CHAPTER XVI of Anne of Geyerstein, Vol. 2 by Sir Walter Scott, and is the hostile troop arrived, and have they won the day?  Sleep did not close the eyes of the Earl of Oxford or his son, for although the success or defeat of the Duke of Burgundy could not now be of importance to their own private or political affairs, yet the father did not cease to interest himself in the fate of his former companion in arms, and the son, with the fire of youth always eager after novelty, expected to find something to advance or thwart his own progress in every remarkable event which agitated the world. Arthur had risen from his bed, and was in the act of attiring himself when the tread of a horse arrested his attention. He had no sooner looked out of the window than exclaiming. News, my father, news from the army, he rushed into the street, where a cavalier, who appeared to have ridden very hard, was inquiring for the two Phillipsons, father and son. He had no difficulty in recognizing Colvin, the master of the Burgundian ordinance, his ghastly look bespoke distress of mind. His disordered array and broken armor, which seemed rusted with rain, or stained with blood, gave the intelligence of some fray in which he had probably been worsted, and so exhausted was his gallant steed that it was with difficulty the animal could stand upright. The condition of the rider was not much better when he alighted from his horse to greet Arthur. He reeled so much that he would have fallen without instant support. His horny eye had lost the power of speculation. His limbs possessed imperfectly that of motion, and it was with a half-suffocated voice that he muttered, only fatigue, want of rest, and of food. Arthur assisted him into the house, and refreshments were procured, but he refused all except a bowl of wine. After tasting which, he set it down, and looking at the Earl of Oxford with an eye of the deepest affliction, he ejaculated, the Duke of Burgundy. Slane replied the Earl, I trust not. It might have been better if he were, said the Englishman, but dishonor has come before death. Defeated then, said Oxford, so completely and fearfully defeated, answered the soldier, that all I have seen of loss before was slight in comparison. But how, or where, said the Earl of Oxford, you were superior in numbers as we were informed. Two to one, at least, answered Colvin, and when I speak of our encounter at this moment, I could rend my flesh with my teeth for being here to tell such a tale of shame. We had sat down for about a week before that paltry town of Merton, or Morat, or whatever it is called. The Governor, one of those stubborn mountain bears of burn, bet us defiance, he would not even condescend to shut his gates. But when we summoned the town, returned for answer, we might enter. If we pleased, we should be suitably received. I would have tried to bring him to reason by a salvo or two of artillery, but the Duke was too much irritated to listen to good counsel. Stimulated by that black traitor, Campo Basso, he deemed it better to run forward with his whole force upon a place, which, though I could soon have battered it about their German ears, was yet too strong to be carried by swords, lances, and hagbats. We were beaten off with great loss and much discouragement to the soldiers. We then commenced more regularly, and my batteries would have brought these mad switzers to their senses. Walls and ramparts went down before the lusty canoneers of Burgundy. We were well secured also by entrenchments against those whom we heard of as approaching to raise the siege. But on the evening of the 20th of this month, we learned that they were close at hand, and Charles, consulting only his own bold spirit, advanced to meet them, relinquishing the advantage of our batteries and strong position.  We broke up on the next morning, and had not advanced far before we saw the lances and thick array of hullbirds and two-handed swords, which crusted the mountain. Heaven, too, added its terrors, a thunderstorm, with all the fury of those tempestuous climates descended on both armies, but did most annoyance to ours, as our troops, especially the Italians, were more sensible to the torrents of rain which poured down and the rivulets which swelled into torrents inundated and disordered our position. The Duke, for once, saw it necessary to alter his purpose of instant battle. He wrote up to me and directed me to defend with the cannon the retreat which he was about to commence, adding that he himself would in person sustain me with the men at arms. The order was given to retreat, but the movement gave new spirit to an enemy already sufficiently audacious. The ranks of the Swiss instantly prostrated themselves in prayer, a practice on the field of battle which I have ridiculed, but I will do so no more, when after five minutes they sprang again on their feet and began to advance rapidly, sounding their horns and crying their war cries with all their usual ferocity. Behold, my lord, the clouds of heaven opened, shedding on the Confederates the blessed light of the returning sun, while our ranks were still in the gloom of the tempest. My men were discouraged, the host behind them was retreating. The sudden light thrown on the advancing Swissers showed along the mountains a profusion of banners, a glancing of arms giving to the enemy the appearance of double the numbers that had hitherto been visible to us. I exhorted my followers to stand fast, but in doing so I thought a thought and spoke a word which was a grievous sin. Stand fast, my brave canineers, I said, we will presently let them hear louder thunders and show them more fatal lightnings than their prayers have put down. My men shouted, but it was an impious thought, a blasphemous speech, and evil came after it. We leveled our guns on the advancing masses as fairly as canon were ever pointed. I can vouch it, for I laid the grand Duchess of Burgundy myself. Ah, poor Duchess, what rude hands manage thee now. The volley was fired, and ere the smoke spread from the muzzles, I could see many a man and many a banner go down. It was natural to think such a discharge would have checked the attack, and whilst the smoke hid the enemy from us, I made every effort again to load our cannon and anxiously endeavored to look through the mist to discover the state of our opponents. But ere our smoke was cleared away, or the cannon again loaded, they came headlong down on us, horse and foot, old men and boys, men at arms and violets charging up to the muzzle of the guns and over them, with total disregard to their lives. My brave fellows were cut down, pierced through, and overrun, while they were again loading their pieces, nor do I believe that a single cannon was fired a second time. And the Duke, said the Earl of Oxford, did he not support you? Most loyally and bravely answered Colvin, with his own bodyguard of Walloons and Burgundians, but a thousand Italian mercenaries went off and never showed face again. The past, too, was combered with the artillery, and in itself narrow, bordering on mountains and cliffs, a deep lake close beside. In short, it was a place totally unfit for horsemen to act in, in spite of the Duke's utmost exertions, and those of the gallant Flemmings who fought around him, all were born back in complete disorder. I was on foot fighting as I could, without hopes of my life, or indeed thoughts of saving it when I saw the guns taken and my faithful canoneers slain. But I saw Duke Charles hard-pressed and took my horse from my page that held him. Thou, too, art lost, my poor orphan boy. I could only aid Monsignor, De La Croix, and others to extricate the Duke. Our retreat became a total rout, and when we reached our rearguard, which we had left strongly encamped, the banners of the Switzers were waving on our batteries, for a large division had made a circuit through the mountain passes, known only to themselves, and attacked our camp vigorously seconded by that accursed Adrien de Boebenberg, who sailed from the beleaguered town so that our entrenchments were stormed on both sides at once. I have more to say, but having ridden day and night to bring you these evil tidings, my tongue clings to the roof of my mouth, and I feel that I can speak no more. The rest is all flight and massacre, disgraceful to every soldier that shared in it. For my part, I confess my contumelious self-confidence and insolence to man, as well as blasphemy to heaven. If I live, it is but to hide my disgraced head in a cowl and expiate the numerous sins of a licentious life. With difficulty, the broken-minded soldier was prevailed upon to take some nourishment and repose, together with an opiate which was prescribed by the physician of King Rene, who recommended it as necessary to preserve even the reason of his patient exhausted by the events of the battle and subsequent fatigue. The Earl of Oxford, dismissing other assistants, watched alternately with his son at Colvin's bedside, notwithstanding the draft that had been