The Lumley Autograph by Susan Fenimore Cooper. Not long since, an American author received an application from a German correspondent for A Few Autographs. The number of names applied for amounting to more than a hundred, and covering several sheets of full scrap. A few years since, an Englishman of literary note sent his album to a distinguished poet in Paris for his contribution, when the volume was actually stolen from a room where every other article was left untouched, showing that autographs were more valuable in the eyes of the thief than any other property. Amused with the recollection of these facts and others of the same kind, some idle hours were given by the writer to the following view of this mania of the day. The month of November of the year 1600 and, blank, was cheerless and dark, as November has never failed to be within the foggy, smoky bounds of the great city of London. It was one of the worst days of the season. What light there was seemed an emanation from the dull earth. The heavens would scarce have owned it, veiled as they were, by an opaque canopy of fog which weighed heavily upon the breathing multitude below. Gloom penetrated everywhere, no barrier so strong, no good influences so potent, as wholly to ward off the spell thrown over that mighty town by the spirits of chill and damp. They clung to the silken draperies of luxury. They were felt within the busy circle of industry. They crept about the family hearth, but abroad in the public ways, and in the wretched haunts of misery, they held undisputed sway. Among the throng which choked the passage of Temple Bar toward evening, an individual, shabbily clad, was dragging his steps wherely along, his pallid countenance bearing an expression of misery, beyond the more common cares of his fellow passengers. Turning from the great thoroughfare, he passed into a narrow lane, and reaching the door of a mean dwelling he entered, ascended a dirty stairway four stories high, and stood in his garret lodging. If that garret was bare, cold and dark, it was only like others, in which many a man before and since has pined away years of neglect and penury, at the very moment when his genius was cheering, enriching, enlightening his country and his race. That the individual whose steps we have followed was indeed a man of genius, could not be doubted by one who had met the glance of that deep, clear, piercing eye, clouded though it was at that moment by misery of body and mind that amounted to the extreme of anguish. The garret of the stranger contained no food, no fuel, no light. Its occupant was suffering from cold, hunger, and wretchedness. Throwing himself on a broken chair, he clenched his fingers over the manuscript, held with a pale and emaciated hand. Shall I die of hunger, or shall I make one more effort? He exclaimed, in a voice in which bitterness gave a momentary power to debility. I will write once more to my patron, possibly— Without waiting to finish the sentence, he groped about in the dull twilight for ink and paper, resting the sheet on a book he wrote in a hand barely legible. November twentieth, sixteen, blank. My lord, I have no light, and cannot see to right. No fire and my fingers are stiff with cold. I have not tasted food for eight and forty hours, and I am faint. Three times, my lord, I have been at your door to-day, but could not obtain admittance. This note may yet reach you in time to save a fellow creature from starvation. I have not a farthing left, nor credit for a half-penny.  Unless relieved within a few hours, I must perish. Your lordship's most humble, most obedient, most grateful servant—blank, blank. This letter, scarcely legible from the agitation and misery which enfeebled the hand that wrote it, was folded and directed, and again the writer left his garret lodging on the errand of beggary. He descended the narrow stairway, slowly dragged his steps through the lane, and sought the dwelling of his patron. Whether he obtained admittance or was again turned from the door, whether his necessities were relieved, or the letter was idly thrown aside unopened, we cannot say. Once more mingled with the crowd, we lose sight of him. It is not the man but the letter which engages our attention today. There is still much doubt and uncertainty connected with the subsequent fate of the poor poet. But the note written at that painful moment has had a brilliant career—a history eventful throughout. If the reader is partial to details of misery and poverty, any volume of general literary biography will furnish him with an abundant supply. For such has too often proved the lot of those who have built up the noble edifice of British literature. Like the bands of labourers on the Egyptian pyramid, theirs was too often a mess of leaks, while milk and honey and oil were the portion of those for whom they toiled, those in whose honour and for whose advantage the monument was raised. Patrons, whether single individuals or nations, have too often proved but indifferent friends. Caillus and forgetful of those whom they proudly pretend a foster. But leaving the poor poets, with his sorrows, to the regular biographer, we choose rather the lighter task of relating the history of the letter itself. A man's works are often preferred before himself, and it is believed that in this, the day of autographs, no further apology will be needed for the course taken on the present occasion. We hold ourselves indeed, entitled to the special gratitude of collectors, for the following sketch of a document maintaining so high a rank in their estimation. And justly might the Lumley letter claim a full share of literary homage. Boasting a distinguished signature, it possessed the first essential of a superior autograph. For, although a rose under any other name may smell as sweet, yet it is clear that with regard to everything coming from the pen, whether folio or billet due, imaginative poem or matter-of-fact note of hand, there is a vast deal in this important item, which is often the varied life and stamina of the whole production. Then again, the subject of extreme want is one of general interest, while the allusion to the unpublished poem must always prove and a special attraction to the curious. Such were the intrinsic merits of the document, in addition to which, so birth time, lent his aid to enhance its value, and capricious fortune added a peculiar charm of mystery, which few papers of the kind could claim to the same extent. The appearance also of this interesting paper was always admitted to be entirely worthy of its fame. The handwriting fully carried out the idea of extreme debility and agitation corresponding with its nature, while a larger and a lesser blot bore painful testimony to that recklessness of property which a starving man might be supposed to feel. One corner had been ruthlessly abstracted at the time it was seen by the writer of this notice, and with it the last figures of the date. A considerable rent crossed the sheet from left to right, but happily without injuring its contents. Several punctures were also observed, one of these encroaching very critically upon the signature. But I need not add that these marks of age and harsh treatment, like the scars on the face of a veteran, far from being blemishes, were acknowledged to be so many additional embellishments. The colouring of the piece was of that precious hue, verging here and there on the dingy, the very tint most charming in the eyes of an antiquary, and which time alone can bestow. In fact, one rarely sees a relic of the kind, more perfect in colour, more expressive in its general aspect, or more becoming to an album, from the fine contrast between its poverty-stricken air, torn, worn, and soiled, and the rich, embossed, unsullied leaf on which it reposed, like some dark rembrant within its gilded frame. In short, it was the very torso of autographs. Happily the position which it finally attained was one worthy of its merits, and we could not have wished it a more elegant shrine than the precious pages of the Halberton album, a volume encased in velvet, secured with jeweled clasps, reposing on a tasteful étagère. Etagère, a small table or shelf for displaying curios, French. But I proceeded without further delay to relate some of the more important steps in the progress of this interesting paper, from the garret of the starving poet to the drawing-rooms of Halberton Hals, merely observing by way of preface that the following notice may be relied on so far as it goes, the writer, Colonel Jonathan Howard of Trenton, New Jersey, having had access to the very best authorities, and having also had the honour of being enlisted in the service of the Lumley autograph upon an occasion of some importance, as will be shown by the narrative. It was just one hundred years since, in 1745, that this celebrated letter was first brought to light from the obscurity in which it had already lain some half a century, and which no subsequent research has been able to fully clear away. In the month of August of that year, the Reverend John Lumley, tutor to Lord Gee, had the honour of discovering this curious relic under the following circumstances. Mr. Lumley was one day perched on the topmost step of a library ladder, looking over a black velvet volume of holling-shed from the well-filled shelves of his pupil. Suddenly he paused, and his antiquarian instincts were aroused by the sight of a sheet of paper, yellow and time-worn. He seized it with the eagerness of a bookworm, and in so doing dropped the volume of holling-shed alarmingly near the wig-covered head of his youthful pupil, who, with closed eyes and open mouth, lay reclining on a sofa below. The book, grazing the curls of the young Lord's wig, he sprang up from his nap, alive in sound, though somewhat startled. Holling-shed, Raphael Holling-shed, D. 1580, famous writer of British historical chronicles, used by Shakespeare as source for some of his plays. Hang it, Lumley! What a rumpus you keep up among the books! You well neither have that old volume into my head! By a process more summary than usual. The learned tutor made a thousand apologies, as he descended the ladder, but on touching the floor his delight burst forth. It was this paper, my Lord, which made me so awkward. I have lighted on a document of the greatest interest. What is it? asked the pupil, looking a scanset letter and tutor. An original letter which comes to hand, just in time for my lives of the Tragedians, the volume to be dedicated to your Lordship, it is a letter of poor Autway. Autway. Thomas Autway. 