12. As when some great painter dips his pencil in the gloom of earth, earthquake and eclipse, Shelly's revolt of Islam. Reader, who have thus far accompanied me, I must request your attention to a brief explanatory note on three points. One, for several reasons I have not been able to compose the notes for this part of my narrative into any regular and connected shape. I give the notes disjointed as I find them, or have now drawn them up from memory. Some of them point to their own date. Some I have dated, and some are undated. Whenever it could answer my purpose to transplant them from the natural or chronological order, I have not scrupled to do so. Sometimes I speak in the present, sometimes in the past tense. Few of the notes, perhaps, were written exactly at the period of time to which they relate, but this can little affect their accuracy as the impressions were such that they can never fade from my mind. Which has been omitted. I could not, without effort, constrain myself to the task of either recalling or constructing into a regular narrative the whole birthing of horrors which lies upon my brain. This feeling, partly, I plead in excuse, and partly that I am now in London, and am a helpless sort of person, and cannot even arrange his own papers without assistance, and I am separated from the hands which I won't to perform for me the offices of an emmanuensis. Two, you will think, perhaps, that I am too confidential and communicative of my own private history. It may be so, but my way of writing is rather to think aloud and follow my own humours than much to consider who is listening to me. And if I stop to consider what is proper to be said to this or that person, I shall soon come to doubt whether any part at all is proper. The fact is, I place myself at a distance of fifteen or twenty years ahead of this time, and suppose myself writing to those who will be interested about me hereafter, and wishing to have some record of time the entire history of which no one can know but myself. I do it as fully as I am able, with the efforts I am now capable of making, because I know not whether I can ever find time to do it again. Three, it will occur to you often to ask, why did I not release myself from the horrors of opium by leaving it off or diminishing it? To this I must answer briefly. It might be supposed that I yielded to the fascinations of opium too easily. It cannot be supposed that any man can be charmed by its terrors. The reader may be sure, therefore, that I made attempts innumerable to reduce the quantity. I add that those who witnessed the agonies of those attempts, and not myself, were the first to beg me to desist. But could not have I reduced it a drop a day, or by adding water, have bisected or trisected a drop? A thousand drops bisected would thus have taken nearly six years to reduce, and that would certainly not have answered. But this is a common mistake of those who know nothing of opium experimentally. I appeal to those who do, whether it is not always found, that down to a certain point it can be reduced with ease, and even with pleasure. But that after that point further reduction causes intense suffering. Yes, say many thoughtless persons who know not what they are talking of, you will suffer a little low spirits and dejection for a few days. I answer no. There is nothing like low spirits. On the contrary, the mere animal spirits are uncommonly raised. The pulse is improved, the health is better. It is not there that the suffering lies. It has no resemblance to the sufferings caused by renouncing wine. It is a state of unutterable irritation of stomach, which surely is not much like dejection, accompanied by intense perspirations, and feelings such as I shall not attempt to describe without more space at my command. I shall now enter in medias race, and shall anticipate from a time when my opium pains might be said to be at their acme, an account of their pausing effects on the intellectual faculties. My studies have now been long interrupted. I cannot read to myself with any pleasure, hardly with a moment's endurance. Yet I read aloud sometimes for the pleasure of others, because reading is an accomplishment of mine, and in the slang use of the word accomplishment as a superficial and ornamental attainment, almost the only one I possess. And formally, if I had any vanity at all connected with any endowment or attainment of mine, it was with this, for I had observed that no accomplishment was so rare.  Reads vilely, and Mrs. Ha, who is so celebrated, can read nothing well but dramatic compositions. Milton, she cannot read sufferably. People in general either read poetry without any passion at all, or else overstep the modesty of nature, and read not like scholars. Of late, if I have felt moved by anything, it has been by the grand lamentations of Samson agonistis, or the great harmonies of the satanic speeches in paradise regained, when read aloud by myself. A young lady sometimes comes and drinks tea with us. At her request and Ems, I now and then read W's poems to them. W, by the by, is the only poet I ever met who could read his own verses. Often indeed he reads admirably. For nearly two years I believe that I read no book but one, and I owe it to the author in discharge of a great debt of gratitude to mention what that was. The sublimer and more passionate poets I still read, as I have said by snatches and occasionally. But my proper vocation, as I well know, was the exercise of the analytic understanding. Now, for the most part, analytic studies are continuous, and not to be pursued by fits and starts, or fragmentary efforts. Mathematics, for instance, intellectual philosophy, etc., were all become insupportable to me. I