administered. His repose was far from sound. Sudden starts, the perspiration which started from his brow, the distortions of his countenance, and the manner in which he clenched his fists and flung about his limbs showed that in his dreams he was again encountering the terrors of a desperate and forlorn combat. This lasted for several hours, but about noon fatigue and medicine prevailed over nervous excitation, and the defeated commander fell into a deep and untroubled repose till evening. About sunset he awakened, and after learning with whom and where he was, he partook of refreshments and, without any apparent consciousness of having told them before, detailed once more all the particulars of the battle of Merton. It were little wide of truth, he said, to calculate that one half of the Duke's army fell by the sword or were driven into the lake. Those who escaped are great part of them scattered, never again to unite. Such a desperate and irretrievable route was never witnessed. We fled like deer, sheep, or any other timid animals, which only remain in company because they are afraid to separate, but never think of order or of defense. And the Duke, said the Earl of Oxford, we hurried him with us, said the soldier, rather from instinct than loyalty, as men flying from a conflagration snatch up what they have of value without knowing what they are doing. Knight and nave, officer and soldier, fled in this same panic, and each blast of the horn of Urie in our rear added new wings to our flight. And the Duke repeated Oxford. At first he resisted our efforts and strove to turn back on the foe. But when the flight became general, he galloped along with us without a word spoken, or a command issued. At first we thought his silence and passiveness so unusual, in a temper so fiery, were fortunate for securing his personal safety. But when we rode the whole day without being able to obtain a word of reply to all our questions, when he sternly refused refreshments of every kind, though he had tasted no food all that disastrous day, when every variation of his moody and uncertain temper was sunk into silent and sullen despair, we took counsel what was to be done, and it was by the general voice that I was dispatched to entreat that you, for whose counsels alone Charles has been known to have had some occasional deference, would come instantly to his place of retreat and exert all your influence to awaken him from this lethargy which may otherwise terminate his existence. And what remedy can I interpose, said Oxford, you know how he neglected my advice when following it might have served my interest as well as his own. You are aware that my life was not safe among the miscreants that surrounded the Duke and exercised influence over him. Most true, answered Colvin, but I also know he is your ancient companion in arms, and it would ill become me to teach the noble Earl of Oxford what the laws of chivalry require. For your lordship's safety, every honest man in the army will give willing security. It is for that I care least, said Oxford indifferently, and if indeed my presence can be of service to the Duke, if I could believe that he desired it. He does, he does, my lord, said the faithful soldier with tears in his eyes. We heard him name your name, as if the words escaped him in a painful dream. I will go to him. Such being the case, said Oxford, I will go instantly. Where did he propose to establish his headquarters? He had fixed nothing for himself on that or other matters, but Montsour Des Contes named La Rivière near Solens in Upper Burgundy as the place of his retreat. Thither, then, will we, my son, with all haste of preparation. Thou, Colvin, hast better remain here and see some holy man to be a soil-seed. For thy hasty speech on the battlefield of Marat, there was a fence in it without doubt, but it will be ill-atoned for by quitting a generous master when he hath most need of your good service, and it is but an act of cowardice to retreat into the cloister till we have no longer active duties to perform in this world. It is true, said Colvin, that should I leave the duke now, perhaps not a man would stay behind that could stell a cannon properly. The sight of your lordship cannot but operate favorably on my noble master since it has waked the old soldier in myself. If your lordship can delay your journey till tomorrow, I will have my spiritual affairs settled and my bodily health sufficiently restored to be your guide to La Rivière, and for the cloister I will think of it when I have regained the good name which I have lost at Merton, but I will have masses said and these write powerful for the souls of my poor canineers. The proposal of Colvin was adopted, and Oxford, with his son attended by Tybalt, spent the day in preparation, accepting the time necessary to take formal leave of King Rene, who seemed to part with them with regret. In company with the ordnance officer of the discomfited duke, they traversed those parts of Provence, Duffine, and Franc Comte, which lie between aches, and the place to which the duke of Burgundy had retreated, but the distance and inconvenience of so long a route consumed more than a fortnight on the road, and the month of July 1476 was commenced when the travellers arrived in Upper Burgundy, and at the castle of La Rivière, about twenty miles to the south of the town of Solence. The castle, which was but of small size, was surrounded by very many tents, which were pitched in a crowded, disordered, and unsoldier-like manner, very unlike the discipline usually observed in the camp of Charles the Bold, that the duke was present there, however, was attested by his broad banner, which, rich with all its quarterings, streamed from the battlements of the castle. The guard turned out to receive the strangers, but in a manner so disorderly that the earl looked to Colvin for explanation. The master of the ordnance shrugged up his shoulders and was silent. Colvin, having sent in notice of his arrival and that of the English earl, Missour de Conte caused them presently to be admitted and expressed much joy at their arrival. A few of us, he said, true servants of the duke are holding council here, at which your assistance, my noble Lord of Oxford, will be of the utmost importance. Missour's de Lacroix, de Creon, Rubenpre, and others, nobles of Burgundy, are now assembled to superintend the defense of the country at this exigence. They all expressed delight to see the earl of Oxford and had only abstained from thrusting their attentions on him. The last time he was in the duke's camp, as they understood it was his wish to observe incognito. His grace, said de Creon, has asked after you twice and on both times by your assumed name of Philipson. I wonder not at that, my Lord of Creon replied the English nobleman. The origin of the name took its rise in former days when I was here during my first exile. It was then said that we poor Lancastrian nobles must assume other names than our own. And the good duke Philip said, as I was brother-in-arms to his son Charles, I must be called after himself by the name of Philipson. In memory of the good sovereign, I took that name when the day of need actually arrived, and I see that the duke thinks of our early intimacy by his distinguishing me so. How fair is his grace? The Burgundians looked at each other, and there was a pause. Even like a man stunned, brave Oxford, at length, de Conte replied, Sior de Argentin, you can best inform the noble earl of the condition of our sovereign. He is like a man distracted, said the future historian of that busy period. After the battle of Granson, he was never to my thinking of the same sound judgment as before, but then he was capricious, unreasonable, peremptory, and inconsistent, and resented every council that was offered as if it had been meant in insult, was jealous of the least trespass in point of ceremonial as if his subjects were holding him in contempt. Now there is a total change as if this second blow had stunned him and suppressed the violent passions which the first called into action. He is silent as a Carthusian, solitary as a hermit, expresses interest in nothing, least of all in the guidance of his army. He was, you know, anxious about his dress so much so that there was some affectation even in the rudenesses which he practiced in that matter, but woes me, you will see a change now. He will not suffer his hair or nails to be trimmed or arranged. He is totally heedless of respect or disrespect towards him, takes little or no nourishment, uses strong winds which however do not seem to affect his understanding. He will hear nothing of war or state affairs as little of hunting or of sport. Suppose an anchorite brought from a cell to govern a kingdom, you see in him, except in point of devotion, a picture of the fiery active Charles of Burgundy. You speak of a mind deeply wounded, Sior de Argentin replied the Englishman, think you it fit. I should present myself before the Duke. I will inquire, said Conte, and