1652-1685. English playwright who wrote a number of important tragedies in verse, but who died destitute at the age of 33. The Coopers were familiar with his work. James Fenimore Cooper used quotations from Autway's The Orphan, four three chapter-heading epigraphs in his 1850 novel The Ways of the Hour. Autway. What? The fellow you were boring me about last night. The same, my Lord. The poet Autway. You may remember we saw his Venice preserved last week. It is a highly interesting letter, written in great distress, and confirms the story of his starvation. You see the signature. Venice preserved. A well-known play by Autway. Written in 1682. That name. Autway. Well, to my mind it is as much like Genghis Khan. Oh, my Lord. Thomas Autway clearly. Signatures are always more or less confused. Well, have it your own way. It may be Tom, Dick, or Harry for all I care. To the youth, stretching himself preparatory to a visit to his kennels. And such was his indifference to this literary treasure that he readily gave it to his tutor. In those days few lords were literary. Mr. Lumley's delight at this discovery was very much increased by the fact that he was at that moment anxious to bring out an addition of the English tragedians of the seventeenth century. The lives of several of these authors had already been written by him, and he was at that moment engaged on that of Autway. A noted publisher had taken the matter into consideration, and if the undertaking gave promise of being both palatable to the public and profitable to himself, a prospectus was to be issued. Now here was a little tit-bit, which the public would doubtless relish, for it was beginning to feel some interest in not waste starvation, the poet having been dead half a century. It is true that the signature of the poor starving author, whoever he may have been, was so illegible that it required some imagination to see it, the name of Autway, but Mr. Lumley had enough of the true antiquarian spirit to settle the point to his own entire satisfaction. The note was accordingly introduced into the life of Autway, with which the learned tutor was then engaged. The work itself, however, was not destined to see the light. Its publication was delayed, while Mr. Lumley accompanied his pupil on the usual continental tour. And from this journey the learned gentleman never returned, dying at Rome, of a cold caught in the library of the Vatican. By his will, the MS, Life of Autway, with all his papers, passed into the hands of his brother, an officer in the army. Unfortunately, however, Captain Lumley, who was by no means a literary character, proved extremely indifferent to this portion of his brother's inheritance, which he treated with contemptuous neglect. After this first stage on the road to fame, twenty more years passed away and the letter of the starving poet was again forgotten. At length, the papers of the Reverend Mr. Lumley fell into the hands of a nephew, who inherited his uncle's antiquarian tastes and clerical profession. In looking over the MSS, he came to the life of Autway, and was struck with the letter given there, never having met with it in print. There was also a note appended to it, with an account of the manner in which it had been discovered by the editor, in the library of Lord G., and affirming that it was still in his own possession. The younger Lumley immediately set to work to discover the original letter, but his search was fruitless. It was not to be found, either among the papers of his uncle or of those of his father. It was gone. He was himself a tutor at Cambridge at the time, and returning to the university, he carried with him his uncle's life of Autway, in MSS. Some little curiosity was at first excited among his immediate companions by these facts, but it soon settled down into an opinion unfavorable to the veracity of the late Mr. Lumley. This netled the nephew, and as Lord G. was still living, a gouty bloated rue, he had length wrote to inquire if his lordship knew anything of the matter. His lordship was too busy, or too idle, to answer the inquiry. Sometime later, however, the younger Lumley, than a chaplain in the family of a relative of Lord G., accidentally met his uncle's former people. And, being of a persevering disposition, he ventured to make a personal application on the subject. Now you recall the matter to me, Mr. Lumley. I do recollect something of the kind. I remember one day, giving my tutor some musty old letter he found in the library at G., and by the by he came near cracking my skull on the same occasion. Mr. Lumley was not a little pleased by this confirmation of the story, though he found that Lord G. had not even read the letter, nor did he know anything of its subsequent fate. He only remembered looking at the signature. Not long after the meeting at which this explanation had taken place, Mr. Lumley received a visit from a stranger, requesting to see the MS. Life of Otway in his possession. It was handed to him. He examined it, and was very particular in his inquiries on the subject, giving the chaplain to understand that he was the agent of the third person who wished to purchase, either the original letter if possible, or if that could not be found, the MS containing the copy. Mr. Lumley always believed that the employer of this applicant was no other than the arch-gatherer Horace Walpole, who gave such an impulse to the collecting mania. He declined selling the work, however, for he had thoughts of printing it himself. The application was mentioned by him, and, of course, the manuscript gained notoriety, while the original letter became a greater desiderato than ever. The library at G. was searched most carefully by a couple of brother bookworms, who crept over it from cornice to carpeting, but to no purpose. Horace Walpole. Horace Walpole 1717-1797, a prolific writer, connoisseur, and collector best known for his extensive correspondence. He established a taste for literary collecting by would-be culture gentlemen in England. Some ten years later still, about the time, by the by, when Chatterton's career came to such a miserable close in London, and when Gilbert was dying in a hospital at Paris, it happened that a worthy physician, well known in the town of Southampton for his benevolence and eccentricity, was on a professional visit to the child of a poor journeyman-trunk-maker in the same place. A supply of old paper had just been brought in for the purpose of lining trunks, according to the practice of the day. A workman was busy sorting these, rejecting some as refuse, and preserving others, when the doctor stopped to answer an inquiry about the sick child. Chatterton.  Chatterton committed suicide at the age of eighteen, when a poem of his, allegedly by Rowley, was rejected. He was buried in a pauper's grave. Susan Fenimore Cooper, no doubt, has, this in mind, in naming a character in this story, the Edogea Rowley. Gilbert, Nicholas Gilbert 1751-1780, French poet who died in Paris at the age of twenty-nine. The French writer Count Alfred de Vigny, 1797-1863, in his book of essays, Stella, 1832, popularized a legend that Gilbert had died insane, and in abject poverty, at the charity hospital of the Hotel du in Paris, and compared his miserable end with that of Chatterton. It seemed likely that Vigny, whose book appeared, while Susan Fenimore Cooper was studying in Paris, was her source for this reference to Gilbert. In fact, Gilbert was not impoverished, and died of injuries after falling from his horse. Better Hopkins, doing well! But what have you here? I never see old papers, but I have an inclination to look them over. If a man has leisure, he may often pick up something amusing among such rubbish. Don't you ever read the papers that pass through your hands? No, sir. I is no time for that, sir. And then I was never taught to read writing, and these air papers is all written ones. We put them as written for one trunk, and them as printed for another, as you see, sir. One must have a high to the looks of the work. Why, yes. You seem to manage the job very well, and I have a trunk by the by that once patching up before my boy carries it off with him. I'll send it round to you, Hopkins, but stay. What's this? And the doctor took up a soiled yellow sheet of paper, from the heap rejected by the workmen. It contained a scroll which proved to be the identical letter of the poor poet, the Lumley autograph. Though in what manner it became mingled with that heap of rubbish, has never been satisfactorily ascertained. Here's a poor fellow who had a hard fate, Hopkins, said the benevolent man thoughtfully. It is as good as a sermon on charity to read that letter. The trunk-maker begged to hear it. Well, poor journeyman, as I be, I was never yet in so bad a way as that, sir. And never will be, I hope. But this was a poet, Hopkins, and that's but an indifferent trade to live by. I'll tell you what, my good friend, said the doctor suddenly, that letter is worth keeping, and you may paste it in the trunk I'll send round this afternoon. Put it in the lid where it can be read. The trunk was sent, and the letter actually pasted in it as part of the new lining. Dr. H., who, as we have observed, was rather eccentric in his ways, had a son about to commence his career as a soldier, and the worthy man thought the letter might teach the youth a useful lesson of moderation and temperance by showing him every time he opened his trunk the extreme wants to which his fellow beings were occasionally reduced. What success followed the plan we cannot say. The trunk, however, shared the young soldier's wondering life. It carried the cornets uniform to America. It was besieged in Boston, and it made part of the besieging barrage at Charleston. It was not destined, however, to remain in the new world, but followed its owner to the East Indies, carrying on this second voyage a lieutenant's commission. At length, after passing five and twenty years in Bengal, the trunk returned again to Southampton, as one among some dozen others, which made up the baggage of the gallant Colonel H., now bridged in laurels and rupees. The old trunk had even the honourable duty assigned to it of carrying its master's trophies, doubtless the most precious portion of the Colonel's possessions, though at the same time the lightest. As for the rupees, the old worn-out box would have proved quite unequal to transporting a single bag of them, for it was now sadly unfit for service, thanks to the ravages of time and the white ants, and indeed owed its preservation and return to its native soil solely to the letter pasted in the lid, which in the eyes of Colonel H. was a memento of home and the eccentric character of a deceased parent. Cornet, the lowest officer rank in a British cavalry regiment, below that of Lieutenant, now obsolete. The time had now come, however, when the Lumley autograph was about to emerge forever from obscurity, and receive the full homage of collectors. The hour of triumph was at hand, the neglect of a century was to be fully repaid, by the highest honours of fame. The eye of beauty was about to kindle as it rested on the Lumley autograph. Jeweled fingers were to be raised, eager to snatch the treasure from each other. Busy literati stood ready-armed for a war of controversy in its behalf. It happened that Colonel H. was invited to a fancy ball, and it also happened that the lady whom he particularly admired was to be present on the occasion. Such being the case, the most becoming costume was to be selected for the evening. What if the locks of the gallant Colonel were slightly sprinkled with grey? He was still a handsome man, and knew very well that the dress of an Eastern Amir was particularly well suited to his face and figure. This dress, preserved in a certain old trunk in the garret, was accordingly produced. The trunk was brought down to the dressing-room, the costume examined piece by piece, pronounced in good condition by the valet, and declared very becoming by the military friend, called in as counsellor. Amir, Amir, a Muslim title signifying commander in Arabic.  It's one I've had these hundred years, replied the Colonel. So you think this trumpery will do, D? Do. To be sure it will, my dear fellow, it gives your Malaysian skin the true Nawab dye. But I was just trying to make out an old letter pasted in the lid of your trunk, under my nose here.  