shrunk from them with a sense of powerless and infantine feebleness that gave me an anguish the greater from remembering the time when I grappled with them to my own hourly delight. And for this further reason, because I had devoted the labour of my whole life, and had dedicated my intellect, blossoms and fruits, to the slow and elaborate toil of constructing one single work, to which I had presumed to give the title of an unfinished work of spinosas, vis de emendatione umani intelectus. This was now lying locked up as piefrost, like any Spanish bridge or aqueduct, begun upon two greater scale for the resources of the architect. And instead of reviving me as a monument of wishes at least, and aspirations, and a life of labour dedicated to the exultation of human nature, in that way in which God had best fitted me to promote so great an object, it was likely to stand a memorial to my children of hopes defeated, of baffled efforts, of materials uselessly accumulated, of foundations laid that were never to support a superstructure, of the grief and the ruin of the architect. In this state of imbecility, I had, for amusement, turned my attention to political economy. My understanding, which formerly had been as active and restless as a hyena, could not, I suppose, so long as I lived at all, sink into utter lethargy. And political economy offers this advantage to a person in my state, that though it is eminently an organic science, no part, that is to say, but what acts on the whole, as the whole again reacts on each part, yet the several parts may be detached and contemplated singly. Great as was the prostration of my powers at this time, yet I could not forget my knowledge, and my understanding had been for too many years intimate with severe thinkers, with logic, and the great masters of knowledge, not to be aware of the utter feebleness of the main herd of modern economists. I had been led in 1811 to look into loads of books and pamphlets on many branches of economy, and at my desire M sometimes read to me chapters from more recent works or parts of parliamentary debates. I saw that these were generally the very dregs and rinsings of the human intellect, and that any man of sound head, and practised in wielding logic with a scholastic adroitness, might take up the whole academy of modern economists, and throttle them between heaven and earth with his finger and thumb, or pray their fungus heads to powder with a lady's fan. At length, in 1819, a friend in Edinburgh sent me down Mr Ricardo's book, and recurring to my own prophetic anticipation of the advent of some legislator for this science, I said before I had finished the first chapter, Thou Art the Man. Wonder and curiosity were emotions that had long been dead in me. Yet I wondered once more. I wondered at myself that I could once again be stimulated to the effort of reading, and much more I wondered at the book. Had this profound work been really written in England during the nineteenth century, was it possible? I supposed thinking had been extinct in England. Could it be that an Englishman, and he not in academic bowers, but oppressed by mercantile and senatorial cares, had accomplished what all the universities of Europe, and a century of thought, had failed even to advance by one hair's breadth? All other writers had been crushed and overlaid by the enormous weight of facts and documents. Mr Ricardo had deduced our priori from the understanding itself, laws which first gave a ray of light into the unwieldy chaos of materials, and had constructed what had been but a collection of tentative discussions into a science of regular proportions, now first standing on an eternal basis. Thus did one single work of a profound understanding avail to give me a pleasure and an activity which I had not known for years. It roused me even to write, or at least dictate, what Emma wrote for me. It seemed to me that some important truths had escaped even the inevitable eye of Mr Ricardo, and as these were for the most part of such a nature that I could express or illustrate them more briefly and elegantly by algebraic symbols, and in the usual clumsy and loitering diction of economists, the whole would not have filled a pocketbook. And being so brief, with Emma for my amanuensis, even at this time, incapable as I was of all general exertion, I drew up my prolegomena to all future systems of political economy. I hope it will not be found redolent of opium, though indeed to most people the subject is a sufficient opiate. This exertion, however, was but a temporary flash, as the sequel showed, for I designed to publish my work. Arrangements were made at a provincial press, about 18 miles distant, for printing it. An additional compositor was retained for some days on this account. The work was even twice advertised, and I was in amanu pledged to the fulfilment of my intention. But I had a preface to write, and a dedication, which I wished to make a splendid one, to Mr Ricardo. I found myself quite unable to accomplish all this. The arrangements were countermanded, the compositor dismissed, and my prolegomena rested peacefully by the side of its elder and more dignified brother. End of section 12. Recording by Martin Giesen in Hazelmere Surrey. Sections 13 of Confessions of an English Opium Eater. This LibriVox recording is in the public domain. Recording by Martin Giesen. Confessions of an English Opium Eater by Thomas De Quincey. Section 13. I have thus described and illustrated my intellectual torpor in terms that apply more or less to every part of the four years during which I was under the Cercian spells of opium. But for misery and suffering I might indeed be said to have existed in a dormant state. I seldom could prevail