leaving the apartment returned presently and made a sign to the Earl to follow him. In a cabinet or closet, the unfortunate Charles reclined in a large armchair his legs carelessly stretched on a footstool, but so changed that the Earl of Oxford could have believed what he saw to be the ghost of the once fiery Duke, indeed the shaggy length of hair which streaming from his head mingled with his beard, the hollowness of the caverns at the bottom of which rolled his wild eyes. The falling in of the breast and the advance of the shoulders gave the ghastly appearance of one who has suffered the final agony which takes from mortality the signs of life and energy. His very costume, a cloak flung loosely over him, increased his resemblance to a shrouded phantom. De Conte named the Earl of Oxford, but the Duke gazed on him with a lusterless eye and gave him no answer. Speak to him brave Oxford, said the Burgundian in a whisper, he is even worse than usual, but perhaps he may know your voice. Never when the Duke of Burgundy was in the most palmy state of his fortunes did the noble Englishman Neil to kiss his hand with such sincere reverence. He respected in him not only the afflicted friend but the humbled sovereign upon whose tower of trust the lightning had so recently broken. It was probably the falling of a tear upon his hand which seemed to awake the Duke's attention, for he looked towards the Earl and said, Oxford, Philipson, my old, my only friend, hast thou found me out in this retreat of shame and misery? I am not your only friend, my lord, said Oxford. Heaven has given you many affectionate friends among your natural and loyal subjects, but though a stranger and saving the allegiance I owe to my lawful sovereign, I will yield to none of them in the respect and deference which I have paid to your grace in prosperity and now come to render to you in adversity. Adversity indeed, said the Duke, irremediable intolerable adversity. I was lately Charles of Burgundy called the bold, now I am twice beaten by a scum of German peasants, my standard taken, my men at arms put to flight, my camp twice plundered, and each time of value more than equal to the price of all Switzerland fairly lost, myself hunted like a catif goat or chamois, the utmost spite of hell could never accumulate more shame on the head of a sovereign. On the contrary, my lord, said Oxford, it is a trial of heaven which calls for patience and strength of mind. The bravest and best knight may lose the saddle. He is but a laggard who lies rolling on the sand of the lists after the accident has chanced. Ha, laggard, sayest thou, said the Duke, some part of his ancient spirit awakened by the broad taunt. Leave my presence, sir, and return to it no more till you are summoned thither, which I trust will be no later than your grace quits your dishabile and disposes yourself to see your vassals and friends with such ceremony as befits you and them, said the Earl, composedly.  If I be, my lord, I am taught my ill-breeding by circumstances. I can mourn over fallen dignity, but I cannot honour him who dishonours himself by bending, like a regardless boy, beneath the scourge of evil fortune. And who am I that you should term me such, said Charles, starting up in all his natural pride and ferocity? Or who are you but a miserable exile that you should break in upon my privacy with such disrespectful upbraiding? For me, replied Oxford, I am, as you say, an unrespected exile, nor am I ashamed of my condition since unshaken loyalty to my king and his successors has brought me to it.   It is well for thee I have no sword, or thou should never boast of thine insolence going unpunished. Conte, step forth like a good night, and confute that calumniator. Say, are not my soldiers arrayed, disciplined, and in order? My lord said Conte, trembling brave as he was in battle, at the frantic rage which Charles exhibited.  I see it, I see it, said the Duke, idle and evil counselors are ye all.  But my troops must fall into such scandalous disorder as exposes me to the scorn and reproach of each beggarly foreigner. My lord, replied Conte, more firmly, we have done what we could, but your grace has accustomed your mercenary generals and leaders of free companies to take their orders only from your own mouth or hand. They clamor also for pay, and the treasurer refuses to issue it without your grace's order, as he alleges it might cost him his head, and they will not be guided and restrained either by us or those who compose your counsel. The Duke laughed sternly, but was evidently somewhat pleased with the reply. Ha, ha, he said, it is only burgundy who can ride his own wild horses and rule his own wild soldiery. Hark, they Conte, tomorrow I ride forth to review the troops, for what disorder has passed allowance shall be made, pay also shall be issued, but woe to those who shall have offended too deeply. Let my grooms of the chamber know to provide me with fitting dress and arms. I have got a lesson, glancing a dark look at Oxford, and I will not again be insulted without the means of wreaking my vengeance. Be gone, both of you, and Conte send the treasurer hither with his accounts, and woe to his soul if I find ought to complain of. Be gone, I say, and send him hither. They left the apartment with suitable obeisance as they retired. The Duke said abruptly, Lord of Oxford, a word with you. Where did you study medicine? In your own famed university, I suppose. Thy physic hath wrought a wonder. Yet, Dr. Philipson, it might have cost thee thy life. I have ever thought my life cheap, said Oxford, when the object was to help my friend. Thou art indeed a friend, said Charles, and a fearless one. But go, I have been sore troubled, and thou hast tasked my temper closely. Tomorrow we will speak further. Meantime, I forgive thee, and I honor thee. The Earl of Oxford retired to the council hall, where the Burgundian nobility, aware of what had passed, crowded around him with thanks, compliments, and congratulations. A general bustle now ensued. Orders were hurried off in every direction. Those officers who had duties to perform, which had been neglected, hastened to conceal or to atone for their negligence. There was a general tumult in the camp, but it was a tumult of joy. For soldiers are always most pleased when they are best in order for performing their military service. And license or inactivity, however acceptable at times, are not, when continued, so agreeable to their nature as strict discipline and a prospect of employment. The treasurer, who was luckily for him a man of sense and method, having been two hours in private with the Duke, returned with looks of wonder and professed that never, in Charles's most prosperous days, had he showed himself more acute in the department of finance, of which he had but that morning seemed totally incapable. And the merit was universally attributed to the visit of Lord Oxford, whose timely reprimand had, like the shot of a cannon, dispersing foul mists, awakened the Duke from his black and bilious melancholy. On the following day, Charles reviewed his troops with his usual attention, directed new lovies, made various dispositions of his forces, and corrected the faults of their discipline by severe orders, which were enforced by some deserved punishments of which the Italian mercenaries of Campo Basso had a large share, and rendered palatable by the payment of arrears, which was calculated to attach them to the standard under which they served. The Duke, also after consulting with his council, agreed to convote meetings of the states in his different territories, redress certain popular grievances, and grant some boons which he had hitherto denied, and thus began to open a new account of popularity with his subjects in place of that which his rashness had exhausted. End of Chapter 16 Chapter 17 of Anne of Geyerstein Volume 2 by Sir Walter Scott. This LibriVox recording is in the public domain, recording by Dion Giants, Salt Lake City, Utah. Here's a weapon now shall shake a conquering general in his tent, a monarch on his throne, or reach a prelate, however holy be his offices, even while he serves the altar, old play. From this time all was activity in the Duke of Burgundy's court and army. Money was collected, soldiers were levied, and certain news of the Confederate's motions only were wanting to bring on the campaign. But although Charles was, to all outward appearance, as active as ever, yet those who were more immediately about his person were of the opinion that he did not display the soundness of mind or the energy of judgment which had been admired in him before these calamities, he was still liable to fits of moody melancholy, similar to those which descended upon soul, and was vehemently furious when aroused out of them. Indeed the Earl of Oxford himself seemed to have lost the power which he had exercised over him at first. Nay, though in general Charles was both grateful and affectionate towards him, he evidently felt humbled by