Malaysian, slang term for Irish, from Malaysia's, mythical Spanish conqueror of Ireland's, Nawab, from Nabab, Anglo-Indian slang for one who has returned home from India with a large fortune. That letter is really a curiosity in its way, said the Colonel, turning from the glass and relating its history, so far at least as it was known to himself. His friends belt it through. My dear fellow, why don't you give this letter to the father of your fair Louisa? He's quite rabid on such points. You'll make him a friend for life by it. The advice was followed. The letter was cut from its old position in the lid of the trunk, and presented to Sir John Blank, the father of the lovely Louisa, who, in his turn, soon placed the hand of his daughter in that of Colonel H. Sir John, a noted follower in the steps of Horace Waple, had no sooner become the owner of this interesting letter than he set to work to find out its origin and to fill up its history. Unfortunately the sheet had received some wounds in the wars, as well as the gallant Colonel. One corner had been carried away by an unlucky thrust from a razor, not a sword, while the date and signature had also been half-eaten out by the white ants of Bengal. But such difficulties as these were only pleasing obstacles in the way of antiquarian activity. Sir John had formed an hypothesis, perfectly satisfactory to himself. His mother's name was Butler, and he claimed some sort of affinity with the author of Hoodabris, as the Christian name of the poor poet had been almost entirely devoured by the ants, while the surname had also suffered here and there. Sir John ingeniously persuaded himself that what remained had clearly belonged to the signature of the great satirist, as for the date the abbreviation of November 20th and the figures 16 marking the century were really tolerably distinct. Accordingly Sir John wrote a brief notice of Butler's life, dwelling much upon his well-known poverty, and quoting his epitaph, with the allusion to his indigence, underscored, lest he who living wanted all things should when dead want a tomb, and placed these remarks opposite the letter of our starving poet, which was registered in the volume in conspicuous characters as an autograph of Samuel Butler, author of Hoodabris, showing to a distress he was at one time reduced. Samuel Butler, 1612 to 1680, another English author popularly believed to have died in great poverty, he is best known for his long satiric mock epic poem Hoodabris, 1663 to 1678. Here the sheet remained several years until it lengthed chance that Sir John's volume of autographs was placed in the hands of a gentleman who had recently read Mr. Lumley's MS, Life of Ottway. The identity of this letter, with that copied by Mr. Lumley, immediately suggested itself, and now the first sparks of controversy between the Ottwazians and the Butlerites were struck in Sir John's library. From thence they soon spread to the forewinds of heaven, felling on combustible materials wherever they lighted on a literary head, or collecting hands. By the by the rapidity with which this collecting class has increased of late years is really alarming. Who can foresee the state of things likely to exist in the next century should matters go on at the same rate? Reflect for a moment on the probable condition of distinguished authors, lions of the loudest roar, if the number of autograph hunters were to increase beyond what it is at present. Is it not to be feared that they will yet exterminate the whole race, that the great lion literary, like the mastodon, will become extinct? Or perhaps by taming him down to a mere producer of autographs, his habits will change so entirely that he will no longer be the same animal, no longer bear a comparison with the lion of the past. On the other hand, should the great race become extinct, what will be the fate of the family of autograph feeders? What a fearful state of things would ensue, even in our day, were the supply to be reduced but acquired. The heart sickens at the picture which would then be presented, collectors turning on each other, wedging a fierce war over every autographic scrap, making a battlefield of every social circle. Happily nature seems always to keep up the balance in such matters, and it is a consoling reflection that if the million are now consumers, so have they become producers of autographs. It is therefore probable that the evil will work its own remedy, and we may hope that the great writers of the next century will be shielded in some measure by the diversion made in their favor through the lighter troops of the lion corps. As for the full merits of the controversy so hotly waged over the Lumley autograph, between the Ottwazians and the Butlerites, dividing the collecting world into two rival parties, we shall not here enter into it. In all such matters it is better to go at once to the fountain-head. If the reader is curious on the subject, as doubtless he must be, he is referred to one octavo and five to a decim of volumes, with fifty pamphlets which have left little to say on the point. Let it not be supposed, however, for an instant that the writer of this article is himself undecided in his opinion on this question, by no means, and he hastens to repeal the unjust suspicion by declaring himself one of the warmest Ottwazians. It is true that he has some private grounds for believing that a dispassionate inquiry might lead one to doubt whether Ottway or Butler ever saw the Lumley autograph, but what of that, who has time or inclination for dispassionate investigation in these stirring days? In the present age of universal enlightenment we don't trouble ourselves to make up our opinions. We take and give them, we beg, borrow, and steal them. True, there are controversies involving matters so important in their consequences, so serious in their nature, that one might conceive either indifference or fanaticism equally inexcusable with regard to them, but there are also a thousand other subjects of discussion, at the present day, of that peculiar character which can only thrive when supported by passion and prejudice, and falling in with the dispute of this nature. It is absolutely necessary to jump at once into fanaticism. Accordingly I had no sooner obtained a glimpse of the letter of the starving poet, embalmed within the precious leaves of one of the most noted albums of Europe, than I immediately enlisted under Lady Halberton's colours as a faithful Ottwazian. With that excellent lady I take a tragical view of the Lumley letter, conceiving that a man must be blind as a bat, not to see that it was written by the author of Venice Preserved, and this in spite of other celibrated collectors, who find in the same sheet so much that is comical and heodobrastic. As we have already observed, the controversy began in the library of Sir John Blank, and it continued throughout the lifetime of that excellent and well-known collector. At his death, a few years since, it passed into the hands of his daughter, the widow of Colonel H. And it will be readily imagined that although the main question is still as much undecided as ever, yet the value of the document itself has immeasurably increased by a controversy of twenty years standing on its merits. I wish I could add that the fortune of Colonel H. had documented in the same proportion, but unhappily for his widow, the reverse was the case. And it was owing to this combination of circumstances that Lady Halberton at length obtained possession of the Lumley autograph. Mrs. H. became very desirous of procuring for her eldest son a cornicy in the regiment once commanded by his father, as she was now too poor to purchase. The matter required management of the letter. How it was brought about, I cannot exactly say. Suffice it to declare that the young man received his commission, through the influence of Lady Halberton, in a high military quarter, while the Lumley autograph was placed on the ground floor. It so happened that I dined at Halberton House on the eventful day upon the arrival of the young man. And I thought that the young man would be a good man. I thought that the young man would be a good man. I thought that the young man would be a good man. It so happened that I dined at Halberton House on the eventful day upon which the Lumley letter changed owners. I saw immediately, on entering the drawing room, that Lady Halberton was an excellent spirit. She received me very graciously, and spoke of her son, with whom I had just travelled between Paris and Algiers. Wish me joy, Mr. Howard! exclaimed the lady after a short conversation. Of course I was very happy to do so, and replied by some remarks on the recent success of her friends in a parliamentary measure, just then decided, Lady Halberton being a distinguished politician. But I soon found it was to some matter of still higher moments, she then alluded. I never had a doubt as to our success in the house. Last night, no, rather wish me joy that I had at last triumphed in a negotiation of two years' sanding. The Lumley autograph is mine, Mr. Howard. The letter of poor Artway, actually written in the first stages of starvation, only conceived its value. Other guests arriving, I was obliged to make way. Not however before Lady Halberton had promised me a sight of her recent acquisition in the evening. In the meantime I fully entered into her satisfaction, for I had already seen her album in Paris, and heard her sigh for this very addition to its treasures. During dinner the important intelligence that the Lumley letter was her own, was imparted to the company generally. I knew it, I was sure of it from her smile, the moment I entered the room, exclaimed Mr. T., the distinguished collector who sat next to me. Another guest, Miss Rowley, also a collecting celebrity, was sitting opposite, and turned so pale at the moment that I was on the point of officially recommending a glass of water. Have you albums in America, Mr. Howard? inquired a charming young lady on my right. There is no lack of them, I assure you, I replied. Really? Adele, Mr. Howard, tells me they have albums in America, repeated the young lady to a charming sister near her, while on my left I had the satisfaction of hearing some gratifying remarks from Mr. T., as to the state of civilization in my native country, as shown by such a fact. And what are your albums like? again inquired my lovely neighbor. Not like Lady Holbertons, perhaps, but pretty well for a young nation.  Why yes, we get most of them from Paris and London. Oh dear, how strange, but don't you long to see this new treasure of Lady Holbertons, that dear nice letter of hot ways, written while he was starving? inquired the charming Emily, helping herself to a bit of pate de perigorde. Pate de perigorde, an expensive French delicacy, goose liver pate with truffles. Yes, I am exceedingly curious to see it. You don't believe it was written by that coarse vulgar butler, do you? No indeed, it is the pathetic odd ways beyond a doubt. My neighbor, the butlerite, gave a contemptuous shrug, but I paid him no attention, preferring to coincide with the soft eyes on my right, rather than dispute with the learned spectacles to the left. After dinner, when we had done full justice to the bill of fare, concluding with pines, grapes, and Newton-pippins, we were all gratified with the sight of the poor poet's letter, by way of bon bouche. A little volume, written by Lady Holberton, printed but not published, relating its past history from the date of its discovery in the Library of Lord G., her grandfather, to the present day, passed from hand to hand, and this review of its various adventures, of course, only added forth. To the congratulations, offered upon the acquisition of the celebrated autograph. Pine, pineapple, Newton-pippin, a green, tart, tangy American apple, originally from Long Island, a favorite of George Washington and Thomas Jefferson. Bon bouche, a tasty morsel, French. While the company were succeeding each other in offering their homage to the great album, my attention was called off by a tap on the shoulder from a friend, who informed me that Miss Rowley, a very clever, handsome woman of a certain age, had expressed a wish to make my acquaintance. I was only too happy to be presented. After a very gracious reception, and an invitation to a party for the following evening, Miss Rowley observed, You have autographs in America, I understand, Mr. Howard. Both autographs and collectors, I replied. Really, perhaps you are a collector yourself, continued the lady, with an indescribable expression, half-interest, half-disappointment. No, merely a humble admirer of the labor of others. Then, added the lady more blandly, perhaps you will be good-natured enough to assist me. And after a suspicious glance toward the spot where Lady Holberton and Mr. T. were conversing together, she droidly placed herself in a position to give to our conversation the privacy of a diplomatic, tattle-tat. Could you possibly procure me some American autographs for my collection? I find a few wanting under the American head, perhaps a hundred or two. I professed myself ready to do anything in my power in so good a cause. Here is my list. I generally carry it about me. You will see those that are wanting, and very possibly may suggest others. As the lady spoke, she drew from her pocket a roll of paper as long, and as well-covered with names as any minority petition to Congress. However, I had lived too much among collectors of late to be easily dismayed. The list was headed by Black Hawk. I expressed my fears that the gallant warrior's ignorance of letters might prove an obstacle to obtaining anything from his pen. I volunteered, however, to procure, instead, something from a Cherokee friend of mine, the editor of a newspaper. Black Hawk. Black Hawk, 1767-1838. An American Indian. Sack. Chieftain. One of the U.S. Army in 1832, whose autobiography, 1833, became an American classic. How charming! exclaimed Miss Rowley, clasping her hands. How very obliging of you, Mr. Howard. Are you fond of shooting? My brother's preserves are in fine order, or perhaps you are partial to yachting? Bowing my thanks for these amiable hints, I carelessly observed that the letter of the Cherokee editor was no sacrifice at all, the chief and myself were regular correspondents. I had a dozen of his letters, and had just given one to Mr. T. This intelligence evidently lessened Miss Rowley's excessive gratitude. She continued her applications, however, casting an eye on her list. Perhaps you correspond also with some rowdies, Mr. Howard. Could you oblige me with a rowdy letter? Rowdies. In the mid-19th century, an American slang term for a backwardsman were other rough and disorderly types. I drew up a little at this request. My correspondents, I assured the lady, were generally men of respectability, though one of them was of a savage race. No doubt, but in the way of autographs, you know, one would correspond with... The sentence remained unfinished, for the lady added. I wrote myself to Madame Lafarge, not long since. I am sorry to say Lady Halberton has two of hers, but although an excellent personage in most respects, yet it cannot be denied that as regards autographs, Lady Halberton is very illiberal. I offered her Griselle Bailey, two Cardinals, William Pitt, and Grace Darling, for one of her Lafarges, but she would not part with it, yet the exchange was very fair, especially as Madame Lafarge is still living. Madame Lafarge. Marie Lafarge. 