself erect,and moved in a big way. Now, as he advanced into the large andlofty room, the thought came to the King, that here was a man forwhom the room was neither too large, nor too lofty. While he himselfwas apt to feel lost in the library, overpowered by its size, andoppressed by the weight of its inanimate objects, the Duke movedas if in his natural and fitting surroundings. The force, the vigour, ofthe wonderful old man at once relegated the huge room to itsproper place in the background. The effect was very much as if thelibrary had been a stage scene, in which the scenery hadpredominated, until this, the moment when a great actor entered,and drew all eyes.It was characteristic of the Duke that he should be dressed with acarelessness bordering on deliberate eccentricity. The roomy,comfortable, sombre black office suit, which he was wearing, lookedundeniably shabby, and hung loosely on his giant frame. His headwas large. His hair, which he wore a little longer than most men,snow-white now but still abundant, was brushed back from his broadforehead in a crescent wave. His features were massive, andstrongly moulded. His nose was salient, formidable, pugnacious. Hismouth was wide. His lips had even more than the usual fulnesscommon to most public speakers. But his eyes were the dominantfeature of his face. His eyebrows were still black, thick, andaggressively bushy. Underneath them, his eyes shone out, luminousand a clear blue, with the peculiar, piercing, penetrative quality,which seems to endow its possessor with the power to read thesecret, unspoken, thoughts of other men."Enter—the Duke!" the King exclaimed, with an engagingly boyishsmile, as the veteran Prime Minister approached the writing table."The Duke could not have entered at a more opportune moment. Iwas just taking an 'easy.' Shall we stay here, or go out into thegarden, or up on to the roof?""We will stay here, I think, if the decision is to rest with me, sir," theDuke replied, in his sonorous, deep, and yet attractively mellowvoice. "I bring news, sir. As usual, I have come to talk!""Good," the King exclaimed. "Allow me—"Placing his own revolving chair in position for the Duke, a little wayback from the writing table, as he spoke, he invited him to beseated, with a gesture.Then he perched himself on the writing table, facing the oldstatesman.The Duke settled himself, deliberately, in the revolving chair,swinging it round to the right, so that he could escape the brilliant,summer sunshine, which was streaming into the room, through therow of tall windows, on his left. His side face, as it was revealed nowto the King, wrinkled and lined by age as it was, had the compelling,masterful appeal, the conspicuous, uncompromising strength, of anantique Roman bust."I had just begun a letter to my sister, the Princess Elizabeth, whenyou came in," the King remarked, maintaining the boyish attitude,which he could never avoid, which, somehow, he never wished toavoid, in the Duke's presence. "It suddenly occurred to me, thismorning, that I am the Head of the Family now. I am a poorsubstitute for my immediate predecessors, I am afraid." He lookedup, as he spoke, at the portraits on the opposite side of the room."But I have decided that I must do my best in my new command."The Duke looked up in turn. Following the King's glance, hisluminous, piercing eyes rested, for a moment or two, on theportraits."None of your immediate predecessors were ever called upon to playso difficult a part, as you have to play, sir," he said.Something in the Duke's manner, a note of unexpected vehemencein his sonorous voice, arrested the King's wandering attention.His boyishness fell from him."What is it?" he asked. "I remember, now, you said you broughtnews. Is it—bad news?""No. It is good news, sir. I could not bring you better news," theDuke replied. "But, I am afraid, in spite of all my warnings, you arenot prepared for the announcement which I have to make."He paused there, for a moment, and looked away from the King."The storm, which we have been expecting, for so long, sir," headded, slowly, dwelling on each word, "is about to break."The King started, and winced, as if he had been struck."The storm?" he exclaimed."Is about to break, sir," the Duke repeated.There was a long, tense pause.Then, suddenly, the King laughed, a bitter, ironic laugh."I have been a fool," he exclaimed. "In my mind, the glass was 'SetFair.' I had—forgotten—the storm! I was going to take hold of myjob. I was going to put my full weight into my work. I was evengoing to cultivate the Family, as I was telling you—"He checked himself abruptly."What is going to happen?" he asked.The Duke drew out his watch, an old-fashioned, gold-cased, halfhunter, and looked at it judicially."It is now nearly eleven o'clock. In an hour's time, at twelve noonprecisely, a universal, lightning strike will take effect, throughout thelength and breadth of the country, sir," he replied. "All the publicservices will cease to run. The individual workman, no matter where,or how, he is employed, as the clock strikes twelve, will lay down histools, put on his coat, and leave his work. Such a strike is no newthing, you will say. But this is no ordinary strike, sir. Although wholesections of trades unionists, up and down the country, we have goodground to believe, have no very clear idea, why they are striking,although many of their local leaders appear to have been deceivedinto the belief that the strike has been called for purely industrialreasons, we have indubitable evidence that it is designed as a firststep in the long delayed conspiracy to secure the politicalascendency of the proletariat. A little company of revolutionaryextremists have, at last, captured the labour machine, sir. It is theywho are behind this strike. Behind them, I need hardly tell you, arethe Internationalists, and the Communists, on the Continent, ready,and eager, to supply arms, ammunition, and money, if theopportunity arises, on a lavish scale."Although we have been expecting the storm for so long, this strikeform, which it has taken, I may confess to you, sir, has come to usas something of a surprise. The strike leaders, I surmise, are relying,very largely, on that surprise effect, for their success. They imagine,they hope, no doubt, that they will find the Government, elated andthrown off their guard by the success of the Coronation, unprepared;that, in the chaos, which they believe must ensue, the whole nationwill be at their mercy; that, having demonstrated their power, theywill be able to dictate their own terms. What those terms would be,sir, there can be no question. Internationalism. Communism. ARepublic. That persistent delusion of the fanatic, and the unpracticalidealist—the Perfect State. Armed revolt was their original plan, sir.Thanks to the vigilance of our Secret Service Agents, thatcontingency has, I believe, been obviated. But the Red Flag is stilltheir symbol, sir. In the absence of arms, a bloodless revolutionappears now to be their final, desperate dream. They will have arude awakening, sir. In less than twenty-four hours they will be—crushed!"You will remember the alternative, protective schemes, for use inthe event of a national emergency, which I had the honour to laybefore you, for your consideration, a few weeks ago, sir? One ofthose schemes, the 'Gamma' scheme, is already in force. At a fullmeeting of the Cabinet, held in Downing Street, this morning, sir, theimmediate operation of the 'Gamma' scheme, and the declaration ofMartial Law, on which it is based, were unanimously approved. Themilitary, and the naval authorities are already making theirdispositions. By this time, the Atlantic, the North Sea, and theChannel Fleets, will be concentrating. The closing of all the ports,and the blockade of the whole coast line, provided for in thescheme, will follow automatically. The military authorities, you willremember, are to take over the control of the railways, aviationcentres, and telegraphic and wireless stations, and support, andreinforce, the police, as required. The Home Secretary assures methat the police can be relied upon implicitly to do their duty. TheChief of the General Staff declares that the Army, regrettably smallas it is, is sufficient to meet all the demands which are likely to bemade upon it. Of the Navy, there is no need for me to speak to you,sir. In the circumstances, I feel justified in assuring you, that wehave the situation well in hand."The Duke stood up. To him, the orator, the practised debater, speechalways came more easily, and naturally, when he was on his feet. Heturned now, and faced the King, towering head and shoulders abovehim,a formidable, and dominating figure. When he spoke again,there was an abrupt, compelling, personal note in his sonorousvoice."I want you to leave the palace, sir. I want you to remove the Court,at once, into the country," he said. "Do not misunderstand me, sir. Ido not believe that your person is in any danger. I do not anticipate,as I have already indicated, that we shall be called upon to meetarmed revolt. In any case, Londoners are proverbially loyal. Butthere will be rioting, and window smashing, in places, no doubt.Something of the sort may be attempted, here, at the palace. In thecircumstances, it will be as well, that you should be elsewhere."In urging you to leave the palace, and to remove the Court into thecountry, I have, too, another, and a more important motive, sir," hecontinued. "It is, of course, a fundamental condition, a constitutionaltruism, of our democratic monarchy, that the King must take no side.How far that consideration must govern the King's actions, when hisown position is directly attacked, is a question which, I imagine, veryfew of our leading jurists would care to be called upon to decide! ButI attach the very greatest importance to the preservation of