the recollection of his having witnessed his impotent and disastrous condition, and was so much afraid of Lord Oxford being supposed to lead his councils that he often repelled his advice merely as it seemed to show his own independence of mind. In these froward humours the Duke was much encouraged by Campo Basso, that wily traitor now saw his master's affairs tottering to their fall, and he resolved to lend his lover to the work, so as to entitle him to a share of the spoil. He regarded Oxford as one of the most able friends and counsellors who adhered to the Duke. He thought he saw in his looks that he fathomed his own treacherous purpose, and therefore he hated and feared him, besides in order perhaps to colour over, even to his own eyes, the abominable perfidy he meditated, he affected to be exceedingly enraged against the Duke for the late punishment of marauders belonging to his Italian bands. He believed that chastisement to have been inflicted by the advice of Oxford, and he suspected that the measure was pressed with the hope of discovering that the Italians had not pillaged for their own emolument only, but for that of their commander. Believing that Oxford was thus hostile to him, Campo Basso would have speedily found means to take him out of his path, had not the Earl himself found it prudent to observe some precautions, and the lords of Flanders and Burgundy, who loved him for the very reasons for which the Italian abhorred him, watched over his safety with a vigilance of which he himself was ignorant, but which certainly was the means of preserving his life. It was not to be supposed that Ferrand of Lorraine should have left his victory so long unimproved, but the Swiss Confederates, who were the strength of his forces, insisted that the first operations should take place in Savoy and the Pays-de-Vaud, where the Burgundians had many garrisons, which though they received no relief, yet were not easily or speedily reduced. Besides the Swissers being, like most of the national soldiers of the time, a kind of militia, most of them returned home to get in their harvest and to deposit their spoil in safety. Ferrand, therefore, though bent on pursuing his success with all the ardour of youthful chivalry, was prevented from making any movement in advance until the month of December 1476. In the meantime, the Duke of Burgundy's forces to be least burdensome to the country were cantant in distant places of his dominions, where every exertion was made to perfect the discipline of the new levies. The Duke, if left to himself, would have precipitated the struggle by again assembling his forces and pushing forward into the Helvetian territories. But though he inwardly foamed at the recollection of Granson and Merton, the memory of these disasters was too recent to permit such a plan of the campaign. Meantime, weeks glided past, and the month of December was far advanced when, one morning, as the Duke was sitting in council, Campo Basso suddenly entered with a degree of extravagant rapture in his countenance, singularly different from the cold, regulated and subtle smile which was usually his utmost advance towards laughter. Gwantes, he said, Gwantes, for luck's sake, if it please your grace, and what of good fortune comes nigh us, said the Duke, me thought she had forgot the way to our gates. She has returned to them, please your Highness, with her cornucopia full of choicest gifts ready to pour her fruit, her flowers, her treasures, on the head of the sovereign of Europe most worthy to receive them. The meaning of all this, said Duke Charles, riddles are for children, the hair-brained young madman Ferrand, who calls himself of Lorraine, has broken down from the mountains at the head of a desultory army of scapegraces like himself, and what think you, ha, ha, ha, they are overrunning Lorraine, and have taken Nancy, ha, ha, ha. By my good faith, sir Count, said Conte, astonished at the gay humor with which the Italian treated a matter so serious, I have seldom heard a fool laugh more gaily at a more scurvy jest than you, a wise man, laugh at the loss of the principal town of the province we are fighting for. I laugh, said Campo Basso, among the spears, as my warhorse does, ha, ha, among the trumpets. I laugh also over the destruction of the enemy, and the dividing of the spoil, as eagles scream their joy over the division of their prey. I laugh. You laugh, said the lord of Conte, waxing impatient, when you have all the mirth to yourself, as you laughed after our losses at Grenson and Merton. Peace, sir, said the duke, the count of Campo Basso has viewed the case as I do, this young knight-errant ventures from the protection of his mountains, and heaven deal with me as I keep my oath, when I swear that the next fair field on which we meet shall see one of us dead. It is now the last week of the old year, and before twelfth day we will see whether he or I shall find the bean in the cake. To arms, my lords, let our camp instantly break up, and our troops move forward towards Lorraine. Send off the Italian and Albanian-like cavalry and the Stradiots to scour the country in the van. Oxford, thou wilt bear arms in this journey, wilt thou not? Surely, said the Earl, I am eating your highness's bread, and, when enemies invade, it stands with my honour to fight for your grace, as if I was your born subject. With your grace's permission I will dispatch a pursuant who shall carry letters to my late kind host, the landman of Unterwalden, acquainting him with my purpose. The duke, having given a ready assent, the pursuant was dismissed accordingly, and returned in a few hours so near had the armies approached to each other. He bore a letter from the landman in a tone of courtesy and even kindness, regretting that any cause should have occurred for bearing arms against his late guest, for whom he expressed high personal regard. The same pursuant also brought greetings from the family of the beatermans to their friend Arthur, and a separate letter addressed to the same person of which the contents ran thus. Rudolph Donnerhugel is desirous to give the young merchant Arthur Philipson the opportunity of finishing the bargain which remained unsettled between them in the castle court of Geierstein. He is the more desirous of this, as he is aware that the said Arthur has done him wrong in seducing the affections of a certain maiden of rank, to whom he, Philipson, is not and cannot be anything beyond an ordinary acquaintance. Rudolph Donnerhugel will send Arthur Philipson word when a fair and equal meeting can take place on neutral ground. In the meantime he will be as often as possible in the first rank of the skirmishers. Young Arthur's heart leapt high as he read the defiance, the peaked tone of which showed the state of the writer's feelings, and argued sufficiently Rudolph's disappointment on the subject of Geierstein and his suspicion that she had bestowed her affections on the youthful stranger. Arthur found means of dispatching a reply to the challenge of the Swiss assuring him of the pleasure with which he would attend his commands either in front of the line or elsewhere as Rudolph might desire. Meantime the armies were closely approaching to each other and the light troops sometimes met. The Stradiots from the Venetian territory, a sort of cavalry resembling that of the Turks, performed much of that service on the part of the Burgundian army, for which indeed if their fidelity could have been relied on, they were admirably well qualified. The Earl of Oxford observed that these men, who were under the command of Campobasso, always brought in intelligence that the enemy were in indifferent order and in full retreat. Besides, information was communicated through their means that sundry individuals against whom the Duke of Burgundy entertained peculiar personal dislike and whom he specially desired to get into his hands had taken refuge in Nancy. This greatly increased the Duke's ardor for retaking that place, which became perfectly ungovernable when he learned that Ferrand and his Swiss allies had drawn off to a neighboring position called St. Nicholas on the news of his arrival. The greater part of the Burgundian counselors together with the Earl of Oxford protested against his besieging a place of some strength, while an active enemy lay in the neighborhood to relieve it. They remonstrated on the smallness of his army, on the severity of the weather, on the difficulty of obtaining provisions, and exhorted the Duke that having made such a movement as had forced the enemy to retreat, he ought to suspend decisive operations till spring. Charles at first tried to dispute and repel these arguments, but when his counselors reminded him that he was placing himself and his army in the same situation as at Granson and Merton, he became furious at the recollection, foamed at the mouth, and only answered by oaths and implications that he would be master of Nancy before twelfth day. Accordingly, the army of Burgundy sat down before