1816-1853. French woman convicted in 1840 for poisoning her husband. Later pardoned. Griselle Bailey. Lady Griselle Bailey. 1665-1746. Scottish poet. William Pitt. Either William Pitt the Elder, 1708-1778, or William Pitt the Younger. 1759-1806. Both British Prime Ministers. Grace Darling. Grace Darling. 1815-1842. English heroine and lighthouse keeper's daughter, famous for her rescue of castaways in 1838. I bowed in ascent to the remark. And then she herself actually once made proposals for Schindler Hans, to a friend of mine, offering Howard the philanthropist, Talma, William Penn, and Fennelin, for him. All commonplace enough, you know, and Schindler Hans quite unique. My friend was indignant. Schindler Hans. German bandit chief. Executed in 1803. Howard, John Howard. 1726-1790. English philanthropist and prison reformer. Talma. French wall Talma. 1763-1826. Popular French playwright. William Penn. 1644-1718. Quaker founder of Pennsylvania. Fennelin, Francois Fennelin. 1651-1715. French archbishop and writer. I ventured to excuse Lady Holberton by suggesting that probably at the time her stock of notabilities was low. Miss Raleigh shook her head.  On one point, however, I have carried the day, Mr. Howard. Lady Holberton is not a little proud of her vedoc. But I have obtained one far superior to hers, one addressed to myself so pecanic and gallant, too. I called on a dear old burglar on purpose, to coax him into writing me a note. Vedoc. Francois Vedoc. 1775-1857. French police detective who turned robber, and was exposed in 1832. I wondered in petto whether I should meet any illustrious convicts at Miss Raleigh's party the next evening. But remembering to have heard her called an exclusive, it did not seem very probable. In petto. Silently to oneself. Latin. After running her eye over the list again, Miss Raleigh made another inquiry. Mr. Howard, could you get me something from an American colonel? I assured the lady we had colonels of all sorts, and begged to know what particular variety she had placed on her catalogue. Was it an officer of the regular service, or one of no service at all? Oh, the last, certainly. Officers who have seen service are so commonplace. My own pen was immediately placed at Miss Raleigh's disposal, as my sword would have been had I owned one. As I had been called colonel a hundred times without having commanded a regiment once, my own name was as good as any other on a present occasion. You are very obliging. Since you are so good, may I also trouble you to procure me a line from a very remarkable personage of your country, a very distinguished man. He has been president, or speaker of the Senate, or something of that sort. To which of our head men did Miss Raleigh allude? He is called Uncle Sam, I believe. Uncle Sam. Uncle Sam became a popular personification of the United States during the War of 1812, replacing Brother Jonathan, and was often using contradistinction to the British John Bull. This was not so easy a task, for though we have thousands of colonels, there is but one Uncle Sam in the world. On hearing that such was the case, Miss Raleigh's anxiety on the subject increased immeasurably. But I assured her the old gentleman only put his name to treaties and tariffs. And although his sons were wonderfully gallant, yet he himself had never condescended to notice any woman but a queen regnant. And I further endeavored to give some idea of his identity. Miss Raleigh stopped me short, however. Only procure me one line from him, Mr. Howard, and I shall be indebted to you for life. It will be time enough to find out all about him when I once have his name. That is the essential thing. I shrunk from committing myself, however, declaring that I would as soon engage to procure a billed due from Prestor John. Prestor John, mythical ruler believed in the Middle Ages to head a powerful Christian kingdom somewhere in Asia, later identified with the Christian kings of Ethiopia in Africa. Prestor John, that would indeed be quite invaluable. This Asiatic diversion was a happy one, and came very a promise, for it carried Miss Raleigh into China. She inquired if I had any Chinese connections. Though altogether I am pretty well satisfied with my Chinese negotiations, as soon as the celestial empire was open to the civilized world I engaged an agent there to collect from me. But could you put me on the track of a Confucius? Opened to the civilized world, following the so-called Opium War, Britain had in 1842 forced China to open trade with her. I was obliged to admit my inability to do so, and at the same moment the collecting instincts of Lady Holberton and Mr. T. drew their attention to the corner where Miss Raleigh and myself were conversing. As they moved toward us, Miss Raleigh pocketed her list, throwing herself upon my honor not to betray the deficiencies in her ruled equipage, or the collecting negotiations just opened between us. Lady Holberton, as she advanced, invited Miss Raleigh with an ill-concealed air of triumph, to feast her eyes once more on the Lumley autograph, and not long after the party broke up. Roll to equipage. Muster roll. French. Here, Miss Raleigh's list of her autographs. The next day, in passing Holberton house, I observed the chariots of a fashionable physician before the door, and at Miss Raleigh's party in the evening learned from Mr. T. that Lady Holberton was quite unwell. The following morning I called to inquire, and received for answer that her ladyship was very much indisposed. It was not until a week later that I saw Lady Holberton herself, taking the air in Hyde Park. She looked wretchedly thin and pale. I inquired from the English friend with whom I was writing if there was any probability of a change of ministry. He looked surprised, and then catching the direction of my eye he observed, you ask one Lady Holberton's account, but Sir A. B. tells me her illness was caused by the loss of the Lumley autograph. This unexpected intelligence proved only too true. On returning to my lodgings I found a note from Lady Holberton, requesting to see me, and of course immediately obey the summons. Lost. Lost. Lost, Mr. Howard, said the lady, endeavoring to conceal her emotion as she gave me the details of her affliction. It must have been stolen, basely stolen, on the evening of my party. Oh, why did I so foolishly exhibited among so many people, and collectors among them, too? Never again will I admit more than one collector at a time into the room with my album," she exclaimed with energy. I was shocked. Surely Lady Holberton did not conceive it possible that any of her guests could be guilty of such base conduct.  But it is that, Mr. Howard, which has interested me in your favor, you have so much naivety and ignorance of the moral turbitude of the old world, that I feel convinced you never could be guilty of such an action yourself. I assured Lady Holberton that in this respect she only did me justice, and in fact a theft of the kind she alluded to, appealed to me all but incredible. Remember that it was only the other day that Blank lost his invaluable album. Remember that last winter Madame de Blank had all her notes on botanical subjects stolen from her own portfolio, and I could mention a dozen instances of the same wickedness. These facts were already known to me, but I had forgotten them. I remarked with a glow of national pride that we certainly were much more virtuous in these matters across the ocean. In America we are much above pilfering autographs. When we do steal, it is by the volume. We seize all an author's stock in trade at one swoop, and without condescending to say even, thank you for it. Author's stock in trade. Though ostensibly referring to the stealing of autographs, Susan Fenimore Cooper is also clearly referring to the widespread pirating of British and other foreign literary works by American publishers, in the absence of international copyright laws, which not only cheated the authors but made life difficult for American authors expecting to be paid for their creations. So I have always understood Mr. Howard, and I felt that my album was safe with you, observed Lady Holberton with tears in her eyes. Wishing to relieve this distress, I proposed advertising for the lost treasure, applying to the police. Lady Holberton smiled through her tears, as she assured me that the police, old and new, had been enlisted in her service an hour after the discovery of her loss, while communications had been opened with municipal governments of Brussels, Paris, and Vienna on the same subject. Police, old and new. The first modern English police force had been established in 1829 by Sir Robert Peel, from which the British nickname of Bobby for policemen. And have you no clue? No suspicions? Your servants? Your maid? The aspersion on her household was indignantly repelled. You will readily believe, Mr. Howard, that a collector, the owner of such an album as I, have the honor of possessing, is particularly careful as to whom she admits into her family. I will vouch for all about me. Still I have suspicions, but... I begged her to speak, if she thought I could be of the least assistance. Yes, I will trust my son's friend. Mr. Howard, I hear solemnly accused Theodosia Rowley of having stolen the Lumley autograph. The dignity of the matter, the concentrated passion of expression, the strength of emphasis with which Lady Holberton spoke, would have done honor to ascitants. The natural start of horror and amazement on my part was also no doubt very expressive, for I was speechless with surprise. I see you do not credit this," continued the lady. But thought, like a flash of lightning, had already recalled some circumstances of the last evening at Holberton House. I did credit the accusation, and immediately informed Lady Holberton of what I had observed, but forgotten until reminded of the facts by her own remarks. I had seen Miss Rowley bending low over the album at a moment when someone was telling an exceedingly humorous story which engrossed the attention of the rest of the company. Could she have had an accomplice? cried the lady with dashing eyes. I knew nothing on that point, but I added that soon after Miss Rowley had left the room very quietly, and as I followed her to fulfill another engagement, she had started, turned pale, and betrayed nervousness. Scarcely allowing me to assist her to her carriage, although we left the house at the same instant. Lady Holberton's suspicions were now confirmed beyond doubt. And yet it seems incredible that any lady should be guilty of such conduct. I exclaimed, almost repenting having allowed the previous remarks to pass my lips. Miss Rowley is undoubtedly a woman of