yourabsolute neutrality, in the present crisis, sir. When the impendingstorm has spent its force, and the danger, such as it is, hassubsided, there will be a considerable body of people, up and downthe country, who will contend that the Government have actedprecipitately, unconstitutionally, and with wholly unnecessaryviolence. In meeting such criticism, I wish to be able to emphasizethe fact that the Government have acted throughout on their ownresponsibility, on my responsibility, without any reference to you atall, sir. I do not propose to advance, on your behalf, the time-honoured excuse that His Majesty accepted the advice tendered tohim by his advisers. I propose to emphasize the fact that you atonce removed the Court into the country, and took no part whateverin the suppression of the rebellion. In the result, your position will bemaintained inviolate, but you will not share in the unpopularity, andthe odium, which a demonstration of strength inevitably, andinvariably, evokes. This is why I said that you have a more difficultpart to play than any of your immediate predecessors were evercalled upon to play, sir. Although the battle is joined, and you are sointimately concerned with its result, you will have to stand on oneside, and take no part in the conflict. And you are a young man, anda high spirited young man. You will resent your neutrality."But I am the lightning conductor, sir! It is my duty, as I see it, and Iregard it as the honour of my life, to take the full shock of thelightning flash, so that the Crown may remain on your headunshaken. And the Crown will not only remain on your headunshaken. It will be more firmly fixed there than before. In twenty-four, or forty-eight, hours, at the most, sir, you will be more surelyestablished on the throne than any of your immediate predecessors."That is why I said, at the outset, that this is good news which Ihave brought you, sir; that I could not bring you better news. This isgood news, sir. Never have I dared to hope that the battle, which wehave been expecting so long, would be joined, at a time, and onground, so wholly favourable to the forces of law and order. I haveno doubt of the adequacy, and the smooth working of the 'Gamma'scheme, in the existing crisis, sir. It will be many years, probably thewhole of your reign, perhaps a generation, before the revolutionaryextremists in this country recover from the overwhelming disastertowards which they are rushing at this moment."It was then, and not until then, that the King slipped down from hisperch on the writing table to his feet.Instinctively, he turned to the row of tall windows, on his right.He wanted light. He wanted air.Outside, in the palace garden, the brilliant morning sunshine laygolden on the green of the grass, and on the darker green of thetrees.The whistling of a thrush, perched on a tree near the windows,seemed stridently audible.Behind him, beside the writing table, the Duke stood, motionless,silent, expectant.The magnetism for which the veteran Prime Minister was notorious,the magnetism which he seemed to be able to invoke at will, hadnot failed him, whilst he talked. For the time being, he hadcompletely dominated the King. But now, the King's own personalityreasserted itself, with all the force of a recoil.A bitter realization of his own impotence, of his own insignificance,was the King's first personal thought.It was to be as he had feared, as he had always known, it would be.The battle was joined, the fight for his place in the procession wasabout to begin, in the market-place, and he, the man mostconcerned, was the one man who could not take a side.The Duke had gone out of his way to emphasize that fact."I attach the very greatest importance to the preservation of yourabsolute neutrality in the present crisis, sir."Neutrality! The most contemptible part a live man could play."Fight for your place in the procession, Alfred."He was not to be allowed to fight.The decision whether he should fight for his place, step to one side,or fall out, altogether, to the rear, had been taken out of his hands.The desire for self-assertion, for self-expression, which he had felt,so strongly, only an hour or two previously, flamed up, hotly, anew,within the King. An unwilling King, a half-hearted King, he might be;but to be a nonentity, a man of no account—The very workman, the individual workman, who—in less than anhour now—as the clock struck twelve, would lay down his tools, puton his coat, and leave his work, was of more account than he was!Ignorant, and deceived, as he might be, the individual workman, instriking, would be asserting himself, expressing himself.And he?He could not even strike!If only he could have gone on strike!The fantastic idea caught the King's fevered fancy. It was in tunewith the bitter, wilful, rebellious mood which had swept over him. Hecould not resist the temptation of giving it ironic expression."It seems to me, if there is one man, in the whole country, whowould be justified in striking, in leaving his work, I am that man!" heexclaimed. "I never wanted, I never expected to have to fill—mypresent command. To be 'a sailor, not a Prince,' was always my idea.Do people, do these people, who are coming out on strike, and hopeto run up the Red Flag, imagine that I get any pleasure, that I getanything but weariness, out of—my place in the procession? If Ifollowed my own wishes now—I should strike, too! I should be thereddest revolutionary of them all. Liberty, Equality, and Fraternity istheir war cry, isn't it? Those are the very things I want!"The Duke smiled grimly."Where will you remove the Court, sir?" he asked. "To Windsor? Orto Sandringham?"The King began to drum, impatiently, with his fingers, on thewindow pane.The Duke's pointed impenetrability, his persistence, irritated him, atthe moment, almost beyond his endurance.Of course he would have to do as the Duke wished. The Duke wasthe lightning conductor. He would have to fall in with the Duke'ssuggestions. His suggestions? His orders! And yet—Windsor? Sandringham?Windsor and Sandringham were merely alternative cells in the sameintolerable prison house!Perhaps it was the blithe whistling of the thrush perched on the treenear the windows; perhaps it was the sunlit peace of the palacegarden—whatever the cause, the King thought, suddenly, andirrelevantly, of Paradise.And then the irrelevance of his thought disappeared.A man was talking beside him.It was not the Duke.It was Uncle Bond."Whether you fight for your place or not, whether you come out atthe head, or the tail, of the procession, wherever the head and thetail may be, whether you step to one side, or fall out altogether,whateverhappens to you, my boy, Judith and I, will always be gladto welcome you to the inn at the corner, and give you a seat at ourwindow. You will remember that!"A thrill of exultation ran through the King.Here, surely, was an opening, an opportunity, for the self-assertion,the self-expression, which he so ardently desired!Where should he go, now that the time had come for him to stepout of the procession, but into Paradise, to Judith and to Uncle Bond,to stand beside them, at their window, in the old inn, at the cornerof the market-place, the old inn, on the signboard of which waswritten in letters of gold "Content"?If he must seek a rural retreat, an asylum, a city of refuge, whatbetter retreat could he have than Judith's and Uncle Bond's oasis, inParadise, where no strangers ever came?In this matter, at any rate, he could assert himself.In this matter, at any rate, he would have his own way.Swinging round from the windows, he fronted the Duke, flushedwith excitement wholly defiant."I will leave the palace, at once, as you wish," he announced. "Ihave no alternative, of course. I recognize that. But I shall leave theCourt behind, too! Neither Windsor, nor Sandringham, attract me. Ibegin to feel the need of—a holiday. I shall run out into the country.I have—friends in the country."He laughed recklessly."This is my way of going on strike!"An odd, dancing light, which almost suggested a suddenly awakenedsense of humour, shone, for a moment, in the Duke's luminous,piercing eyes.But he pursed up his lips doubtfully, "It is a private, incognito visit,that you are suggesting, I take it, sir?" he remarked. "In the presentcrisis, such a visit would involve—serious risks. But, I am bound toconfess, that it would not be without—compensating advantages!"His grim smile returned. "No one would know where you were. Andyour departure from the palace, which must not be delayed, wouldattract little or no attention. If you left the Court behind you, as youpropose, you would merely take one or two members of thehousehold staff with you, I presume?""I shall take nobody with me. I shall go by myself," the Kingdeclared.Yes. In this matter, at any rate, he would have his own way.The Duke shot one of his keen, searching glances at the King. Thenhe swung round on his heel, and paced slowly down the wholelength of the library.The King watched him, fascinated, curious, exalted.At the far end of the room, the Duke paused, turned, and retracedhis steps.His first words, as he halted, once again, beside the writing tableabsolutely took the King's breath away."I shall offer no opposition whatever to your reckless little excursion,sir," he said. "I surprise you, sir? I hoped to surprise you! But this isno time, there is no time, for—explanations. Reckless as yourproposal is, the more I think about it, the more conscious I becomeof its many advantages. But, with your permission, sir, I will attachtwo conditions to your—holiday." Again he smiled grimly. "In the firstplace, I must know where you are going, so that I can communicatewith you, at once, when the need arises. In the second place I willask you to honour me with an undertaking that you will remain inyour rural retreat, until I have communicated with you."The King could hardly believe his own ears. That the Duke shouldaccept, should even express a guarded approval of his rebellion—that was what his reckless proposal amounted to!