Nancy in a strong position protected by the hollow of a water-course and covered with thirty pieces of cannon which Colvin had under his charge. Having indulged his obstinate temper in thus arranging the campaign, the Duke seemed to give a little more heed to the advice of his counselors touching the safety of his person, and permitted the Earl of Oxford with his son and two or three officers of his household, men of approved trust, to sleep within his pavilion, in addition to the usual guard. It wanted three days of Christmas when the Duke sat down before Nancy, and on that very evening a tumult happened which seemed to justify the alarm for his personal safety. It was midnight, and all in the Ducal pavilion were at rest, when a cry of treason arose. The Earl of Oxford, drawing his sword and snatching up a light, which burned beside him, rushed into the Duke's apartment, and found him standing on the floor totally undressed, but with his sword in his hand, and striking around him so furiously that the Earl himself had difficulty in avoiding his blows. The rest of his officers rushed in, their weapons drawn, and their cloaks wrapped around their left arms. When the Duke was somewhat composed, and found himself surrounded by his friends, he informed them, with rage and agitation, that the officers of the secret tribunal had, in spite of the vigilant precautions taken, found means to gain entrance into his chamber, and charged him under the highest penalty to appear before the Holy Vam upon Christmas night. The bystanders heard this story with astonishment, and some of them were uncertain whether they ought to consider it as a reality or a dream of the Duke's irritable fancy. But the citation was found on the Duke's toilet, written, as was the form, upon parchment, signeted with three crosses, and stuck to the table with a knife. A slip of wood had been also cut from the table. Oxford read the summons with attention. It named, as usual, a place where the Duke was sighted to come unarmed and unattended, and from which it was said he would be guided to the seat of judgment. Charles, after looking at the scroll for some time, gave vent to his thoughts. I know from what quiver this arrow comes, he said, it is shot by that degenerate noble, apostate priest, and accomplice of sorcerers, Albert of Geyerstein. We have heard that he is among the motley group of murderers and outlaws, whom the old fiddler of Provence's grandson has raked together. But by St. George of Burgundy, neither Monk's cowl, soldier's cask, nor conjurer's cap, shall save him, after such an insult as this. I will degrade him from knighthood, hang him from the highest steeple in Nancy, and his daughter shall choose between the meanest herd-boy in my army, and the convent of Phil's repentes. Whatever are your purposes, my lord, said Conte, it were surely best be silent, when, from this late apparition, we may conjecture that more than we want of may be within hearing. The duke seemed struck with this hint, and was silent, or at least only muttered oaths and threats, betwixt his teeth, while the strictest search was made for the intruder on his repose, but it was in vain. Charles continued his researches, incensed at a flight of audacity higher than ever had been ventured upon by these secret societies, who whatever might be the dread inspired by them had not as yet attempted to cope with sovereigns. A trusty party of Burgundians were sent on Christmas night to watch the spot, a meeting of four crossroads named in the summons, and make prisoners of any whom they could lay hands upon, but no suspicious persons appeared at or near the place. The duke, not the less, continued to impute the affront he had received to Albert of Geierstein. There was a price set upon his head, and Campo Basso, always willing to please his master's mood, undertook that some of his Italians, sufficiently experienced in such feats, should bring the obnoxious baron before him alive or dead. Colvin, Conte, and others laughed in secret at the Italians' promises. Subtle as he is, said Colvin, he will lure the wild vulture from the heavens before he gets Albert of Geierstein into his power. Arthur, to whom the words of the duke had given subject for no small anxiety on account of Anne of Geierstein, and of her father, for her sake, breathed more lightly on hearing his menaces held so cheaply. It was the second day after this alarm that Oxford felt a desire to reconnoiter the camp of Ferrand of Lorraine having some doubts whether the strength and position of it were accurately reported. He obtained the duke's consent for this purpose, who at the same time made him and his son a present of two noble steeds of great power and speed which he himself highly valued. So soon as the duke's pleasure was communicated to the Italian Count, he expressed the utmost joy that he was to have the assistance of Oxford's age and experience upon an exploratory party and selected a chosen band of Anne Hundred Stradiots whom he said he had sent sometimes to skirmish up to the very beards of the Switzers. The Earl showed himself much satisfied with the active and intelligent manner in which these men performed their duty and drove before them and dispersed some parties of Ferrand's cavalry. At the entrance of a little ascending valley, Campo Basso communicated to the English noblemen that if they could advance to the farther extremity they would have a full view of the enemy's position. Two or three Stradiots then spurred on to examine this defile and returning back communicated with their leader in their own language who, pronouncing the passage safe, invited the Earl of Oxford to accompany him. They proceeded through the valley without seeing an enemy, but on issuing upon a plane at the point intimated by Campo Basso, Arthur, who was in the van of the Stradiots and separated from his father, did indeed see the camp of Duke Ferrand within half a mile's distance, but a body of cavalry had that instant issued from it and were riding hastily towards the gorge of the valley from which he had just emerged. He was about to wheel his horse and ride off, but conscious of the great speed of the animal he thought he might venture to stay for a moment's more accurate survey of the camp. The Stradiots who attended him did not wait his orders to retire, but went off, as was indeed their duty, when attacked by a superior force. Meantime Arthur observed that the knight who seemed leader of the advancing squadron mounted on a powerful horse that shook the earth beneath him, bore on his shield the bear of burn, and had otherwise the appearance of the massive frame of Rudolph Donerhugel. He was satisfied of this when he beheld the Cavalier halt his party and advance towards him alone, putting his lance in rest and moving slowly, as if to give him time for preparation. To accept such a challenge in such a moment was dangerous, but to refuse it was disgraceful, and while Arthur's blood boiled at the idea of chastising an insolent rival, he was not a little pleased at heart that their meeting on horseback gave him an advantage over the Swiss through his perfect acquaintance with the practice of the tourney in which Rudolph might be supposed more ignorant. They met, as was the phrase of the time, manful under shield. The lance of the Swiss glanced from the helmet of the Englishman, against which it was addressed, while the spear of Arthur directed right against the center of his adversary's body was so justly aimed, and so truly seconded by the full fury of the career as to pierce not only the shield which hung round the ill-fated warrior's neck, but a breastplate and a shirt of mail which he wore beneath it. Passing clear through the body, the steel point of the weapon was only stopped by the back piece of the unfortunate Cavalier, who fell headlong from his horse as if struck by lightning, rolled twice or thrice over on the ground, tore the earth with his hands, and then lay prostrate a dead corpse. There was a cry of rage and grief among those men at arms whose ranks Rudolph had that instant left, and many couched their lances to avenge him. But Ferrand of Lorraine, who was present in person, ordered them to make prisoner, but not to harm, the successful champion. This was accomplished, for Arthur had not time to turn his bridle for flight, and resistance would have been madness. When brought before Ferrand, he raised his visor and said, Is it well, my lord, to make captive an adventurous knight for doing his devour against a personal challenger? Do not complain, Sir Arthur of Oxford, said Ferrand, before you experience injury, you are free, Sir Knight, your father and you were faithful to my royal aunt Margaret, and although she was my enemy, I do justice to your fidelity in her behalf, and from respect to her memory, disinherited, as she was, like myself, and to please my grandfather, who I think had some regard for you, I give you your freedom. But I must also care for your safety during your return to the camp of