principle, or good moral standing. Moral standing, principle! exclaimed Lady Holberton bitterly. Yes, where an autograph is concerned, Theodosia Rowley has all the principle of a magpie. Magpie, European bird known for stealing and hiding small bright objects. Whatever might have been the fact, it was clear at least that Lady Holberton's opinion was now unalterably made up. Remember, she is a butlerite, added the lady, thus putting the last touch to the circumstantial evidence against Miss Rowley. Weeks passed by. The advertisements remained unanswered. The police could give no information. Lady Holberton was in despair. The physicians declared that her health must eventually give way under the anxiety and disappointment consequent upon this melancholy affair. Much sympathy was felt for the afflicted lady, even Miss Rowley called often to condole, but she was never admitted. I could not see the crocodile, exclaimed Lady Holberton, quite thrown off her guard one day by the sight of Miss Rowley's card which she threw into the fire. Some consolation, however, appeared to be derived from the assiduous attentions of Mr. T., who personally admired Lady Holberton. At least he professed to do so, though some persons accused him of interested views, and aiming at her album rather than herself. But although his attentions were received, yet nothing could afford full consolation. At length, all other means failing, at the end of a month, it was proposed that two persons, mutual friends of Lady Holberton and Miss Rowley, should call on the latter lady and appeal privately to her sense of honour, to restore the autograph if it were actually in her possession. This plan was finally agreed on, but the very day it was to have been carried into execution, Miss Rowley left town, for an excursion in Finland. As for myself, I was also on the wing, and left London about the same time. The parting with Lady Holberton was melancholy, she was much depressed, and the physicians had recommended the waters of Weisbeiden. Mr. T. was also preparing for an excursion to Germany, and he was suspected of vacillating in his butlerite views, brought over by Lady Holberton's tears and logic. Returning to London some three months later, I found many of my former acquaintances were absent, but Lady Holberton, Miss Rowley, and Mr. T. were all in town again. The day after I arrived, it was Tuesday the twentieth of August, as I was walking along Piccadilly about five o'clock in the afternoon, my eye fell on the windows of Mr. Thorpe's great establishment. I was thinking over his last catalogue of autographs, when I happened to observe a plain, modest-looking young girl, casting a timid glance at the door. There was something anxious and hesitating in her manner, which attracted my attention. I accustomed, like most Americans, to assist a woman in any little difficulty, and with notions better suited perhaps to the meridian of Yankee lands than that of London. I asked if she were in any trouble. How richly was I rewarded for the act of good nature? She blushed and curtsied. Tuesday the twentieth of August. Does this date the final composition of the Lumley Autograph or of its setting? August twenty fell on a Tuesday in eighteen forty-four and eighteen fifty. Please, sir, is it true that they pay money for old letters at this place? They do. Have you anything of the kind to dispose of? Judge of my gratification, my amazement, when she produced the Lumley Autograph. Of course I instantly took it, at her own price, only half a guinea, and I further gave her Lady Hobarton's address that she might claim the liberal reward promised for the precious letter. Tears came into the poor child's eyes when she found what awaited her, and I may as well observe at once that this young girl proved to be the daughter of a poor, bedridden artisan of Clapham, who had seen better days, but was then in great want. It is an ill wind that blows no good luck, and the contest for the Lumley Autograph was a great advantage to the poor artisan and his family. The girl had picked up the paper early one morning in a road near Clapham, as she was going to her work. Lady Hobarton gave her a handful of guineas as the promised reward, a sum by the by just double in amount what the poor poet had received for his best poem, and she also continued to look after the family in their troubles. But to return to the important document itself, never can I forget the expressive gratitude that beamed on the fine countenance of Lady Hobarton when I restored it once more to her possession. She rapidly recovered her health and spirits, and it was generally reported that, seizing this favourable moment, Mr. T. had offered himself and his collection, and that both had been graciously accepted. Miss Rowley Culled, and a sort of pay platree, was made up between the ladies. A cargo of American autographs arrived, containing the letters of the Cherokee editor, the signed manual of governors and colonels without number, and I even succeeded in obtaining epistles from several noted rowdies, especially to gratify the ladies. Lady Hobarton made her selection, and the rest were divided between Miss Rowley and Mr. T. Joy at the recovery of the lovely autograph seemed to diffuse an unusual spirit of harmony among collectors. Many desirable exchanges were brought about, and things looked charmingly. Alas, how little were we prepared for what ensued! Pay platree, patched up peace, French. On the occasion of the presence in London of two illustrious royal travellers, Lady Hobarton gave a large party. So said the papers at least, but I knew better. It was chiefly to celebrate the recovery of the lovely autograph, and its restoration to her celebrated album that defeat was given. The album was produced, in spite of a half-formed vow of Lady Hobarton to the contrary, but then his royal highness, Prince Blanc Blanc, had particularly requested to see the letter of the poor poet, having heard it mentioned at dinner. The evening passed off brilliantly, their royal highnesses came, saw, and departed. The crowd followed them to another house, while a favored few, chiefly collectors, remained lingering about the table on which lay the album. I should have said earlier that Lady Hobarton had appointed a new office in her household, the very day after the loss of the lovely autograph. This was no other than a pretty little page, dressed in the old costume of a student of Padua, whose sole duty it was to watch over the album whenever it was removed from the rich and heavy case, in which it usually lay enshrined. He was the guard of the album, and was strictly enjoined never for one instant, to remove his eyes from the precious volume from the moment he was placed on duty, until relieved. Well, there we were, some dozen of us, collected about the table, Lady Hobarton looking triumphant, Mr. T., very proud, and there stood the page of the album, dressed in his Prutasoi gown, with eyes fastened on the book, according to orders, while he supported its gorgeous case in his arms. Some remark was made as to the extraordinary manner in which the precious autograph had been lost, and then found again. My blood actually boiled as one of the company turned to me, and asked in a suspicious tone, if I did not know more of its history than I chose to converse. My indignation was boundless, fortunately I could produce the friend walking with me in Piccadilly, and the artisan's family at Clapham, as witnesses in my favour. Miss Rowley was standing near me at the moment. Prutasoi, a strong corded or gross grain, silk fabric, traditionally associated with Padua Italy. Still, Mr. Howard, observed that lady, I really cannot see why you should resent the insinuation so warmly. Now, do you know, I am not at all sorry to have it in my power, to declare that I have some knowledge of the fate of the paper during its eclipse. All eyes were instantly fixed on the speaker. The lady smiled and continued, Lady Halberton thinks the lonely autograph was stolen. I understand she even thought it was stolen by myself. She here turned deliberately toward our hostess, who looked uneasy. If such were your suspicions, Lady Halberton, continued Miss Rowley, speaking with great deliberation, I am happy to say that they were quite correct. You only did me justice. I am proud to declare the deed was mine. We were all speechless at hearing this sudden and bold avowal.  So long as the treasure was mine, the consciousness of possessing it was sufficient in itself. But having afterward lost it from my pockets by unpardonable carelessness, I shall at least now glory in the daring deed which made it once my own. Conceive the amazement which these remarks, delivered with calm enthusiasm, produced among the listening circle. We all know that high crimes and misdemeanors enough are committed by men and women too, but somehow or other the delinquents are not often given to talking of them. They would just as leave in general that the act should not be known. The effect of Miss Rowley's words was different on different individuals. As for myself, I voluntarily felt for the handkerchief in my pocket. The page of the album drew nearer. Lady Halberton looked aghast as though she had seen a cannibal. Some bit their lips, others opened their eyes. Mr. T., however, who held the album at the moment, and was bending over it when Miss Rowley began her extraordinary disclosure, raised his eyes, fixed his glasses on the fair speaker, and sent through them such a glance as no words can fully describe. It was a glance of intense admiration. What exalted views! What sublime sentiments! he exclaimed in an estacy. But Mr. T.'s blaze of admiration was not the only flame at work, while he was gazing at the heroine of the moment. In a sudden burst of enthusiasm roused by the fair perloiner, he forgot all else. The precious volume in his hand drooped, touched the flame of a wax light on the table, and in another instant the great Halberton album, that album of European reputation, was burning before our eyes. Its invaluable leaves were curling and blackening, and smoking under the devouring flame. A shriek from Lady Halberton, an unearthly cry from the page of the album. Both echoed by the spectators, came too late. The volume was half consumed. Of the Lumley autograph, not a line remained. Such was the ill-fated end of the letter of the poor starving poet. It was written amid gloom and distress. Its career closed in a stormy hour. The loss of the album, of course, broke off the engagement between Lady Halberton and Mr. T. This, however, could scarcely have been regretted under the circumstances, for their union, after the catastrophe, must have been one long series of miserable reproaches. The sudden change in Mr. T's feelings toward Miss Rowley was not a momentary one. The admiration first kindled by that lady's bold declaration grew to be the strongest sentiment of his heart, and only a few weeks later he was made the happiest of men by receiving as his own the fair hand which accompanied the deed. Miss Rowley and Mr. T. were united in the bands of matrimony and collectorship. Lady Halberton was still inconsolable when I left Lonten. She was thinking of travelling among the Hottentots, or in any other climb where albums are unknown, and her loss could be forgotten. The journey to Cafirland was, however, postponed until the next change of ministry, and I have learned recently that the lady has so far recovered her spirits as to be thinking of an omnibus. The very last packet, indeed, brought a flattering application to myself. Lady Halberton graciously declaring that the name of Jonathan Howard is not only valued by herself as that of a friend, but interesting to collectors generally, as having been once connected with the much lamented document now lost to the world, the letter of the poor starving poet known as the Lumley autograph. Omnibus, in this context, an omnibus bill, i.e., one dealing with a variety of subjects, in Parliament.