—was whollyunbelievable. It could not be true!A sudden sense of unreality, the consciousness, which had been sofrequently with him, of late, here in the palace, that he was living ina dream, a wild, grotesque, nightmare dream, swept over the King.Of all the unreal scenes in his dream, this surely, was the mostunreal!He had expected opposition, and argument. What he had wanted,he realized now, was opposition and argument—But he had gone too far to withdraw. And he had no wish towithdraw. At any rate he would see Judith. He would see UncleBond. He would be—in Paradise—Without speaking, words at the moment, were quite beyond him,the King drew up his revolving chair to the writing table, once again,and sat down. Picking up the sheet of note-paper on which he hadbegun to write to his sister—how long ago that seemed!—he tore offthe unused half of the paper, crumpling the other half up in hishand. Then he found his pen, and wrote—"James Bond Esq.,Mymm's Manor,Mymm's Valley,Mymms,Hertfordshire."Turning in his chair, he handed the half sheet of paper to the Duke."That will be my address. I shall stay there," he said.The Duke glanced at the paper, and then folded it up neatly, andslipped it into his pocket."You have no time to lose, sir," he said. "It is already nearly half pasteleven. Within half an hour, just before noon, all civilian traffic, inand out of London, will cease. The police, and the military will be incontrol in the streets. Barriers will be erected on all the roads. OnlyGovernment traffic will be allowed to pass. You have time to getaway, but only just time."The King sprang up to his feet, and darted across the room. He was,all at once, wild to get away, wild to get away from the Duke, fromthe palace, from himself, from this unreal, grotesque, nightmare lifeof his—But, half way across the room, he paused, and swung round, andfaced the Duke yet once again.A sudden, belated twinge of compunction, a whisper of theconscience which he had all this time been defying, had impelledhim to think of the Duke."Am I letting you down, Duke?" he exclaimed impulsively. "After—allyou have done for me—I wouldn't let you down for worlds!"A smile, in which there was no trace of grimness, lit up the oldDuke's rugged, massive features."Thank you, sir," he said. "You are not letting me down, sir. You canenjoy your—reckless little excursion—with an easy mind. But I didnot like, and I do not like, your use of that ill-omened word 'strike,'sir,—even in jest! Remembering the language of the Service, inwhich, like you, I had the honour to be trained, I prefer to say thatyou are—proceeding on short leave of absence, shall we say, sir? Itwill only be a short leave of absence, sir. Twenty-four, or forty-eight,hours, at the most. You will do well, I think, sir, to remember that!"Incredible as the whole scene was, there could be no doubt aboutthe old statesman's entire sincerity. The King's last fear, his lastscruple fell from him. In his relief he laughed aloud, lightheartedly."Call it whatever you like, Duke," he exclaimed. "But, for me, it is—my way of going on strike!"And with that, he turned, and darted out of the room.Left alone, the Duke remained motionless, for a minute or two. Thesmile, which the King's impulsive ingenuousness had evoked, stilllingered on his lips; but his piercing eyes were clouded now, andheavy with thought.Suddenly he turned to the writing table, and, picking up thetelephone instrument, took down the receiver.The whole manner of the man changed with this decisive littleaction.There was a curt, commanding, masterful ring in his sonorous voice,as he gave his directions to the operator at the palace exchange."The Duke of Northborough is speaking. I want Scotland Yard, andthe War Office, at once, in that order. You will give me 'priority.' Shutout all other calls."CHAPTER X FEELING of light-hearted holiday irresponsibility, such as hehad not known for months, for years as it seemed to him, wasEighth Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixPreface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 State Properties, Units, and Conversions . . . . . . . . . . . . . . . . . . 11.3 Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Stress and Strain: Important Relationships . . . . . . . . . . . . . . . . . . . . . 152.1 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Strain and the Stress–Strain Relations . . . . . . . . . . . . . . . . . . . . 192.3 Stress Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Strain Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5 Mohr’s Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 The Behavior of Bodies under Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1 Methods of Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 Elasticity; Proportionality of Stress and Strain . . . . . . . . . . . . . 463.3 Factors Affecting Elastic Properties . . . . . . . . . . . . . . . . . . . . . . 473.4 Load Deformation Relation for a Body . . . . . . . . . . . . . . . . . . . 483.5 Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.6 Creep and Rupture under Long-Time Loading . . . . . . . . . . . . 483.7 Criteria of Elastic Failure and of Rupture . . . . . . . . . . . . . . . . . 503.8 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.9 Brittle Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.10 Stress Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.11 Effect of Form and Scale on Strength; Rupture Factor . . . . . . . 603.12 Prestressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.13 Elastic Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.14 Tables: Mechanical Properties of Materials . . . . . . . . . . . . . . . . 643.15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 Principles and Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.1 Equations of Motion and of Equilibrium . . . . . . . . . . . . . . . . . . 834.2 Principle of Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.3 Principle of Reciprocal Deflections . . . . . . . . . . . . . . . . . . . . . . . 844.4 Method of Consistent Deformations (Strain Compatibility) . . . 844.5 Energy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84iii iv C o n t e n t s C o n t e n t s v4.6 Castigliano’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.7 Dimensional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.8 Remarks on the Use of Formulas . . . . . . . . . . . . . . . . . . . . . . . . 914.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.1 The Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.2 The Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.3 The Boundary Element Method . . . . . . . . . . . . . . . . . . . . . . . . . 1015.4 Zeroes of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.5 Solution of Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 1085.6 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.8 Additional Uncited References in Finite Elements . . . . . . . . . . 110 6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.1 Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 Electrical Resistance Strain Gages . . . . . . . . . . . . . . . . . . . . . . . . 1186.3 Detection of Plastic Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1286.4 Analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.5 Wheatstone Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7 Tension, Compression, Shear, and Combined Stress . . . . . . . . . . . . . 1417.1 Bar under Axial Tension (or Compression); Common Case . . . . 1417.2 Bar under Tension (or Compression); Special Cases . . . . . . . . 1437.3 Composite Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457.4 Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.5 Body under Pure Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.6 Cases of Direct Shear Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 1507.7 Combined Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8 Beams; Flexure of Straight Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1558.1 Straight Beams (Common Case) Elastically Stressed . . . . . . . 1558.2 Composite Beams and Bimetallic Strips . . . . . . . . . . . . . . . . . . 1658.3 Three-Moment Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688.4 Rigid Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1698.5 Beams on Elastic Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1748.6 Deformation Due to the Elasticity of Fixed Supports . . . . . . . 1788.7 Beams under Simultaneous Axial and Transverse Loading . . . 1798.8 Beams of Variable Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.9 Slotted Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1898.10 Beams of Relatively Great Depth . . . . . . . . . . . . . . . . . . . . . . . . 1898.11 Beams of Relatively Great Width . . . . . . . . . . . . . . . . . . . . . . . . 1938.12 Beams with Wide Flanges; Shear Lag . . . . . . . . . . . . . . . . . . . . . 1968.13 Beams with Very Thin Webs . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1988.14 Beams Not Loaded in Plane of Symmetry; Flexural Center . . . 199 iv C o n t e n t s C o n t e n t s v8.15 Straight Uniform Beams (Common Case); Ultimate Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2008.16 Plastic, or Ultimate Strength, Design . . . . . . . . . . . . . . . . . . . . . 2048.17 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2088.18 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 9 Curved Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2959.1 Bending in the Plane of the Curve . . . . . . . . . . . . . . . . . . . . . . . 