Burgundy. On this side of the hill, we are loyal and true-hearted men. On the other, they are traitors and murderers. You, Sir Count, will, I think, gladly see our captive placed in safety. The knight to whom Ferrand addressed himself, a tall, stately man, put himself in motion to attend on Arthur, while the former was expressing to the young Duke of Lorraine the sense he entertained of his chivalrous conduct, Farewell, Sir Arthur Devere, said Ferrand, you have slain a noble champion, and to me a most useful and faithful friend. But it was done nobly and openly, with equal arms, and in the front of the line, and evil befall him, who entertains, feud first. Arthur bowed to his saddle-bow. Ferrand returned the salutation, and they parted. Arthur and his new companion had ridden but a little way up the ascent when the stranger spoke thus. We have been fellow travellers before, young man, yet you remember me not. Arthur turned his eyes on the cavalier, and observing that the crest which adorned his helmet was fashioned like a vulture, strange suspicions began to cross his mind, which were confirmed when the knight opening his helmet showed him the dark and severe features of the priest of St. Paul's. Count Albert of Geyerstein, said Arthur, the same replied the count, though thou hast seen him in other garb and headgear. But tyranny drives all men to arms, and I have resumed, by the license and command of my superiors, those which I had laid aside, a war against cruelty and oppression is holy as that waged in Palestine, in which priests bear armor. My Lord Count, said Arthur eagerly, I cannot too soon entreat you to withdraw to serve Ferrand of Lorraine's squadron. Here you are in peril, where no strength or courage can avail you. The duke has placed a price on your head, and the country betwixt this and Nancy swarms with Stradiots and Italian light horsemen. I laugh at them, answered the Count, I have not lived so long in a stormy world amid intrigues of war and policy to fall by the mean hand of such as they. Besides, thou art with me, and I have seen but now that thou canst bear thee nobly. In your defense, my Lord, said Arthur, who thought of his companion as the father of Anne of Geyerstein, I should try to do my best. What youth, replied Count Albert with a stern sneer that was peculiar to his countenance, what's thou aid the enemy of the Lord, under whose banner thou serviced against his waged soldiers? Arthur was somewhat abashed at the turn given to his ready offer of assistance, for which he had expected at least thanks, but he instantly collected himself and replied, My Lord Count Albert, you have been pleased to put yourself in peril to protect me from partisans of your party. I am equally bound to defend you from those of our side. It is happily answered, said the Count, yet I think there is a little blind partisan of whom troubadours and minstrels talk, to whose instigation I might, in case of need, owe the great zeal of my protector. He did not allow Arthur, who was a good deal embarrassed, time to reply, but proceeded, Hear me, young man, thy lance has this day done an evil deed, to Switzerland, to Bern, and Duke Ferrand, in slaying their bravest champion. But to me the death of Rudolf Donnerhugel is a welcome event. Know that he was, as his services grew more indispensable, become importunate in requiring Duke Ferrand's interest with me for my daughter's hand, and the Duke himself, the son of a princess, blushed not to ask me to bestow the last of my house, for my brother's family are degenerate mongrels upon a presumptuous young man, whose uncle was a domestic in the house of my wife's father, though they boasted some relationship, I believe, through an illegitimate channel, which Yonder Rudolf was want to make the most of, as it favoured his suit. Surely, said Arthur, a match with one so unequal in birth, and far more in every other respect, was too monstrous to be mentioned. While I lived, replied Count Albert, never should such union have been formed, if the death both of Bride and Bridegroom, by my dagger, could have saved the honour of my house from violation. But when I, I, whose days, whose very hours are numbered, shall be no more, what could prevent an undaunted suitor fortified by Duke Ferrand's favour, by the general applause of his country, and perhaps by the unfortunate prepossession of my brother Arnold, from carrying his point against the resistance and scruples of a solitary maiden. Rudolf is dead, replied Arthur, and may heaven assoils I him from guilt. But were he alive, and urging his suit on Anne of Geyerstein, he would find there was a combat to be fought. Which has been already decided, answered Count Albert. Now mark me, Arthur Devere, my daughter has told me of the passages betwixt you and her. Your sentiments and conduct are worthy of the noble house you descend from, which I well know ranks with the most illustrious in Europe. You are indeed disinherited. But so is Anne of Geyerstein, save such pittance as her uncle may impart to her of her paternal inheritance. If you share it together till better days, always supposing your noble father gives his consent, for my child shall enter no house against the will of its head. My daughter knows that she has my willing consent and my blessing. My brother shall also know my pleasure. He will approve my purpose, for though dead to thoughts of honour and chivalry, he is alive to social feelings, loves his niece, and has friendship for thee and for thy father. What sayeth thou, young man, to take a beggarly countess to aid thee in the journey of life? I believe, nay, I prophecy, for I stand so much on the edge of the grave, that me thinks I command a view beyond it, that a luster will one day, after I have long ended my doubtful and stormy life, beam on the cornets of Devere and Geyerstein. Devere threw himself from his horse, clasped the hand of Count Albert, and was about to exhaust himself in thanks. But the Count insisted on his silence. We are about to part, he said, the time is short, the place is dangerous. You are, to me, personally speaking, less than nothing. Had any one of the many schemes of ambition which I have pursued led me to success, the son of a banished earl had not been the son in law I had chosen. Rise and remount your horse, thanks are unpleasing when they are not merited. Arthur arose and mounting his horse through his raptures into a more acceptable form, endeavouring to describe how his love for Anne and efforts for her happiness should express his gratitude to her father, and observing that the Count listened with some pleasure to the picture he drew of their future life, he could not help exclaiming, and you, my lord, you who have been the author of all this happiness, will you not be the witness and partaker of it? Believe me, we will strive to soften the effect of the hard blows which fortune has dealt to you, and should a ray of better luck shine upon us, it will be the more welcome that you can share it. For bear such folly, said the Count Albert of Geierstein, I know my last scene is approaching, hear and tremble, the Duke of Burgundy is sentenced to die, and the secret and invisible judges who doom in secret and avenge in secret, like the deity, have given the cord and the dagger to my hand. Oh, cast from you these vile symbols, exclaimed Arthur, with enthusiasm, let them find butchers and common stabbers to do such an office, and not dishonor the noble Lord of Geierstein. Peace, foolish boy, answered the Count, the oath by which I am sworn is higher than that clouded sky, more deeply fixed than those distant mountains. Nor think my act is that of an assassin, though for such I might plead the Duke's own example. I send not hirelings like these base stradiots to hunt his life without imperiling mine own. I give not his daughter, innocent of his offenses, the choice betwixt a disgraceful marriage, and a discreditable retreat from the world. No, Arthur Devere, I seek Charles with the resolved mind of one who, to take the life of an adversary, exposes himself to certain death. I pray you speak no further of it, said Arthur, very anxiously. Consider I serve for the present, the prince whom you threaten, and art bound, interrupted the Count, to unfold to him what I tell you. I desire you should do so, and though he hath already neglected a summons of the tribunal, I am glad to have this opportunity of sending him personal defiance. Say to Charles of Burgundy that he has wronged Albert of Geyerstein. He who is injured in his honor loses all value for his life, and whoever does so has full command over that of another man. Bid him keep himself well from me, since, if he see a second son of the approaching year rise over the distant Alps, Albert of Geyerstein is foresworn. And now be gone, for I see a party approach under a Burgundian banner. They will ensure your safety, but should I remain longer would endanger mine. So saying the Count of Geyerstein turned his horse and rode off. End of Chapter 17.