on myself to write a letter. An answer of a few words to any that I received was the utmost that I could accomplish, and often that not until the letter had lain weeks or even months on my writing table. Without the aid of M, all records of bills paid or to be paid must have perished, and my whole domestic economy, whatever became of political economy, must have gone into irretrievable confusion. I shall not afterwards allude to this part of the case. It is one however which the opium eater will find in the end as oppressive and tormenting as any other from the sense of incapacity and feebleness, from the direct embarrassments incident to the neglect or procrastination of each day's appropriate duties, and from the remorse which must often exasperate the stings of these evils to a reflective and conscientious mind. The opium eater loses none of his moral sensibilities or aspirations. He wishes and longs as earnestly as ever to realize what he believes possible, and feels to be exacted by duty. But his intellectual apprehension of what is possible infinitely outruns his power, not of execution only, but even of power to attempt. He lies under the weight of incubus and nightmare. He lies inside of all that he would feign perform, just as a man forcibly confined to his bed by the mortal languor of a relaxing disease, who is compelled to witness injury or outrage, offered to some object of his tenderest love. He curses the spells which chain him down from motion. He would lay down his life if he might, but get up and walk. But he is powerless as an infant, and cannot even attempt to rise. I now pass to what is the main subject of these latter confessions, to the history and journal of what took place in my dreams, for these were the immediate and proximate cause of my acutist suffering. The first notice I had of any important change going on in this part of my physical economy was from the reawakening of a state of eye, generally incident to childhood, or exalted states of irritability. I know not whether my reader is aware that many children, perhaps most, have a power of painting, as it were, upon the darkness, all the sorts of phantoms. In some that power is simply a mechanical affection of the eye. Others have a voluntary or semi-voluntary power to dismiss or summon them, or as a child once said to me when I questioned him on this matter, I can tell them to go, and they go, but sometimes they come when I don't tell them to come. Whereupon I told him that he had almost as unlimited a command over apparitions as a Roman centurion over his soldiers. In the middle of 1817 I think it was that this faculty became positively distressing to me. At night when I lay awake in bed vast processions passed along in mournful pomp, freezes of never-ending stories that to my feelings were as sad and solemn as if they were stories drawn from the times before Oedipus or Priam, before Tyre, before Memphis, and at the same time a corresponding change took place in my dreams. A theatre seemed suddenly opened and lighted up within my brain, which presented nightly spectacles of more than earthly splendour, and the four following facts may be mentioned as noticeable at this time. One, that as the creative state of the eye increased, a sympathy seemed to arise between the waking and the dreaming states of the brain in one point. That whatsoever I happened to call up and to trace by a voluntary act upon the darkness was very apt to transfer itself to my dreams, so that I feared to exercise this faculty. For has Midas turned all things to gold that yet baffled his hopes and defrauded his human desires, so whatsoever things capable of being visually represented I did but think of in the darkness immediately shaped themselves into phantoms of the eye, and by a process apparently no less inevitable, when thus once traced in faint and visionary colours, like writings in sympathetic ink, they were drawn out by the fierce chemistry of my dreams into insufferable splendour that fretted my heart. Two, for this and all other changes in my dreams were accompanied by deep-seated anxiety and gloomy melancholy, such as are wholly incommunicable by words. I seemed every night to descend, not metaphorically, but literally to descend into chasms and sunless abysses, depths below depths, from which it seemed hopeless that I could ever re-ascend. Nor did I, by waking, feel that I had re-ascended. This I do not dwell upon, because the state of gloom which attended these gorgeous spectacles amounting at last to utter darkness as of some suicidal despondency cannot be approached by words. Three, the sense of space, and in the end the sense of time, were both powerfully affected. Buildings, landscapes, etc., were exhibited in proportion so vast as the bodily eye is not fitted to receive. Space swelled and was amplified to an extent of unutterable infinity. This, however, did not disturb me so much as the vast expansion of time. I sometimes seemed to have lived for seventy or a hundred years in one night. Nay, sometimes had feelings representative of a millennium past in that time, or, however, of a duration far beyond the limits of any human experience. Four, the minutest incidents of childhood, or forgotten scenes of later years, were often revived. I could not be said to recollect them, for if I had been told of them when waking, I should not have been able to acknowledge them as parts of my past experience, but placed as they were before me in dreams like intuitions, and clothed in all their evanescent circumstances and accompanying feelings, I recognised them instantaneously. I was once told by a near relative of mine that having in her childhood fallen into a river, and being on the very verge of death