2959.2 Deflection of Curved Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3029.3 Circular Rings and Arches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3109.4 Elliptical Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3199.5 Curved Beams Loaded Normal to Plane of Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3209.6 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3269.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 10 Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40110.1 Straight Bars of Uniform Circular Section under Pure Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40110.2 Bars of Noncircular Uniform Section under Pure Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40210.3 Effect of End Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40710.4 Effect of Longitudinal Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . 41310.5 Ultimate Strength of Bars in Torsion . . . . . . . . . . . . . . . . . . . . . 41510.6 Torsion of Curved Bars; Helical Springs . . . . . . . . . . . . . . . . . . 41510.7 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41810.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 11 Flat Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44511.1 Common Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44511.2 Bending of Uniform-Thickness Plates with Circular Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44611.3 Circular-Plate Deflection Due to Shear . . . . . . . . . . . . . . . . . . . . 45011.4 Bimetallic Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45111.5 Nonuniform Loading of Circular Plates . . . . . . . . . . . . . . . . . . . 45511.6 Circular Plates on Elastic Foundations . . . . . . . . . . . . . . . . . . . . 45511.7 Circular Plates of Variable Thickness . . . . . . . . . . . . . . . . . . . . . 45711.8 Disk Springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45811.9 Narrow Ring under Distributed Torque about Its Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45911.10 Bending of Uniform-Thickness Plates with Straight Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46111.11 Effect of Large Deflection; Diaphragm Stresses . . . . . . . . . . . . 46211.12 Plastic Analysis of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46611.13 Ultimate Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46611.14 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46911.15 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 vi C o n t e n t s C o n t e n t s vii 12 Columns and Other Compression Members . . . . . . . . . . . . . . . . . . . . 54912.1 Columns; Common Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54912.2 Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55212.3 Strength of Latticed Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . 55812.4 Eccentric Loading; Initial Curvature . . . . . . . . . . . . . . . . . . . . . 55912.5 Columns under Combined Compression and Bending . . . . . 56112.6 Thin Plates with Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56312.7 Short Prisms under Eccentric Loading . . . . . . . . . . . . . . . . . . . . 56512.8 Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56912.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 13 Shells of Revolution; Pressure Vessels; Pipes . . . . . . . . . . . . . . . . . . . 57513.1 Circumstances and General State of Stress . . . . . . . . . . . . . . . . 57513.2 Thin Shells of Revolution under Distributed Loadings Producing Membrane Stresses Only . . . . . . . . . . . . . . . . . . . . . . 57513.3 Thin Shells of Revolution under Concentrated or Discontinuous Loadings Producing Bending and Membrane Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57813.4 Thin Multielement Shells of Revolution . . . . . . . . . . . . . . . . . . 59113.5 Thin Shells of Revolution under External Pressure . . . . . . . . . 60213.6 Thick Shells of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60413.7 Pipe on Supports at Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60613.8 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60813.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 14 Bodies under Direct Bearing and Shear Stress . . . . . . . . . . . . . . . . . . 70314.1 Stress Due to Pressure between Elastic Bodies . . . . . . . . . . . . . 70314.2 Rivets and Riveted Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70814.3 Miscellaneous Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71014.4 Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71414.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 15 Elastic Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72315.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72315.2 Buckling of Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72415.3 Buckling of Flat and Curved Plates . . . . . . . . . . . . . . . . . . . . . . 72615.4 Buckling of Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72715.5 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73015.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754 16 Dynamic and Temperature Stresses . . . . . . .. . . . . . . . . . . . . . . . . . . . . 75916.1 Dynamic Loadings; General Conditions . . . . . . . . . . . . . . . . . . 75916.2 Body in a Known State of Motion . . . . . . . . . . . . . . . . . . . . . . . . 75916.3 Impact and Sudden Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76716.4 Impact and Sudden Loading; Approximate Formulas . . . . . . 76916.5 Remarks on Stress Due to Impact . . . . . . . . . . . . . . . . . . . . . . . . 77116.6 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77116.7 Temperature Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777 vi C o n t e n t s C o n t e n t s vii16.8 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78216.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798 17 Stress Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80117.1 Static Stress and Strain Concentration Factors . . . . . . . . . . . . . 80117.2 Stress Concentration Reduction Methods . . . . . . . . . . . . . . . . . 80617.3 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80917.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 18 Fatigue and Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83318.1 Fatigue in Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83318.2 Fatigue Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83418.3 Fatigue and Crack Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83518.4 Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83518.5 The Stress Intensity Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83618.6 Fracture Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83918.7 Crack Tip Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84118.8 The Energy Balance Approach of Fracture . . . . . . . . . . . . . . . . 84218.9 The J Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84318.10 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84518.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 19 Stresses in Fasteners and Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85719.1 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85719.2 Analysis of Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85919.3 Strength of Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86219.4 Riveted and Bolted Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86719.5 Shearing and Failure Modes in Riveted Joints . . . . . . . . . . . . . 86819.6 Eccentric Loading of Riveted Joints . . . . . . . . . . . . . . . . . . . . . . 86919.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872 20 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87320.1 Composite Materials Classifications and Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87320.2 Mechanics of Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 87620.3 Macromechanics of a Layer (Lamina) . . . . . . . . . . . . . . . . . . . . 87620.4 Micromechanics of a Layer (Lamina) . . . . . . . . . . . . . . . . . . . . . 88020.5 Failure Criterion for a Layer (Lamina) . . . . . . . . . . . . . . . . . . . . 88320.6 Macromechanics of a Laminate . . . . . . . . . . . . . . . . . . . . . . . . . . 88620.7 Classical Lamination Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88720.8 Macromechanics of a Laminate: Stress and Strain in a Laminate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88920.9 Inversion of Stiffness Equation in a Laminate . . . . . . . . . . . . . . 89520.10 Example of Stresses and Strains in a Laminate . . . . . . . . . . . . . 89720.11 Strength and Failure Analyses of Laminate . . . . . . . . . . . . . . . . 90020.12 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90520.13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916 viii C o n t e n t six 21 Solid Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91921.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91921.2 Biomechanics of Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92021.3 Biomechanics of Articular Cartilage . . . . . . . . . . . . . . . . . . . . . . 92521.4 Biomechanics of Tendons and Ligaments . . . . . . . . . . . . . . . . . 92621.5 Biomechanics of Muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92721.6 Biomechanics of Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92921.7 Biomechanics of the Knee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92921.8 Biomechanics of the Hip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93221.9 Biomechanics of the Spine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93621.10 Biomechanics of the Lumbar Spine . . . . . . . . . . . . . . . . . . . . . . 93621.11 Biomechanics of the Cervical Spine . . . . . . . . . . . . . . . . . . . . . . 94221.12 Biomechanics of the Shoulder . . . . . . . . . . . . . . . . . . . . . . . . . . . 