back to another video. So this video is probably going to be shorter than normal as the actual topic we're going to be covering doesn't take that long. But I just wanted to give it its own dedicated video just to step through and explain the why's and the what's as we're going to use this particular format in videos going forwards. So what we'll do is actually if I add some code in here it'll help to first explain. As always I'll put this into a module and we're going to just do create a subroutine. So recall this sheet underscore ref. So in previous videos when we've been trying to refer to a particular range, and for me I'm going to do cell a one of sheet one. We've had to do something like this. So we had to go define first what the sheet is so going sheets, it's going to be sheet one.  So this simple piece of code is going to just populate the value hello in cell a one here for us. I mean just hit f five to run that and make sure it is indeed correctly working. So we could continue to just populate all of our or define all of our ranges as we've done here. And let's say we then had something else to do here as well. We could then also put sheets sheet one dot cells. And this time let's do it in the next one. Let's go there dot value equals goodbye lack of lack of creativity or what to put in there and we run this and we can now see that next row has got the word goodbye in it. We can tidy our code up ever so slightly by actually storing this reference of sheet number one as a variable as we have done previously in other videos where we're just been storing things like numbers and text. In order to do so we start off very much the same as all the others where we have to find what the variable type is. So for this it's going to be dim and we're going to call this one and you can be again more creative with your name and conventions SHT one as a work sheet. And then the next part again is very similar to what we've done with the numbers and stream at this time we have to actually use the word set so we're actually setting what that variable or the value is or the reference should I even say in this example. So we're going to put set and we're going to put SHT one equals and it's going to be sheets sheet one. So one way to look at this is we're literally just saying we're going to store this first part as this value here and then yeah the rest of this can then continue as it is in this example we're going over anyway. So we've got our variable defined so all we now need to do is simply remove this whole first section here and actually rather than do that I'm going to just get rid of this whole code here and enter it again. So rather than this time typing in sheet sheet one when we're referring to this row two value of goodbye all I need to do now is type in our variable so SHT one and we're going to put oh no we're out of space so SHT one dot cells so you can see it's already understood that our shorthand here or our variable has been defined as a worksheet so it's given us all the drop-down options available to us had we coded in this above example. So cells and we're going to do two one close brackets dot value equals goodbye like so so we can see that it's already a lot short again by all of these characters we have here if we now run this again if we clear the values that might help so you can actually see it's doing something here five you can see the values are now populated in there for us so again another tidy way of doing our code rather than having to type out this every time and as you can appreciate it's a lot easier quicker more efficient to type out four characters than it is to repetitively keep typing this every time and just update this review SHT one and that has automatically been stored for us as well so we clear that hit F5 over here again and you can see it's working for us as designed if we add another sheet and we haven't actually touched on this in other videos so at the moment you can see I've just got sheet one there and then this workbook if I'm to add another sheet you can see how that sheet is automatically added in here so we have it available to us in our sort of navigation pane over the side but we don't need to worry about that we're going to stay obviously module one but if this time and just to mention obviously this tab here says sheet number five as you see on the side here this is only because I have been playing around with this workbook prior to actually recording this video if you're in a new fresh workbook then obviously it would then tell you sheet number two and every sheet you added would incrementally go up by one so if I added another one now you'd see that it goes up to number six just to touch on that if you're confused why it suddenly said sheet number five there so we've now got another sheet we need to reduce six I don't need that so we now got this new sheet number five so we now want to start populating something in there as well if we wanted to find that again same with what other variables we looked at we can just utilize this first then we've got the top here add a comma so we'll call this sht five as a worksheet oh if I go well worksheets yep we need to come down here and we can now go set sht five equals sheets and we'll go into sheet five close brackets like so and then this time we can do something different we'll go sht five dot cells put in the first one dot value equals hello number five or hello sheet hello sheet okay so now when we run this as you probably assume yeah it's going to obviously update for us as required so the purpose of today's video really was to go over that I might have dragged it out longer than it needed to be but the intention was for this video to be shorter than normal I just wanted to do a dedicated video on this topic as we're going to be using this these references going forward rather than typing out each time the actual sheet reference so I hope you found that video useful if you did please do give this video a like as it would be greatly appreciated by me and it also does help that youtube algorithm and lastly if it's the first time watching any of our videos or you have watched previous ones and you've not yet subscribed please do subscribe to the channel and also make sure you hit that bell notification button as they will obviously notify you of all of our future videos as they come out and again it'll be highly appreciated and beneficial to the channel as well so thank you very much for watching and we'll see you in the next video


Motor adaptation is a process by which the brain adjusts to changes in the environment, such as when wearing prism glasses. This process is thought to be primarily unconscious, but can also involve conscious strategies. Research has suggested that the cerebellum plays a role in the unconscious aspects of motor adaptation. To test this hypothesis, researchers used non-invasive brain stimulation to inhibit the cerebellum in healthy participants. The participants then performed a visual motor rotation task with an explicit strategy. The results showed no differences between the experimental group and a control group, suggesting that the cerebellum does not play a significant role in implicit motor adaptation. However, the behavioral findings were consistent with previous studies on the topic. This article was authored by Sarah H. E. M. Woetz, Muriel T. N. Paniers, Ned Jenkinson, and others.


So the reaction rate k was equal to k0 multiplied by e raised to, I'm going to say delta f divided by rt, to save some writing. With the exponent here and 1 over t up in the exponent, it's going to be quite useful to start, try to plot the logarithm of k versus 1 over t. And that might go from say 1 over 350 kelvin to 1 over 300 kelvin. So this is called, that is 1. If I now do that for folding and unfolding, I'm going to get two curves. Do you see that they're going to be quite beautiful and fall almost exactly on straight lines? So first I have one curve process that goes faster. This is going to be folding. Folding will go faster when the temperature is lower, which is a bit strange. Most processes will do the opposite. While unfolding, that will go faster when the temperature is higher, as you normally expect from a chemical process. But given how beautiful and near these are, we would like to know what the derivative here is. Well, we can calculate that. It's not that hard. So let's see what we can do. We have l and k versus 1 over t. So I'm going to start down here in time. I need a bit of space. So I want to calculate the derivative of l and k with respect to 1 over t. That will lead to two parts. Leave some room in the nominator first. The derivative of 1 over t, that's minus 1 over t squared. So I'm going to get minus 1 over t squared falling out and then dt. The derivative of l and k, that's going to be ln derivative of l and k0 plus ln and exponent cancel. And then it's going to be a minus sign. So it's going to be minus delta f divided by rt. But here's the beautiful part. k0 is a constant that describes the fundamental process. So that is roughly going to be 0, the derivative of it, that is. And minus 1 over t2.  So here I get t2 multiplied by the derivative of delta f divided by rt with respect to t. This is still a non-trivial expression but it's not that bad anymore. That's the derivative of a quotient. We have delta f and then divided by rt. But to make that slightly easier we can think of that as delta f multiplied by 1 over rt. So that is going to be t2 multiplied by first the derivative of delta f with respect to t. Multiplied by 1 over rt plus, that is going to be minus sign in a second. So don't write out the sign yet. Delta f multiplied by the derivative of 1 over rt. That's going to be minus 1 over rt squared, right? Minus 1 over rt squared. I could have put the r in front of everything. And now things are actually starting to look pretty nice. I know that you might not think that yet. It says a t2 there in front. I will multiply both these terms by t. And then I can cancel that t2 against both those t2s, right? And then I'll move the 1 over r in front of everything. So we have 1 over r multiplied by... What is the derivative of delta f with respect to t? Well, you know that. We went through that a couple of lectures ago. That's minus s. If you don't remember, we watched an old lecture on what we derived it. So here it says minus s multiplied by t. I'm going to say minus ts. Minus, what was delta f? Well, sorry, not just delta s, f, delta s. Because this is delta f there, right? Well, delta f was delta e minus t delta s. Minus minus is plus, so it's t delta s. Do you see how those two terms cancel? So this is going to be minus delta e divided by r. With delta e, now if I'm looking at folding, this delta e is when I go from the unfolded state up to the transition barrier. This is... I bet you don't see how beautiful this is. The derivative here is positive when I'm folding, and this was unfolded. So when I'm folding, if the derivative is positive, that means that the energy difference is negative. So what I have just shown, that the energy of the unfolded state, based on the experiment, is larger than the energy of the transition state. Cool, right? We can't determine the structure of it, but I can say something about what the energy of it must be based on this curve. If I go in the other direction, the derivative has the other sign. So that means that the energy of the folded state must be lower than the transition state. So I will just continue. So that the energy of the native state must be lower than the energy of the transition state. So as I'm folding, this was what I hand-waved about before, and I'm proving it based on experiments. The energy of the unfolded state is highest, then we drop a bit to the transition state, and then we drop even more to the native state. But it's not that the transition state is going up in energy. If only I had a way to do this for entropy, too. It turns out we do. The book does not go through that, so normally I would just write this down, but since the book does not go through it, I figured I should show you.