Most of this information comes from publication 946 how to depreciate property tax year 2022 you can find on the IRS website irs.gov irs.gov looking at the income tax formula we're focused online one income remember in the first half of the income tax formula is in essence an income statement but just an outline of scaffolding other forms and schedules flowing into these line items one of those being the schedule C the schedule C being an essence and income statement in and of its health business income minus business expenses gets to the net business income which flows in to line one income of the income tax formula we see here looking at the first page of the form 1040 noting that the schedule C flows into the schedule one which flows into page one of the form 1040 line number eight schedule C profit or loss from business has an income statement format income minus expenses we are focused here on the expense side of things looking specifically at the depreciation depreciation being and a cruel concept we're forced to deal with even if we're on a cashed based system because we have to put it on the books as an asset in essence according to the tax code allocate the cost over the useful life although we might have some special depreciation some 179 depreciation that could muddy up the waters so given that when does depreciation begin and end you might think it's a straightforward type of question here because you would think it would begin when you buy the equipment or whatever it is you're purchasing that you have to depreciate but it can be a little bit confusing in terms of when you're going to actually put that into operations and when you look at the conventions being used you might have different conventions like a half-year convention or a mid-month convention when you purchase certain types of depreciable property so when does the depreciation actually start can be somewhat more confusing than you would think at first so you begin to depreciate your property when you place it in service for use in your trade or business or for the production of income so clearly why are we buying the stuff it's an ordinary and business ordinary and necessary type of thing for business or related to consuming it for an ordinary or necessary purpose that's why it would be an expense so when we put it in place for the production of income revenue generation being our business goal then you would think that would be when you're going to put it on the books as a depreciable item so you stop depreciating property either when you have fully recovered your cost or other basis or when you retire it from service whichever happens first so if we purchase something for like let's say just $100,000 for a round number then we're going to put it on the books when we put the piece of equipment in service in service for use in our trade or business meaning for example if you had to include shipping costs or something like that in order to get it ready and in service then you would include it at the point in time that it's in service for business use then again you might use different methods to account for the depreciation in terms of when does the accounting calculation basically start is are you using a mid-month or mid-year convention depending on what's required or what options we have from the tax code and then of course you're trying to allocate that $100,000 over the useful life that's the general accounting concept meaning the cost should be allocated to the same period it was used to consume to generate revenue but the tax code could accelerate the depreciation for reasons other than generally accepted accounting or accounting principles to try to stimulate the economy using accelerated methods in the first years for example makers is a double declining balance method and then they might use 179 deduction special depreciation to deduct more upfront the general idea then would be after you've allocated the full $100,000 in that example you can't keep on depreciating after that point in time even if you're still using the piece of equipment in business which is likely if they allow you this big accelerated depreciation type of method because you can't depreciate more than the equipment actually costs that would be the general idea so you're going to fully depreciate the equipment over its useful life or whatever depreciable property you have or you might dispose of it before that time which means you might either sell it or you might just dispose of it just throw it away before it's been fully depreciated at which point you've got to calculate what's going to happen at that point in time in terms of possibly a gain or a loss at the point of sale or disposition okay


I'm laughing from Colorado State University on the asymptotics of orthogonal polynomials ensemble via integrable methods. Can you hear me? Thank you, Marco. And I'd like to thank the organizers, Andre, Sasha, Tamara, Alice, and Sergei. Thank you very much for inviting me. Beautiful place. A lot of great friends, so thanks. So I couldn't actually decide what, I'm not working in this exact area right now. And so I wasn't sure what to talk about. But then I decided I would talk about orthogonal polynomial ensembles and their asymptotics via integrable methods, mostly because of Sasha's lectures on determinant point processes. And this is sort of the integrable connection to that. This is a review of kind of old work of Jinho, Baik, Thomas Krikabauer, myself, and Peter Miller. But there's, well, maybe interesting reasons to reconsider this work. OK. But it is supposed to be introductory, and so ask questions if you have any. And I'll try to keep a monotone so that you can, if you wish, sleep. OK. So at the top of the screen is the orthogonal polynomial of degree J. The coefficients are disgusting, but the leading coefficient, kappa jj, is positive. And they all depend upon a parameter n. And so there's usually the superscript n floating around. Sometimes that will be there, and sometimes that will have forgotten to latech it. And then the orthogonality is, today, for the next 45 minutes, it will either be on the real axis or it will be on a discrete set. And so these points are called the nodes. And there are n nodes, and they started index 0 and go through index n minus 1. And if you're on a discrete set, then the orthogonality condition is this condition here. So that is really an integral, but it's a discrete sum instead of an integral. And let's see the first, let's see. This should be m. That letter should be m. My apologies. I think the first two slides had no typos. Yeah, right. But I did say that sometimes that wouldn't appear. So yeah, OK. And the interest is in studying the behavior of these polynomials when degree n and parameter capital n go to infinity. And a goal is the uniform axiomatic description for all z in the plane. And these are the applications. I wrote down the applications thinking of the discrete case. So I'll spend most of the time talking about its discrete orthogonal polynomials. And so, well, the first application is not discrete, it's random matrix theory. And you can compute the asymptotics of any statistical quantities in sight for unitary and variant ensembles using orthogonal polynomials. And then the rest of the examples are really, I guess, they're either discrete orthogonal polynomial applications or orthogonal polynomials on a curve in the plane, OK? Now, so we're thinking about them as generating ensembles of random variables. So you think that lambda, which is a vector up there, lambda 1 through lambda n, is either it's living in the real axis or the individual entries are living in this node set. And in the case that you're living in the real axis, lambda has a probability density given by this formula there. And we've encountered that a lot today and yesterday. So I won't speak too much about that. In the discrete case, here's the probabilistic interpretation. The probability that there are particles at locations x1 up through xk is given by this formula here. And the x1 through xk have to be in this collection of node points, OK? k should be less than capital N, so that it makes sense, OK? And the typical behavior, the typical question is to ask what's going on when capital N is growing to infinity, k is growing to infinity, and the ratio is going to a constant c, which is less than 1. If c were to equal 1, then you wouldn't be random. All the particles would be sitting at all of the node sites, and there'd be nothing random going on. And with, yes, OK. So this is just up there as a repeat of what I had in the previous slide. The probability that there are particles at the sites x1 through xk is given by this formula. And n is going to be growing to infinity. And the weights, so on the two or three slides ago, I wrote down an orthogonal polynomial, discrete orthogonal polynomial here. And I had these weights, which should have been wn comma m, OK? The m goes with the node. So each node has a weight, OK? If you have all of these weights at the nodes, then you can really think of as a function w of x, where x is living on the nodes. And you have to pick, given an x in the nodes, you find the j corresponding to x, and that's how you define the weight function, OK? If there are k particles at these locations, and I've got a total of n nodes, then there are n minus k holes at the complementary nodes. And I guess I labeled those y1 through y sub n minus k. And so that gives me x1 through xk. And all the rest of the locations, this has to be the entire collection of possible nodes. And the reason I'm saying that is because, oops, I'm moving too fast. You can also ask, what's the probability that there are n minus k holes at these locations? Of course, it's got to be the same thing as that probability. But you can rewrite the formula in this way, where now instead of thinking of the locations of the x's, you can write down a probability measure using the locations of the y's. And that k bar means n minus k. And that k bar means n minus k. And you have a different weight function. So this weight w bar is related to the old weight by this formula here, OK? So there's really, there's particles, and there's holes. And those are two collections of particles. And they're dual to each other for obvious reasons, OK? So a simple example of what kind of questions you might ask, the product of what two things is one. No, the two probabilities are equal, right? They're equal, yeah. So the first thing you might ask about is this random variable at the top of the screen. I should use the laser to point at it there, OK? The number of particles that are less than x. So that's a random variable. You can compute its average. Sorry, it's a fraction of particles less than x. And that is represented as an integral in the case of random matrix theory of a density function rho 1, which is written there in terms of orthogonal polynomials. So rho 1 is this function kn of xx. And the function kn is the function of two variables. It's called the reproducing kernel. And it's written there to sum over the first n minus 1 orthogonal polynomials. It's a projection kernel under the first n polynomials. OK, times the weight function. In the discrete case, what you have instead is a sum instead of an integral. But the function rho 1 that you're computing the sum of is built in the same way. It's a function knk of xx. And knk is this finite sum over the orthogonal polynomials. The sum stops at k minus 1. And that is right. So you're thinking I have a collection of k particles living on n nodes. And they can dance around. And you want to compute their statistics. And that's the formula for it. So you need to use the orthogonal polynomials up to degree k, or degree k minus 1. Good. And as I pointed out before, or maybe I said it and didn't explain it. But a lot of statistical properties can be expressed in terms of the orthogonal polynomials. So this is a slight generalization of what I wrote before, but it's basically the average of 1 over n times the sum of functions evaluated at the eigenvalues of a random matrix can be expressed as the integral of f times rho 1. And if you're in the discrete case, it's this sum. That's pretty cool. And then the variance of the same random variable is expressed in this way. Again, all in terms of the orthogonal polynomials. If you're in the discrete case, the integrals are just sums. And if you ask for the probability of having no eigenvalues in an interval a, b, it's a Fred Holm determinant of 1 minus kn, calligraphic k subscript n. And that is an integral operator whose kernel is kn, but it's restricted to the interval a, b. And the only place where a, b appear on the right-hand side is that you're dealing with an operator on the interval a, b. And again, if you're in the discrete case, it's a operator on little l, 2, and it's a sum instead of an integral. Yeah, it depends on the problem at hand. But so you look at the equilibrium measure. And if the equilibrium measure achieves an upper constraint, then it's actually easier to look at the dual polynomials because there's no upper constraint achieved. Sometimes. Yeah, whichever equilibrium measure looks simpler, you use that one. But I'll show you an example, or a grotesque example, but you'll see what I mean. OK? Yeah, it's advantageous to find the one for which you need to do fewer machinations. OK? So the first application, OK, I'll go through this quickly, but we've heard a lot about this. But the first application of orthogonal polynomial ensembles is unitary invariant, or the unitary ensemble of random matrices. So that means that the matrix entries aren't independent, and I must use a measure more or less like this. You start with a measure on matrices, but I've written it down already on the eigenvalues. And the very first thing that you have to do if you're going to compute anything is understand the equilibrium measure. And so here's the first, it's a well-known fact that the mean, the average density of eigenvalues converges to a function psi, and it's actually the density of a probability measure. And the function psi solves a well-known variational problem. I pose it here in terms of over the space of probability measures. You try to find the maximum of this functional. OK? Now if v is convex, then you know that the measure that achieves this is a single interval.  