94321.13 Biomechanics of the Elbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94521.14 Human Factors in Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94621.15 Implants and Prostheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94621.16 The Knee Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95121.17 Other Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95221.18 Biomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95221.19 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95621.20 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96021.21 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963 A Properties of a Plane Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965 B Mathematical Formulas and Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 995 C Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035 viii C o n t e n t sixPreface to the Eighth EditionIn recent years, it has been recognized that the use of computers and the incorporation of computational mechanics, with graphic pre- and post-processors, has dominated the engineering profession. However, the very essence of engineering is rooted in the power of classical closed-form solutions and established analytical methods. It is these two components that uphold the main woven fabrics of the profession and keep it alive and progressive.In the 10 years since the publication of the 7th edition of Roark’s Formulas for Stress and Strain, we have witnessed significant advances in engineering methodology in solving stress analysis problems. This has motivated the authors to embark on an improved edition of this book.To this end, in preparation of this 8th edition, the authors had three continuing objectives. Firstly, to modernize and update the contents as required. Secondly, to introduce new topics and chapters that will maintain the high standard of this book. Finally, to improve upon the material retained from the 7th edition. The 8th edition of Roark’s is intended to make available a compact, comprehensive summary of the formulas and principles pertaining to strength of materials for both practicing engineers and students.This book is intended primarily to be a reference book that is authoritative and covers the field of stress analysis in a comprehensive manner. Similar to the 7th edition, the tabular format is continued in this edition. This format has been particularly successful when implementing problem solutions on user-friendly computer software such as MATLAB, MathCAD, TK Solver, and Excel. Commercial packages are available which integrate the above-mentioned software with Roark’s. Tabulated coefficients are in dimensionless form for convenience in using either system of units. Design formulas drawn from works published in the past remain in the system units originally published or quoted.The authors are mindful of the competing requirements to offer the user a broad spectrum of information that has made this book so useful for over 70 years. Therefore, in this edition, the authors have included a number of new chapters and topics. The main organizational change in the 8th edition is that the three parts in the 7th edition have been eliminated and the chapters are arranged sequentially. Other changes/additions included in the 8th edition are as follows:• Chapter 1, Introduction: The conversion tables are expanded.• Chapter 2, Stress and Strain: Important Relationships: The construction of Mohr’s circle and additional examples and tables are provided. P r e f a c e t o t h e E i g h t h E d i t i o n xi x P r e f a c e t o t h e E i g h t h E d i t i o n• Chapter 3, The Behavior of Bodies under Stress: Several new tables of material properties are included.• Chapter 4, Principles and Analytical Methods: The energy method and Castigliano’s theorem with examples problems are added.• Chapter 5, Numerical Methods: The formulations of finite difference and finite element methods are expanded. In addition, the different formulations of the boundary element method are presented. The numerical methods for solving polynomials and integrations are included.• Chapter 6, Experimental Methods: The Wheatstone Bridge and examples and tables are added. • Chapter 16, Dynamic and Temperature Stresses: The fundamentals of vibration, vibration isolation, and tables for the natural frequencies of many beams and shapes are added.• Chapter 17, Stress Concentration: The tables are expanded.• Chapter 18, Fatigue and Fracture: This is a new chapter where the following new topics are presented: Fracture Mechanics, The Stress Intensity Factor, Fracture Toughness, Crack Tip Plasticity, and The J Integral. Also, tables of the stress intensity factors of many types of cracks and geometries are presented.• Chapter 19, Stresses in Fasteners and Joints: This is a new chapter where new topics such as welding, welded joints, and riveted and bolted joints, and corresponding tables, are included.• Chapter 20, Composite Materials: This is a new chapter dealing with the mechanics of composite materials. The following topics are presented: Macromechanics of a Lamina, Micromechanics of a Lamina, Failure Criterion for a Lamina, Classical Lamination Theory, Stress and Strain in a Laminate, and Strength and Failure Analyses of Laminates, along with tables of the mechanical properties of many composite materials.• Chapter 21, Solid Biomechanics: Increased recognition of biomechanics and the application of solid mechanics in biological tissues have resulted in this new chapter on solid biomechanics. Here the anatomy, material characteristics, and biomechanics of several generic types of human tissues such as bone, muscles, ligaments, and tendons are presented. In addition, the biomechanics of joints such as knee, hip, cervical and lumbar spine, shoulder, and elbow are discussed. Human factors, types of prostheses, and tables of biomaterial properties are also presented. • Appendix A, Properties of a Plane Area: Several new tables are added.• Appendix B, Mathematical Formulas and Matrices: This is a new appendix where the basic mathematic formulas needed in daily engineering practice are provided.The authors would especially like to thank those individuals, publishers, institutions, and corporations who have generously given permission to use material in this and previous editions, and the many dedicated readers and users of Roark’s Formulas for Stress and Strain. P r e f a c e t o t h e E i g h t h E d i t i o n xiMeticulous care has been exercised to avoid errors. However, if any are inadvertently included in this printing, the authors will appreciate being informed so that these errors can be eliminated in subsequent printings of this edition.Warren C. YoungRichard G. Budynas Ali M. Sadegh x P r e f a c e t o t h e E i g h t h E d i t i o nxiiiAbout the AuthorsWarren C . Young is professor emeritus of mechanical engineering at the University of Wisconsin, Madison, where he was on the faculty for more than 37 years. Richard G . Budynas is professor emeritus of mechanical engineering at the Rochester Institute of Technology. He is the author of Advanced Strength and Applied Stress Analysis, Second Edition (McGraw-Hill, 1999), and coauthor of Shigley’s Mechanical Engineering Design, Ninth Edition (McGraw-Hill, 2011).Ali M . Sadegh is professor of mechanical engineering, former chairman of the department, and the founder and director of the Center for Advanced Engineering Design and Development at the City College of the City University of New York. He is a Fellow of ASME and SME. He is a coauthor of Marks’ Standard Handbook for Mechanical Engineers, 11th Edition (McGraw-Hill, 2007).Preface to the First Edition This book was written for the purpose of making available a compact, adequate summary of the formulas, facts, and principles pertaining to strength of materials. It is intended primarily as a reference book and represents an attempt to meet what is believed to be a present need of the designing engineer. This need results from the necessity for more accurate methods of stress analysis imposed by the trend of engineering practice. That trend is toward greater speed and complexity of machinery, greater size and diversity of structures, and greater economy and refinement of design. In consequence of such developments, familiar problems, for which approximate solutions were formerly considered adequate, are now frequently found to require more precise treatment, and many less familiar problems, once of academic interest only, have become of great practical importance. The solutions and data desired are often to be found only in advanced treatises or scattered through an extensive literature, and the results are not alwayspresented in such form as to be suited to the requirements of the engineer. To bring together as much of this material as is likely to prove generally useful and to present it in convenient form have been the author’s aim. The scope and management of the book are indicated by the contents. In Part 1 are defined all terms whose exact meanings might otherwise not be clear. In Part 2 certain useful general principles are stated; analytical and experimental methods of stress analysis are briefly described; and information concerning the behavior of material under stress is given. In Part 3 the behavior of structural elements under various conditions of loading is discussed, and extensive tables of formulas for the calculation of stress, strain, and strength are given. Because they are not believed to serve the purpose of this book, derivations of formulas and detailed explanations, such as are appropriate in a textbook, are omitted, but a sufficient number of examples are included to illustrate the application of the various formulas and methods. Numerous references to more detailed discussions are given, but for the most part these are limited to sources that are generally available, and no attempt has been made to compile an exhaustive bibliography. That such a book as this derives almost wholly from the work