Hello and welcome to the session on one bit sliding window protocol. At the end of the session, student will be able to describe working of a one bit sliding window protocol. The bidirectional protocols that belong to a class called sliding window protocols are one bit sliding window protocol, go back and sliding window protocol, selective repeat sliding window protocol. Three bidirectional sliding window protocols with maximum sending window size and receiving window size are one bit sliding window protocol has sending window size of one and receiving window size is also one, go back and protocol has sending window size greater than one and receiving window size is one. Selective repeat protocol has sending window size greater than one and receiving window size is also greater than one. These protocols differ among themselves in terms of efficiency, complexity and buffer requirements. Before going further pause the video for some time and find the answer. Once you have done this, you may resume the video. What is the maximum sending window size and receiving window size of a one bit sliding window protocol? Option A. Sending window size greater than one. Receiving window size is equal to one. Option B. Sending window size greater than one. Receiving window size greater than one. Option C. Sending window size is equal to one. Receiving window size is equal to one. Option D. None of these. The answer is sending window size is equal to one and receiving window size is equal to one. Let us see a sliding window protocol with a window size of one. That is one bit sliding window protocol. It is also called as stop and wait protocol since the sender transmits a frame and waits for its acknowledgement before sending the next one. With this protocol the communication is full-duplex that is both machines can send and receive. Problem with stop and wait protocol is that at any moment only one frame is in transition. The sender will have to wait at least one round trip time before sending the next frame. The waiting can be long for a slow network such as satellite link. The last frame to send and frame expected can be either 0 or 1. The acknowledgement field contains the number of the last frame received without error. The protocol uses independent acknowledgement for each frame received. The protocol discards out-of-order frames. A difficult situation arises if both sides simultaneously send an initial packet. This synchronization difficulty is illustrated by figure one. In part A, the normal operation of the protocol is shown. In part B, the difficulty is illustrated. If B waits for A's first frame before sending one of its own, the sequence is as shown in figure A and every frame is accepted. However, if A and B simultaneously initiate communication, their first frames cross and the data link layer then gets into situation shown in figure B. The notation for sending frames is sequence number ACK that is acknowledgement and packet number. Consider an example, A sends 1, 0, A1. Here 1 is the sequence number, 0 is the acknowledgement for frame with sequence number 0, A1 is the packet number. An asterisk indicates a network layer accepts a packet. In figure A, each frame arrival brings a new packet for the network layer. There are no duplicates. In figure B, half of the frames contain duplicates, even though there are no transmission errors. Similar situation can occur as a result of premature timeouts, even when one side clearly starts first. In fact, if multiple premature timeouts occur, frames may be sent three or more times, wasting valuable bandwidth. Figure 2A, case 1, shows the normal operation of the protocol. Figure 2B, case 2, shows the situation if data frame gets lost. The problem here is what if a frame gets lost? The protocol retransmits the frame after timeout. As shown in case 2, after sending a frame, sender starts a timer. If the frame gets lost and transit, the sender will not get the acknowledgement. So after the timeout, frame is retransmitted. Figure 2C, case 3, shows the situation where received frame is with error. As shown in case 3, after sending a frame, sender starts a timer. The receiver recomputes the checksum after receiving the frame. If the frame is erroneous, the receiver will not send the acknowledgement. So after the timeout, sender retransmits the frame. Figure 2D, case 4, shows the situation if acknowledgement gets lost. Here the sender will re-send the frame after timeout. After sending a frame, sender starts a timer. If the receiver gets a frame without error, it sends an acknowledgement. But if the acknowledgement gets lost and transit, the sender will retransmit the frame after the timeout. It creates duplicates at the receiver. Receiver will discard the duplicates. Figure 2E, shows case 5 with early timeout. Suppose a receiver sends an acknowledgement, but if the sender doesn't get the acknowledgement within the timeout period, the sender will retransmit the frame which will create duplicates at the receiver. Receiver will discard the duplicate. Early timeout will cause a loss of bandwidth. Figure 2F, shows case 6. Here data link layer weights a fixed number of milliseconds for a packet from network layer, on which to piggyback the acknowledgement. If a new packet arrives quickly, the acknowledgement is piggybacked onto it. Otherwise, if no new packet has arrived by the end of the time period, the data link layer just sends a separate acknowledgement frame, as shown in figure 2F. Let us see the working of one bit sliding window protocol. Here next frame to send is a sequence number. Frame expected is also a sequence number. These two can be either 0 or 1. R and S are the variables of type frame. Buffer is the variable of type packet. Event is of type event type. Initially the next frame to send and frame expected are initialized to 0. From network layer buffer, here we are fetching the packet from the network layer. And we are creating a frame out of the packet. So S.info equal to buffer, S.sequence number equal to next frame to send that is 0 initially. S.ack equal to 1 minus frame expected. So in this case 1 minus 0 is 1. Now the frame is constructed here. So the constructed frame is sent to the physical layer and sender starts a timer with sequence number. Here the machine is waiting for an event. The event can be either frame arrival, checksum, error or timeout. If the event is frame arrival means the frame has arrived from the other machine, we have to accept it from the physical layer. So from physical layer we are receiving the frame. S.sequence number equal to equal to frame expected. So here if the frame which is received is the expected frame then that frame will be sent to the network layer. So to network layer r.info, here we are sending the frame to the network layer. And here we are inverting the frame expected. Because frame expected can be either 0 or 1. Sender keeps all the frames which are sent in the buffer till the acknowledgement is received because the frame may get lost while transit. So if the next frame is already sent frame and acknowledgement for that frame is received then the sender can get the next frame from the network layer and it can construct the frame and it can send it to the physical layer. So here if the acknowledgement for the frame is received then the sender stops the timer, it gets the new frame from the network layer, it increments or it inverts the next frame to send. It constructs the frame so s.info equal to buffer, s.sequence number equal to next frame to send and s.ack equal to 1 minus frame expected. The frame is constricted and it is sent to the physical layer and the sender starts the timer. Here we will see the advantages and disadvantages of one bit sliding window protocol. Advantages are it is very simple and easy to implement. The disadvantages are it is fairly slow. The sender can send at most one new packet per RTT, RTT is round trip time and inefficient utilization of bandwidth it is done in one bit sliding window protocol. In this video we have seen the working of one bit sliding window protocol. Thank you.