But if you know that v is real analytic with suitable growth at infinity, then the density of the equilibrium measure is supported on finitely many intervals, and it's analytic on the interior of each one. I think it would be interesting, although nobody has, I don't think anyone knows how to do it quite yet, but it would be great to compute the asymptotic behavior or identify interesting phenomena if you have really an infinite gap situation somewhere. But that requires you build a special example where that's going to happen, and that would be cool, I guess, is the way to say it. Now a more refined, a more detailed asymptotic result, I'm referring to this one. This result here is asymptotic in n. A more detailed result is this version of universality. So you pick any a in the support of your equilibrium measure, so there's a point a. This is supposed to be the equilibrium measure, this curve there. And so psi is positive. Pick a where psi is positive and consider this probability. Probably no eigenvalues are in the interval a up to s divided by a parameter n times psi of a. So when n goes to infinity, this interval goes to 0. The density is positive, so you know there's going to be a lot of eigenvalues near a. And if you let the interval go to 0, then, well, so you might expect that there's very few eigenvalues in that small interval. And so you ask for something like the probability that there are no eigenvalues there. You might get a nontrivial answer. And there is the answer. As n goes to infinity, this probability converges to a Fredholm determinants of another interval operator with a sine kernel which we encountered in Alexei's talks. And the first version of universality is this doesn't depend upon a. And then the second version of universality is that it doesn't depend upon v. And then the more recent version of universality are that it works for Wigner type matrices and even more general things than that. So the first result of this kind was in 69 by Gaudan and Mehta. And then it was extended to the case of analytic functions and Lipschitz continuous functions and then even more esoteric functions by Doran Lubinsky. And in the direction of Wigner matrices and their brethren, there's this very fantastic group of people and results there that's only a smattering. But Laszlo showed us a table with which summarized all those results. So I will not go through so much detail on that. Thank you. And then you can also ask about the behavior of the largest eigenvalue. So up there, that was a computationally drawn image of the equilibrium measure in a two-cut case. And that's the upper, sort of the maximum of the support of the equilibrium measure is beta. And so it's easy to convince yourself that this is true. The probability that lambda n minus beta absolute value is bigger than epsilon goes to 0 when n goes to infinity. And the more refined result is up there. So you rescale by an n to the 2 thirds and this distribution function converges. First statement, it converges. Second statement, it's describable in terms of the panel of A2 transcendent. And that was established by, well, Forrester and Tracy Wittem, Forrester established, I guess, the limits existed and Harold and Craig figured out this powerful connection to integrable systems. Yeah, in this picture here, you mean I might have chosen a v which goes to the wrong infinity? There might be an outlier. What is it called that you call that? Yeah, that's true. So this is a, yeah. Sorry, think like that. When I said clear, I meant, oh, I'm thinking of the best possible case where basically there's no variational equality outside of this support set. Thanks, Elise. Sorry about that. OK.  You need convexity for that. OK. So I'm just summarizing that. The second application is sort of random tilings. And so I'll spend a little bit of time going through some examples of, an example of random tilings. And that's where you get, you're describing things in terms of discrete orthogonal polynomials. And so here is a hexagon, side lengths are A, B, and C. And inscribed within it is a triangular lattice, so everyone can see that. If you glue together rhombi along either that way or that way or that way, you get three different types of rhombi. And they've been named horizontal rhombi here, these two, and that's called the vertical rhombus. So you can ask questions like how many tilings are there. And there's a formula for that. That's the formula for the number of tilings that there are given parameters A, B, and C. And maybe an interesting question is the study of the limiting statistics of the tilings when the size of the hexagon goes to infinity. So that's a, I'm just choosing one particular asymptotic problem to study, where A, B, and C scale like a parameter N, and alpha, beta, and gamma are positive constants. So three examples, I guess I have to do that. Amazing, near this corner up here, all of the tiles seem to be green with the same orientation. And oh, that's true of this tiling and that tiling. And it turns out that as the hexagon gets larger and larger, that occurs with overwhelming probability. And one typically enjoys this picture where, OK, that's supposed to be sampled at random. And every single time you sample one of these with overwhelming probability, you see a picture like this, where there's this temperate region in the middle, and then there's a frozen region near the boundaries. And a boundary between them, which is apparently fluctuating from one realization to the next. And I've labeled then the draw vertical line. I've labeled the place where that vertical line enters the frozen region. That's called either C or X-top. Problem study fluctuations of that point on that line as the hexagon size goes to infinity. I forget why that's there, but let me skip it. So here is a picture. And it's an amazing fact that we learned from Kurt Johansson, that if I draw a vertical line right along this place where the middle of the location of any vertical rhombi, then I can put white dots at the bases of the vertical rhombi and black dots at all the other grid locations.  And you pick two different realizations, two different random tilings, but choose the same line. You will always get, along this line, you'll always get the same number of holes and the same number of particles. Their locations, of course, are not the same, and they're really a random configuration if you think that you have a collection of all possible random tilings, and they're equally weighted. OK? And so by selecting tilings at random and fixing this line, you can really think I'm looking at particles and holes, and one might like to study the statistics of the particles or the statistics of the distribution of the holes. OK? And a formula is on the top of the screen, then, that explains the probability of finding, I forget which, the tilde means which thing, particles. Particles at locations x1 through xc is given by this formula here, where so clearly it is an orthogonal polynomial ensemble that happens to be discreet with a finite number of nodes. And the number of nodes is going to grow as the size of your hexagon goes to infinity. And this weight is actually classical, so these polynomials, they're referred to as Han orthogonal polynomials. Yeah, so maybe it wasn't exactly because of this, Jinho and Peter and Thomas and I were interested in discreet orthogonal polynomials more or less because it was there. And we began working on the asymptotic behavior of discreet orthogonal polynomials and then learned about that connection. So this slide shows the Riemann-Hilbert problem and its solution in the continuous case. So for orthogonal polynomials on the real line, that might come from random matrix theory. So capital Y is a matrix. The first column contains the polynomials of degree J and J minus 1 with crazy normalization factors in the second entry. And in the first entry, that's actually just to make it so that the leading coefficient is 1 times z to the j. And then in the second column, you have basically the Cauchy transform of the first column times this weight function, e to the negative nv. And well, so the Cauchy transform satisfies boundary value relationships. And so you can summarize or you can characterize this matrix through these three conditions. You have a matrix valued function. The entries are analytic. In the upper and lower half plane, it behaves in this way as z goes to infinity, so identity plus a correction term times this matrix, e to the j, 0, 0, z to the minus j. And then on the real axis, it has good boundary values. And the boundary values from above and below are not the same. y plus being the boundary value from above, y minus from below, and they're related by what's called a jump relationship. And this matrix is called the jump matrix. So the three things there, they 1, 2, and 3 represent a problem, find y. And it's right there. That's the Riemann-Hilbert problem that characterizes orthogonal polynomials. And the solution is at the top. And so when you start computing asymptotic behavior of the solution of the Riemann-Hilbert problem, you extract information about the orthogonal polynomials. So in the discrete case, this is the Meromorphic Riemann-Hilbert problem at the bottom of the screen. And the solution is this at the top of the screen. It's really the same thing, except the integral is replaced by a sum. So that's the solution of this Meromorphic Riemann-Hilbert problem. And what you have is it's a function. OK, I wrote analytic in C take away R. It's actually Meromorphic in C take away R. It has poles at the nodes. And you can characterize the poles by saying that the residue at each node is given by the right-hand side of this equation. And if you read that, it implicitly is saying the first column has no residues. And I didn't write it carefully, but it's simple poles. And so if it has no residues, the first column is entire. And then the second column, the residues are multiple of the first column evaluated at the node. And so if you look up at the top, you see oh, at each, yeah, the Z should be, I forgot to change the denominator of my sum. So that should be, just so you can see it, the denominator up there should be x nl minus Z. Doesn't matter? Yeah, the right-hand side never uses a second column. It just says that the poles of the second column are obtained by multiples of the first column times the weight. I'm sorry about that. That should say x nl minus Z and x nl minus Z. So there's a pole at each x nl. So on the left is the