of others is self-evident, and it is the author’s hope that due acknowledgment has been made of the immediate sources of all material presented here. To the publishers and others who have generously permitted the use of material, he wishes to express his thanks. The helpful criticisms and suggestions of his colleagues, Professors E. R. Maurer, M. O. Withey, J. B. Kommers, and K. F. Wendt, are gratefully acknowledged. A considerable xiii xiv P r e f a c e t o t h e F i r s t E d i t i o nnumber of the tables of formulas have been published from time to time in Product Engineering, and the opportunity thus afforded for criticism and study of arrangement has been of great advantage. Finally, it should be said that, although every care has been taken to avoid errors, it would be oversanguine to hope that none had escaped detection; for any suggestions that readers may make concerning needed corrections, the author will be grateful.Raymond J. RoarkxvList of Tables Table 1.1 Units Appropriate to Structural Analysis (p. 2) Table 1.2 SI Units (p. 3) Table 1.3 Multiples and Submultiples of SI Units (p. 4) Table 1.4 SI Conversion Table (pp. 4–5) Table 1.5 Multiplication Factors to Convert from USCU Units to SI Units (pp. 5–6) Table 1.6 Conversion Factors (pp. 7–13) Table 2.1 Material Properties (p. 39) Table 2.2 Transformation Matrices for Positive Rotations About an Axis (p. 39) Table 2.3 Transformation Equations (p. 40) Table 2.4 Mohr’s Circle for Some Common State of Stress (pp. 41–43) Table 3.1 Modulus of Elasticity Relationships (p. 65) Table 3.2 Material Classification, Names, and Abbreviations (pp. 65–66) Table 3.3 Moduli and Strength of Materials (pp. 67–68) Table 3.4 Temperature Effects of Elastic Modulus (pp. 69–70) Table 3.5 Extended Mechanical Properties at Room Temperature (p. 71) Table 3.6 Hardness Test Indenters (p. 72) Table 3.7 ANSI Carbon Steel Mechanical Characteristics (pp. 73–74) Table 3.8 Coefficients of Thermal Expansion (pp. 75–77) Table 3.9 Elastic Constants of Selected Polycrystalline Ceramics (p. 78) Table 5.1 Sample Finite Element Library (pp. 100–101) Table 6.1 Change in Resistance with Strain for Various Strain Gage Element Materials (p. 131) Table 6.2 Properties of Various Strain Gage Grid Materials (p. 131) Table 6.3 Strain Gage Rosette Equations Applied to a Specimen of a Linear, Isotropic Material (pp. 132–133) Table 6.4 Corrections for the Transverse Sensitivity of Electrical Resistance Strain Gages (pp. 134–135) Table 6.5 Strain Gauge Equations for Several Types of Bridge Configurations (pp. 136–137) Table 8.1 Shear, Moment, Slope, and Deflection Formulas for Elastic Straight Beams (pp. 209–223) xiv P r e f a c e t o t h e F i r s t E d i t i o nxv L i s t o f T a b l e s xvii xvi L i s t o f T a b l e s Table 8.2 Reaction and Deflection Formulas for In-Plane Loading of Elastic Frames (pp. 225–233) Table 8.3 Numerical Values for Functions Used in Table 8.5 (pp. 234–235) Table 8.4 Numerical Values for Denominators Used in Table 8.5 (pp. 236–237) Table 8.5 Shear, Moment, Slope, and Deflection Formulas for Finite-Length Beams on Elastic Foundations (pp. 239–247) Table 8.6 Shear, Moment, Slope, and Deflection Formulas for Semi-Infinite Beams on Elastic Foundations (pp. 249–251) Table 8.7(a) Reaction and Deflection Coefficients for Beams Under Simultaneous Axial and Transverse Loading: Cantilver End Support (p. 252) Table 8.7(b) Reaction and Deflection Coefficients for Beams Under Simultaneous Axial and Transverse Loading: Simply Supported Ends (p. 253) Table 8.7(c) Reaction and Deflection Coefficients for Beams Under Simultaneous Axial and Transverse Loading: Left End Simply Supported, Right End Fixed (p. 254) Table 8.7(d) Reaction and Deflection Coefficient for Beams Under Simultaneous Axial and Transverse Loading: Fixed Ends (p. 255) Table 8.8 Shear, Moment, Slope, and Deflection Formulas for Beams Under Simultaneous Axial Compression and Transverse Loading (pp. 257–269) Table 8.9 Shear, Moment, Slope, and Deflection Formulas for Beams Under Simultaneous Axial Tension and Transverse Loading (pp. 271–272) Table 8.10 Beams Restrained Against Horizontal Displacement at the Ends (p. 273)Table 8.11(a) Reaction and Deflection Coefficients for Tapered Beams (pp. 274–276)Table 8.11(b) Reaction and Deflection Coefficients for Tapered Beams (pp. 277–279)Table 8.11(c) Reaction and Deflection Coefficients for Tapered Beams (pp. 280–282)Table 8.11(d) Reaction and Deflection Coefficients for Tapered Beams (pp. 283–285) Table 8.12 Position of Flexural Center Q for Different Sections (pp. 286–287) Table 8.13 Collapse Loads with Plastic Hinge Locations for Straight Beams (pp. 288–291) Table 9.1 Formulas for Curved Beams Subjected to Bending in the Plane of the Curve (pp. 327–334) Table 9.2 Formulas for Circular Rings (pp. 335–353) Table 9.3 Reaction and Deformation Formulas for Circular Arches (pp. 355–369) Table 9.4 Formulas for Curved Beams of Compact Cross Section Loaded Normal to the Plane of Curvature (pp. 371–398) Table 10.1 Formulas for Torsional Deformation and Stress (pp. 419–429) Table 10.2 Formulas for Torsional Properties and Stresses in Thin-Walled Open Cross Sections (pp. 431–433) Table 10.3 Formulas for the Elastic Deformations of Uniform Thin-Walled Open Members Under Torsional Loading (pp. 435–442) Table 11.1 Numerical Values for Functions Used in Table 11.2 (pp. 469–470) Table 11.2 Formulas for Flat Circular Plates of Constant Thickness (pp. 471–522) Table 11.3 Shear Deflections for Flat Circular Plates of Constant Thickness (pp. 523–525) L i s t o f T a b l e s xvii Table 11.4 Formulas for Flat Plates with Straight Boundaries and Constant Thickness (pp. 527–543) Table 12.1 Formulas for Short Prisms Loaded Eccentrically; Stress Reversal Impossible (pp. 569–573) Table 13.1 Formulas for Membrane Stresses and Deformations in Thin-Walled Pressure Vessels (pp. 609–618) Table 13.2 Shear, Moment, Slope, and Deflection Formulas for Long and Short Thin-Walled Cylindrical Shells under Axisymmetric Loading (pp. 619–626) Table 13.3 Formulas for Bending and Membrane Stresses and Deformations in Thin-Walled Pressure Vessels (pp. 627–650) Table 13.4 Formulas for Discontinuity Stresses and Deformations at the Junctions of Shells and Plates (pp. 651–695) Table 13.5 Formulas for Thick-Walled Vessels under Internal and External Loading (pp. 697–698) Table 14.1 Formulas for Stress and Strain Due to Pressure onor between Elastic Bodies (pp. 715–718) Table 15.1 Formulas for Elastic Stability of Bars, Rings, and Beams (pp. 731–741) Table 15.2 Formulas for Elastic Stability of Plates and Shells (pp. 743–753) Table 16.1 Natural Frequencies of Vibration for Continuous Members (pp. 783–786) Table 16.2 Natural Frequencies of Vibration of Various Systems (pp. 787–794) Table 16.3 Spring Constants (pp. 795–796) Table 16.4 Longitudinal Wavespeed and Km for Engineering Materials (pp. 797–798) Table 17.1 Stress Concentration Factors for Elastic Stress (Kt) (pp. 809–822) Table 17.2 Graphs for Stress Concentration Factors (pp. 823–828) Table 18.1 Values of Factor C and Exponent m in Eq. (18.3-1) (p. 835) Table 18.2 Fracture Toughness of Some Materials (p. 840) Table 19.1 Minimum Weld Metal Properties (p. 862) Table 19.2 Minimum Fillet Weld Size w (p. 863) Table 19.3 Allowable Loads for Various Sizes of Fillet Welds (p. 864) Table 19.4 Treating a Weld as a Line (p. 865–867) Table 20.1 Density, Strength, and Stiffness of Selected Fibers (p. 875) Table 20.2 Fiber and Matrix Materials Used in a Composite (p. 875) Table 20.3 The Mechanical Properties of Unidirectional Reinforced Composite Materials (p. 882) Table 20.4 Fibers and Matrix Materials and Their Applications (p. 905) Table 20.5 Properties of Key Reinforcing Fibers (p. 905) Table 20.6 Properties of Selected Thermosetting and Thermoplastic Matrices (p. 906) Table 20.7 Effect of Fiber Form and Volume Fraction on Mechanical Properties of E-Glass-Reinforced Polyester (p. 907) Table 20.8 Mechanical Properties of Selected Unidirectional Polymer Matrix Composites (p. 907) xvi L i s t o f T a b l e s xviii L i s t o f T a b l e s Table 20.9 Mechanical Properties of Selected Quasi-Isotropic Polymer Matrix Composites (p. 908) Table 20.10 Fracture Toughness of Structural Alloys, Monolithic Ceramics, and Ceramic Matrix Composites (p. 909) Table 20.11 Mechanical Properties of Selected Unidirectional Continuous Fiber-Reinforced Metal Matrix Composites (p. 909) Table 20.12 Mechanical Properties of Silicon Carbide Particle-Reinforced Aluminum (p. 910) Table 20.13 Physical Properties of Selected Unidirectional Composites and Monolithic Metals (p. 911) Table 20.14 Physical Properties of Isotropic and Quasi-Isotropic Composites and Monolithic Materials Used in Electronic Packaging (pp. 912–913) Table 20.15 Physical Properties of Selected Unidirectional Polymer Matrix Composites (p. 914) Table 20.16 Physical Properties of Selected Quasi-Isotropic Polymer Matrix Composites (p. 915) Table 20.17 Physical Properties of Silicon Carbide Particle-Reinforced Aluminum (p. 915) Table 21.1 Elastic Muduli and Ultimate Strength of Cortical Bone (p. 923) Table 21.2 Representative Properties of the Human Articular Cartilage Taken from the Lateral Condyle of the Femur (p. 926) Table 21.3 Representative Properties of Human Tendon and Ligament under Tensile Loading (p. 927) Table 21.4 Mechanical Properties of a Vertebral Body, A: Cortical Bone, and B: Trabecular Bone (p. 938) Table 21.5 Mechanical Properties of Spinal Elements (p. 939) Table 21.6 Anthropometric (p. 948) Table 21.7 Significant Physical Properties of Different Biomaterials (p. 956) Table 21.8 Compositions of Surface-Active Glasses and Glass Ceramics in Weight Percent (p. 957) Table 21.9 Properties of Polyethylene (p. 957) Table 21.10 Chemical and Mechanical Properties of Alumina for Implants (p. 957) Table 21.11 Mechanical Properties of Cortical Bone, 316L Stainless Steel, Cobalt–Chromium Alloy, Titanium and Titanium-6-Aluminum-4-Vanadium (p. 958) Table 21.12 Properties of Bones at Different Age (p. 958) Table 21.13 Typical Mechanical Properties of Polymer-Carbon Composites (Three-Point Bending) (p. 958) Table 21.14 Mechanical Properties of Some Degradable Polymers (p. 959) Table 21.15 Representative Mechanical Properties of Commercial Sutures (p. 960) Table A.1 Properties of Sections (p. 969–984) Table A.2 Moment of Inertia of Sections (pp. 985–991) Table A.3 Moment of Inertia of Uniform Objects (pp. 993–994)1Chapter 1IntroductionThe widespread use of personal computers, which have the power to solve problems solvable in the past only on mainframe computers, has influenced the tabulated format of this book. Computer programs for structural analysis, employing tech-niques such as the finite element method and the boundary element method, are also available for general use. These programs are very powerful; however, in many cases, elements of structural systems can be analyzed quite effectively independently without the need for an elaborate finite element model. In some instances, finite element models or programs are verified by comparing their solutions with the results given in a book such as this. Contained within this book are simple, accurate, and thorough tabulated formulations that can be applied to the stress analysis of a comprehensive range of structural components.This chapter serves to introduce the reader to the terminology, state property units and conversions, and contents of the book.1.1 TerminologyDefinitions of terms used throughout the book can be found in the glossary in App. C.1.2 State Properties, Units, and ConversionsThe basic state properties associated with stress analysis include the following: geo-metrical properties such as length, area, volume, centroid, center of gravity, and second-area moment (area moment of inertia); material properties such as mass density, modulus of elasti city, Poisson’s ratio, and thermal expansion coefficient; loading proper ties such as force, moment, and force distributions (e.g., force per unit length, force per unit area, and force per unit volume); other properties associated with load-ing, including energy, work, and power; and stress analysis properties such as defor-mation, strain, and stress.Two basic systems of units are employed in the field of stress analysis: SI units and USCU units.∗ SI units are mass-based units using the kilogram (kg), meter (m), second (s), and Kelvin (K) or degree Celsius (°C) as the fundamental units of mass, length, time, and temperature, respectively. Other SI units, such as that used for force, ∗SI and USCU are abbreviations for the International System of Units (from the French Systéme International d’Unités) and the United States Customary Units, respectively. 2 C h a p t e r O n e I n t r o d u c t i o n 3Quantity International Metric (SI) U.S. CustomaryLength (meter) m (foot) ftForce and weight, W (newton) N(kg-m/s2) (pound) lbfTime s sAngle rad radSecond area moment m4 ft4Mass kg lbf-s2/ft (slug)Area m2 ft2Mass moment of inertia kg-m2 lbf-s2-ftMoment N-m lbf-ftVolume m3 ft3Mass density kg/m3 lbf-s2/ft4Stiffness of linear spring N/m lbf/ftStiffness of rotary spring N-m/rad lbf-ft/radTemperature K (Kelvin) °F (degrees of Fahrenheit)Torque, work, energy N-m (Joule) lbf-ftStiffness of torsional spring N-m/rad lbf-ft/radStress or pressure N/m2 (pascal) lbf/ft2 (psi)∗In stress anlaysis, the unit of length used most often is the inch.Table 1.1 Units Appropriate to Structural Analysis*the Newton (kg-m/s2), are derived quantities. USCU units are force-based units using the pound force (lbf), inch (in) or foot (ft), second (s), and degree Fahrenheit (°F) as the fundamental units of force, length, time, and temperature, respectively. Other USCU units, such as that used for mass, the slug (lbf-s2/ft) or the nameless lbf-s2/in, are derived quantities. Table 1.1 gives a listing of the primary SI and USCU units used for structural analysis. Other SI units are given in Table 1.2. Certain prefixes may be appropriate, depending on the size of the quantity. Common prefixes are given in Table 1.3. For exam-ple, the modulus of elasticity of carbon steel is approximately 207 GPa = 207 × 109 Pa = 207 × 109 N/m2. Prefixes are normally used with SI units. However, there are cases where prefixes are also used with USCU units. Some examples are the kpsi (1 kpsi = 103 psi = 103 lbf/in2), kip (1 kip = 1 kilopound = 1000 lbf), and Mpsi (1 Mpsi = 106 psi).Depending on the application, different units may be specified. It is important that the analyst be aware of all the implications of the units and make consistent use of them. For example, if you are building a model from a CAD file in which the design dimen-sional units are given in mm, it is unnecessary to change the system of units or to scale 2 C h a p t e r O n e I n t r o d u c t i o n 3Quantity Unit (SI) FormulaBase UnitsLength meter (m)Mass kilogram (kg)Time second (s)Thermodynamic temperature Kelvin (K)Supplementary UnitsPlane angle radian (rad)Solid angle steradian (sr)Derived UnitsAcceleration meter per second squared m/s2Angular acceleration radian per second squared rad/s2Angular velocity radian per second rad/s Area square meter m2Density kilogram per cubic meter kg/m3Energy joule (J) N-mForce Newton (N) kg-m/s2Frequency hertz (Hz) 1/sPower watt (W) J/sPressure Pascal (Pa) N/m2Quantity of heat joule (J) N-mStress Pascal (Pa) N/m2Thermal conductivity watt per meter-Kelvin W/(m-K)Velocity meter per second m/sViscosity dynamic Pascal-second Pa-sViscosity kinematic square meter per second m2/sWork joule (J) N-mTable 1.2 SI Unitsthe model to units of m. However, if in this example the input forces are in Newtons, then the output stresses will be in N/mm2, which is correctly expressed as MPa. If in this example applied moments are to be specified, the units should be N-mm. For deflections in this example, the modulus of elasticity E should also be specified in MPa and the output deflections will be in mm.Tables 1.4 and 1.5 present the conversions from USCU units to SI units and vice versa for some common state property units. The more detailed conversion units are given in Table 1.6. 4 C h a p t e r O n e I n t r o d u c t i o n 5Prefix Symbol Multiplying Factorexa E 1018 1 000 000 000 000 000 000peta P 1015 1 000 000 000 000 000tera T 1012 1 000 000 000 000giga G 109 1 000 000 000mega M 106 1 000 000kilo k 103 1 000hecto h 102 100deca da 10 10deci d 10-1 0.1centi c 10-2 0.01milli m 10-3 0.001micro µ 10-6 0.000 001nano n 10-9 0.000 000 001pico p 10-12 0.000 000 000 001femto f 10-15 0.000 000 000 000 001atto a 10-18 0.000 000 000 000 000 001Table 1.3 Multiples and Submultiples of SI Units 4 C h a p t e r O n eSI Units From SI to English From English to SILengthkilometer (km) = 1,000 m 1 km = 0.621 mi 1 mi = 1.609 kmmeter (m) = 100 cm 1 m = 3.281 ft 1 ft = 0.305 mcentimeter (cm) = 0.01 m 1 cm = 0.394 in 1 in = 2.540 cmmillimeter (mm) = 0.001 m 1 mm = 0.039 in 1 in = 25.4 mmmicrometer (µm) = 0.000 001 m 1 µm = 3.93 × 10-5 in 1 in = 25400 mmnanometer (nm) = 0.000 000 001 m 1 nm = 3.93 × 10-8 in 1 in = 25400000 mmAreasquare kilometer (km2) = 100 hectares1 km2 = 0.386 mi2 1 mi2 = 2.590 km2hectare (ha) = 10,000 m2 1 ha = 2.471 acres 1 acre = 0.405 hasquare meter (m2) = 10,000 cm2 1 m2 = 10.765 ft2 1 ft2 = 0.093 m2square centimeter (cm2) = 100 mm2 1 cm2 = 0.155 in2 1 in2 = 6.452 cm2Volumeliter (L) = 1,000 mL = 1 dm3 1 L = 1.057 fl qt 1 fl qt = 0.946 Lmilliliter (mL) = 0.001 L = 1 cm3 1 mL = 0.034 fl oz 1 fl oz = 29.575 mLmicroliter (µL) = 0.000 001 L 1 µL = 3.381 × 10-5 fl oz 1 fl oz = 29575 µLTable 1.4 SI Conversion Table 4 C h a p t e r O n e I n t r o d u c t i o n 5 4 C h a p t e r O n eSI Units From SI to English From English to SIMasskilogram (kg) = 1,000 g 1 kg = 2.205 lb 1 lb = 0.454 kggram (g) = 1,000 mg 1 g = 0.035 oz 1 oz = 28.349 gmilligram (mg) = 0.001 g 1 mg = 3.52 × 10-5 oz 1 oz = 28349 mgmicrogram (µg) = 0.000 001 g 1 µg = 3.52 × 10-8 oz 1 oz = 28349523 µgTable 1.4 SI Conversion Table (Continued)To Convert from To Multiply byMassounce (avoirdupois) kilogram (kg) 2.834952 × 10-2pound (avoirdupois) kilogram (kg) 4.535924 × 10-1ton (short, 2000 lb) kilogram (kg) 9.071847 × 10+2ton (long, 2240 lb) kilogram (kg) 1.016047 × 10+3kilogram (kg) ounce (avoirdupois) 3.527396 × 10+1kilogram (kg) pound (avoirdupois) 2.204622kilogram (kg) ton (short, 2000 lb) 1.102311 × 10-3kilogram (kg) ton (long, 2240 lb) 9.842064 × 10-4Mass Per Unit Lengthpound per foot (lb/ft) kilogram per meter (kg/m) 1.488164pound per inch (lb/in) kilogram per meter (kg/m) 1.785797 × 10+1kilogram per meter (kg/m) pound per foot (lb/ft) 6.719689 × 10-1kilogram per meter (kg/m) pound per inch (lb/in) 5.599741 × 10-2Mass Per Area Unitpound per square foot (lb/ft2) kilogram per square meter (kg/m2) 4.882428kilogram per square meter (kg/m2) pound per square foot (lb/ft2) 2.048161 × 10-1Mass Per Unit Volumepound per cubic foot (lb/ft3) kilogram per cubic meter (kg/m3) 1.601846 × 10+1pound per cubic inch (lb/in3) kilogram per cubic meter (kg/m3) 2.767990 × 10+4kilogram per cubic meter (kg/m3) pound per cubic foot (lb/ft3) 6.242797 × 10-2kilogram per cubic meter (kg/m3) pound per cubic inch (lb/in3) 3.612730 × 10-5pound per cubic foot (lb/ft3) pound per cubic inch (lb/in3) 1.728000 × 10+3Lengthfoot (ft) meter (m) 3.048000 × 10-1inch (in) meter (m) 2.540000 × 10-2mil meter (m) 2.540000 × 10-5inch (in) micrometer (µm) 2.540000 × 10+4meter (m) foot (ft) 3.28084meter (m) inch (in) 3.937008 × 10+1meter (m) mil 3.937008 × 10+4micrometer (µm) inch (in) 3.937008 × 10-5Table 1.5 Multiplication Factors to Convert from USCU Units to SI Units 6 C h a p t e r O n e I n t r o d u c t i o n 7To Convert from To Multiply byAreafoot2 square meter (m2) 9.290304 × 10-2inch2 square meter (m2) 6.451600 × 10-4circular mil square meter (m2) 5.067075 × 10-10sq. centimeter (cm2) square inch (in2) 1.550003 × 10-1square meter (m2) foot2 1.076391 × 10+1square meter (m2) inch2 1.550003 × 10+3square meter (m2) circular mil 1.973525 × 10+9Volumefoot3 cubic meter (m3) 2.831685 × 10-2inch3 cubic meter (m3) 1.638706 × 10-5cubic centimeter (cm3) cubic inch (in3) 6.102374 × 10-2cubic meter (m3) foot3 3.531466 × 10+1cubic meter (m3) inch3 6.102376 × 10+4gallon (U.S. liquid) cubic meter (m3) 3.785412 × 10-3Forcepounds-force (lbf) newtons (N) 4.448222Pressure or Stresspound force per sq. inch (lbf/in2)(psi)pascal (Pa) 6.894757 × 10+3kip per sq. inch (kip/in2)(ksi) pascal (Pa) 6.894757 × 10+6pound force per sq. inch (lbf/in2)(psi)megapascals (MPa) 6.894757 × 10-3pascal (Pa) pound force per sq. inch (psi) 1.450377 × 10-4pascal (Pa) kip per sq. inch (ksi) 1.450377 × 10-7megapascals (MPa) pound force per sq. inch (lbf/in2) (psi)1.450377 × 10+2Section Properties section modulus S (in3) S (m3) 1.638706 × 10-5moment of inertia I (in4) I (m4) 4.162314 × 10-7modulus of elasticity E (psi) E (Pa) 6.894757 × 10+3section modulus S (m3) S (in3) 6.102374 × 10+4moment of inertia I (m4) I (in4) 2.402510 × 10+6modulus of elasticity E (Pa) E (psi) 1.450377 × 10-4Temperature degree Fahrenheit degree Celsius t°C = (t°F - 32)/1.8degree Celsius degree Fahrenheit t°F = 1.8 t°C + 32Angle degree radian (rad) 1.745329 × 10-2radian (rad) degree 5.729578 × 10+1Table 1.5 Multiplication Factors to Convert from USCU Units to SI Units (Continued)Random documents with unrelated content Scribd suggests to you: Fight for his place? Must he fight? A fight was something. The otherfellows were treading very hard on his heels. But was his placeworth fighting for? Did he want it? He had not chosen it. It had beenthrust upon him. The moments of decision, when a man had tochoose his place in the files, about which Uncle Bond had spoken soconfidently, had never come to him. Moments of decision? Whatcould he, what did he,ever decide? In the very fight for his place,which was impending, he would not be allowed to commit himself.The fight would be fought for him, all around him, and he, the manmost concerned, was the one man who could not, who would not beallowed, to take a side. It was all arranged for him. The old Duke ofNorthborough, the lightning conductor, would take the shock! Andthe result? Did he know what he wanted? Did he know his ownmind? A half-hearted man! What a faculty Uncle Bond had for hittingon a phrase, a sentence, that stuck, that recurred. It described him.A half-hearted King. A half-hearted friend. A half-hearted—lover.But was it altogether his fault? Was it not his position, his intolerableisolation, his responsibility, which, by a bitter paradox, was withoutresponsibility, that had thrown his whole life out of gear, andparalysed his will? As a sailor, in his own chosen profession, withresponsibility, with the command of men, he had held his own, morethan held his own, with his peers. He had had his place, anhonourable place, amongst men of the same seniority as himself,and the Navy took the best men, the pick of the country. Yes. Heknew what he wanted now. A moment of decision. A moment inwhich he could be himself. A moment in which he could asserthimself, assert his own individuality, recklessly, violently, prove thathe was not a half-hearted man, not an automaton, not anoverdressed popinjay—At this point, the appearance of a certain amount of traffic on theroad, as the car swept into the fringe of the outer suburbs, and themore careful driving which it entailed, broke the thread of the King'sthoughts. The inevitable lowering of the speed of the car whichfollowed, served to remind him anew that he still had a good deal oftime to make up, thanks to his loitering with Uncle Bond, if he wasto be successful in effecting his return to the palace unobserved. Hisrising anxiety about this now all important matter led himthenceforward to concentrate the whole of his attention on hishandling of the car.CHAPTER VIIN the outer suburbs, milkmen, postmen, and boys deliveringnewspapers, were moving from door to door, in the quietstreets of villas. The tramcars, and later the buses, which the carcaught up, and passed, were crowded with workmen, being carriedat "Workmen's Fares." The shop fronts, in the inner suburbs, gay inthe early morning sunlight, with their Coronation flags anddecorations, were still all shuttered; but a thin trickle of men andwomen in the streets, moving in the direction of the railway stations,gave promise already of the impending rush of the business crowd.Coronation Day had come, and gone. The public holiday was over.Now there was work toward.At the far end of Tottenham Court Road, by which broadthoroughfare he approached, as he had escaped from, the town, theKing deliberately varied the route which he had followed the nightbefore. Heading the car straight on down Charing Cross Road,through Trafalgar Square, and so into Whitehall, he turned, at last,into Victoria Street. It was by the side streets, in the vicinity ofVictoria Station, that he ultimately approached the palace, and ranout into Lower Grosvenor Place. He did this to avoid theneighbourhood of the parks, and possible recognition by earlymorning riders, on their way to and from Rotten Row.Lower Grosvenor Place proved, as usual, deserted. In the secluded,shut-in mews, behind the tall houses, no one, as yet, was stirring. Ina very few minutes, the King had successfully garaged the car. Thenhe slipped hurriedly back across Grosvenor Place. The road washappily still empty, and he reached the small, green, wooden door inthe palace garden wall, without encountering anything moreformidable than a stray black cat. A black cat which shared his tastefor night walking. A purring black cat, which rubbed its head againsthis legs. A black cat for luck!Unlocking, and opening, the door, the King slipped into the palacegarden.The door swung to behind him.All need for anxiety, for haste, and for precaution was now at anend.It was only just eight o'clock.Sauntering leisurely through the garden, the King reached the palacewithout meeting any one, on the way. Sometimes, on theseoccasions, he ran into gardeners, early at work, a policeman,patrolling the walks, or some member of the household staff; butsuch encounters never caused him any anxiety. Why should not theKing take a stroll in the garden, before breakfast? Had he not beenknown to dive into the garden lake for an early morning swim, andhad not the fact been duly recorded in all the newspapers?He entered the palace by the door through which he had escapedthe night before, and so, mounting the private staircase, which ledup to his own suite of rooms, regained his dressing room,unchallenged.The creation of a certain amount of necessary disorder in hisbedroom, and a partial undressing, were the work of only a fewminutes.Then he rang his bell, for which, he was well aware, a number of thepalace servants would be, already anxiously listening.It was Smith, as the King had been at some pains to arrange, whoanswered this, the first summons of the official, Royal day."Breakfast in the garden, in half an hour, Smith," the King ordered."See about that, at once. Then you can come back, and get my bathready, and lay out the clothes."Another bath was welcome, and refreshing, after the dust, and theexcitement of the motor run. Smith's choice of clothes was a new,grey, lounge suit, of most satisfactory cut, and finish. At the end ofthe half hour which he had allowed himself, the King left thedressing room, and passed down the private staircase, out into thesunlit garden, with an excellent appetite for his second breakfast.The breakfast table had been placed on one of the lawns, in thegreen shade thrown by a magnificent sycamore tree. A couple ofgorgeously clad footmen were responsible for the service of themeal but they soon withdrew to a discreet distance. Theunpretentious domestic life, traditional for so many years, in thepalace, had made it comparatively easy for the King to reduce to aminimum the distasteful ceremony which the presence of servantsadds to the simplest meal.A few personal letters, extracted by some early rising member of hissecretarial staff, from the avalanche of correspondence in the Royalpost bags, had been placed, in readiness for the King, on thebreakfast table. One of these letters bore the Sandringhampostmark, and proved to be from his youngest sister, the PrincessElizabeth, who was still, officially, a school girl. It was a charmingletter. With a frank and fearless affection, a spontaneous naïveté,that pleased the King, the young Princess wrote to offer him hercongratulations on his Coronation, congratulations which, sheconfessed, she had been too shy to voice in public, the day before.The letter touched the King. He read it through twice, allowing hiseggs and bacon, and coffee, to grow cold, while he did so. Therewas a note of sincere feeling, of genuine affection, of sisterly pridein him, mingled with anxiety for his welfare, in the letter, whichafforded a very agreeable contrast to the subservience of the Familyin general, which had so jarred upon him, at the state banquet, thenight before. This sister of his seemed likely to grow up into a truewoman, a loyal and affectionate woman. She reminded him, in someodd way, of Judith.What would the future bring to this fresh, unspoilt, sister of his? "Awoman, a woman with a heart, at the head of the procession."Another of Uncle Bond's phrases! What an insight the little man hadinto the possibilities of positions, and situations, which he could onlyhave known in imagination, in the imagination which he wasted onthe construction of his grotesquely improbable tales! He must dowhat he could for this fresh, unspoilt sister of his. That would belittle enough in all conscience! Meanwhile he