Meromorphic Riemann-Hilbert problem. And on the right are the standing assumptions that we made in our work on discrete orthogonal polynomials. And so here they are. So there is a finite number of nodes. It's a discrete orthogonal polynomial system in which there's nodes that go from 0 to n minus 1. And capital N is fixed but getting large. And they're described by a density function rho 0 of x. And the nodes are actually defined through this formula right here. So you integrate from a up to xj, the density rho. And you choose the xj so that this integral equals 2j plus 1 over 2n. And that, because rho is assumed to be analytic, that gives you a very regular n positive. It gives you a very regular distribution of nodes. The one point to make is that if you have an infinite number of nodes, then the work that we did doesn't apply directly. And you have to do more gymnastics to make it work. And so the work that we've done does not include cases where there's infinitely many nodes, such as the Meichner-Charlier examples. The weights are defined in this kind of sick way. It's got an e to the negative nv that's natural. And then these terms, this product here and this negative one to the n, those we included because the weight and the dual weight, it's useful if they look the same. And so we put this extra disgusting product factor there so that both weight and dual weight had the same factor. So the product is not essential. But anyway, it's there, sadly. So I promised myself I wouldn't go through a Riemann-Hilbert analysis. So I just have one little picture to show you the first step. So if you look at the formula that appears there on the left, I'm taking the matrix y, which has poles. And I'm not doing anything to the first column of y. I'm multiplying by upper triangular matrix. It doesn't touch the first column of y. And the second column, what I'm doing then in the second column of r is I'm combining y and the first column of y, I'm combining the second column of y plus that sick factor times the first column of y. The sick factor has poles and they cancel the poles that appear in the second column of y. Do it one way in the upper half plane and then another way in the lower half plane. So this term, because I'm assuming that row zero is analytic, this term is a nice analytic function in the upper half plane. And I use a different sign down below, either the negative i pi times the integral down below. And they just happen to hit exactly the right number, what's 2 times pi times an integer at the nodes so they don't affect the pole. So whether I choose plus or minus, the poles have been eliminated and r is actually a function that has no poles left. It still has a jump on the real axis because of that exponential factor out in front, but it has no poles. And so you wind up with the Riemann-Hilbert problem on those three contours with no poles, and then the game is afoot. You just, if you like that sort of thing, you might start doing the rest of the steps in the asymptotic analysis of Riemann-Hilbert problems, which I won't go through. But here's a picture of an example of an equilibrium measure. And so the first thing you have to do in this sort of analysis is you seek the equilibrium measure, which is a probability measure that minimizes this functional. I changed the sign in the earlier. I had a negative sign here, and this was in the numerator. But you try to, and I was maximizing, but now you try to minimize this functional. And the discreteness has an effect. So you minimize this subject to the constraint that all measures are actually bounded. So they're positive, but they're a probability measure, so I don't need to really talk about that. But on this side, all of the measures that you consider have to be bounded from above by the density of nodes, OK, rescaled because you only have k particles, not n particles. Yeah, phi is v minus the term from the product, but think it's just the external field. So then in the asymptotics of discrete orthogonal polynomials and the asymptotics of things like the continuum limit of the total lattice, this upper constraint is both a blessing and a curse because it's bounded, which helps with the analysis a lot. If it's bounded from above, you're easier to prove existence and stuff. But on the other hand, you can have, so here's a picture. The solid curve is the density of the equilibrium measure, and there's a dotted curve, which is the upper constraint rho 0 divided by x. And you don't see the dotted curve sometimes because the upper constraint is achieved by the equilibrium measure. So this is a region where the equilibrium measure hits the upper constraint, and here is a place where the equilibrium measure is like neither 0 nor hidden in the upper constraint, and it typically vanishes at those places like a square root. And then it comes back to the upper constraint, and then, OK, it goes all the way down to hit 0. And so we picked an example that was quite grotesque, but that's the typical behavior you would expect. Places where the constraint is active and places where you hit that the equilibrium measure is 0, where you don't expect to find any particles, and then separated by places where the equilibrium measure is sort of freely determined by the energy constraints. And there's a lot of interesting potential theory. So you could wonder, does it happen ever that your equilibrium measure jumps from the upper constraint to 0? And the answer is not unless something really sick happens. So if you have a nice analytic external field and a nice analytic upper constraint, then in order to jump from one to the other, it has to be a band where you have a discontinuity. That's all I'm trying to say. OK, in order to have a finite number of, sorry, it's going to take me a second to say it right, I should consider both the measure and the dual measure. So if I want to know that the measure has finally many places where the constraints, upper and lower, are active, and finally many places where it's not, and the same thing is true of the dual, then I need everything analytic. And there's no results other than that that I know of. Except probably convexity would give you everything in sight, but you need analyticity to rule out infinite gap situations. So yeah, I couldn't do it off the top of my head right now, but yeah, like upper constraints really become lower constraints, and lower constraints become uppercut. It just flips, you just flip it. I mean, the reason is because there are holes in particles and the union of them is the entire node set. So if you know your particles are doing this, then the holes have to be doing the opposite. If you think intuitively, what this means is that every node, there is a zero of the orthogonal polynomials right next to each node. And that means that for the dual, there's no zeros near those nodes. Similarly for the dual, there'd be lots of zeros occupying those nodes. So it's really flipped it. So if you find that you have a situation where one of the constraints is not active, like for example, you can imagine a case where you have the upper constraint active, and then there's a free region, but you never hit the lower constraint. In that case, it's actually convenient to use the dual. But we picked this sort of because it's maximally nasty. So I'm just stating some results. So here's a collection of node points up there. Bn is nodes xn, j, xn, j plus k1, xn, j plus k2. So the k1, k2, up through k sub m minus 1, those are all fixed integers. And these are nodes, and you fix them. And xn, j is going to converge to some value x. And I want to pick that value x to be someplace where neither constraint is active, so someplace in this zone here, or someplace in this zone here. And because these are finite integers, all of these nodes are in this band, active band. And then you can ask the question, what is the probability that precisely m particles are living in this set Bn? Asymptotically as n goes to infinity. And there's a formula for it. 1 over m factorial, that's the number of particles, right? Could be capital M, I guess. No, sorry, m, little m. 1 over m factorial, derivative raised to the mth power evaluated at t equals 1 of this Fredholm determinant where s is an integral operator with this kernel. So now s is still a discrete operator. I think Sasha showed it to us earlier today. As he was telling us, it squashed a little bit, depending upon where you are. So this coefficient there is the contribution from the equilibrium measure, the local density of eigenvalues. So capital M, the set Bn contains capital M nodes. Capital M is fixed. Yeah, built of the discrete sine kernel, OK? So that's sort of local universality, right? And then if you look at an edge, so you have to know that the end points are next to a void so that you know you're going to have a largest eigenvalue, a largest particle that's allowed to fly around. And so if you're endpoint A, the left-hand endpoint of your node set, is adjacent to a void, you check that with the equilibrium measure, then you can ask for the distribution of the leftmost particle and you get the tracy-widim distribution in that case in the similarly for the right-hand endpoint. So this picture, the left-hand endpoint, is not adjacent to a void. So this example, you would not have tracy-widim for the particles there, but the right-hand endpoint is adjacent to a void and so the largest particle is going to fluctuate around here and the fluctuations will be given by the tracy-widim law, OK? There are constants which are defined up there, but I won't annoy you with that. But there's also the tracy-widim distribution for the location of the leftmost and rightmost holes. So if A is adjacent to a saturated region, as it is in this picture here, then the distribution of the leftmost hole is also given by the tracy-widim law, OK? That's a case where you go to the dual to prove that. And so if you go back and apply that to the random tiling problem up there, you see, so C star is the location of where the random boundary hits the vertical line and n beta is supposed to be the intersection of the Arctic circle with the vertical line and the probability under correct rescaling converges to the tracy-widim law. So interesting directions. So what I described was really sort of an optimal situation regarding the nodes and the external field. If the nodes are not so regular, so for example, the case of q-orthogonal polynomials, the node set is drastically different than the types of nodes that we considered. And it would be great to work out the asymptotic behavior of orthogonal polynomials that were sort of q, like the q-raka polynomials or something like that. Or even if you just said, OK, I want to consider a case where there are infinitely many nodes. Pavel Blecher and Carl Likti considered that situation. And in order to apply it to the six-vertex model, a couple of the parameter regimes they needed, discrete orthogonal polynomials, the weight was e to the negative x squared and x was on the integers, so doubly infinite situation. If the node density vanishes at the endpoints, that is a case where you're going to have active upper constraints at the endpoints. And so that's an interesting case to consider that it hasn't been worked out. We assume the node density was positive up to and including the endpoints. And then a last thing is if you take the GUE beta, I wrote L of 0 because we might think of that as initial data for the total lattice. But the diagonal entries that I wrote there are independent normally distributed random variables. And the chi's that appear off diagonal are chi random variable with parameter k. And it's known that everything is known about this example, that the eigenvalue distribution is exactly GUE beta. And you even know a lot about the eigenvector distribution. And here's an interesting observation. So the quantity pL of lambda is defined by what I wrote there, vL plus 1 divided by vL. The vL plus 1, those are the elements of the eigenvector with eigenvalue lambda. So that ratio is a discrete orthogonal polynomial with respect to a random measure that's generated by that Jacobi matrix. And while it would be very interesting to understand something about asymptotics of those discrete and random orthogonal polynomials.