but for the critical assistance which reached her, she saw in a moment her whole life in its minutest incidents arrayed before her simultaneously as in a mirror, and she had a faculty developed as suddenly for comprehending the whole and every part. This from some opium experiences of mine I can believe. I have indeed seen the same thing asserted twice in modern books, and accompanied by a remark which I am convinced is true, vis that the dread book of account which the scriptures speak of is in fact the mind itself of each individual. Of this at least I feel assured that there is no such thing as forgetting possible to the mind. A thousand accidents may and will interpose a veil between our present consciousness and the secret inscriptions on the mind. Accidents of the same sort will also rend away this veil. But alike, whether veiled or unveiled, the inscription remains forever, just as the stars seem to withdraw before the common light of day, whereas in fact we all know that it is the light which is drawn over them as a veil, and that they are waiting to be revealed when the obscuring daylight shall have withdrawn. Having noticed these four facts as memorably distinguishing my dreams from those of health, I shall now cite a case illustrative of the first fact, and shall then cite any others that I remember, either in their chronological order, or any other that may give them more effect as pictures to the reader. I had been in youth, and even since, for occasional amusement, a great reader of Livy, whom I confess that I prefer both for style and matter to any other of the Roman historians. And I had often felt as most solemn and appalling sounds, and most emphatically representative of the majesty of the Roman people, the two words so often occurring in Livy, consul Romanus, especially when the consul is introduced in his military character. I mean to say that the words king, sultan, regent, etc., or any other titles of those who embody in their own persons the collective majesty of a great people, had less power over my reverential feelings. I had also, though no great reader of history, made myself minutely and critically familiar with one period of English history, this the period of the parliamentary war. Having been attracted by the moral grander of some who figured in that day, and by the many interesting memoirs which survive those unquiet times. Both these parts of my lighter reading, having furnished me often with matter of reflection, now furnished me with matter for my dreams. Often I used to see, after painting upon the blank darkness, a sort of rehearsal whilst waking, a crowd of ladies, and perhaps a festival and dances. And I heard it said, or I said to myself, these are English ladies from the unhappy times of Charles I. These are the wives and the daughters of those who met in peace, and sat at the same table, and were allied by marriage or by blood. And yet, after a certain day in August 1642, never smiled upon each other again, nor met but in the field of battle, and at Marston Moor, at Newbury or at Naysby, cut asunder all ties of love by the cruel sabre, and washed away in blood the memory of ancient friendship. The ladies danced, and looked as lovely as at the court of George IV. Yet I knew even in my dream that they had been in the grave for nearly two centuries. This pageant would suddenly dissolve, and at a clapping of hands would be heard the heart-quaking sound of Consul Romanos, and immediately came sweeping by in gorgeous paludiments, Paulus or Marius, girt round by a company of centurions, with the crimson tunic hoisted on a spear, and followed by the alalagmos yelling of the Roman legions. End of section 13. Recording by Martin Giesen in Hazelmere Surrey, Section 14 of Confessions of an English Opium Eater. This Librivox recording is in the public domain. Recording by Martin Giesen. Confessions of an English Opium Eater by Thomas de Quincey. Section 14. Many years ago, when I was looking over Piranesi's antiquities of Rome, Mr. Coleridge, who was standing by, described to me a set of plates by that artist, called his dreams, and which record the scenery of his own visions during the delirium of a fever. Some of them, I describe only from memory of Mr. Coleridge's account, represented vast gothic halls, on the floor of which stood all sorts of engines and machinery, wheels, cables, pulleys, levers, catapults, etc., etc., expressive of enormous power put forth, and resistance overcome. Creeping along the sides of the walls, you perceived a staircase, and upon it, groping his way upwards, was Piranesi himself. Follow the stairs a little further, and you perceive it come to a sudden and abrupt termination without any balustrade, and allowing no step onwards to him who had reached the extremity, except into the depths below. Whatever is to become of poor Piranesi, you suppose at least that his labours must in some way terminate here. But raise your eyes, and behold a second flight of stairs, still higher, on which again Piranesi is perceived, but this time standing on the very brink of the abyss. Again elevate your eye, and a still more a aerial flight of stairs is beheld, and again is poor Piranesi busy on his aspiring labours. And so on, until the unfinished stairs and Piranesi both are lost in the upper gloom of the hall, with the same power of endless growth and self-reproduction, did my architecture proceed in dreams. In the early stage of my malady the splendours of my dreams were indeed chiefly architectural, and I beheld such pomp of cities and palaces as was never yet beheld by the waking eye, unless in the clouds. From a great modern poet I cite part of a passage which describes, as an appearance actually beheld in the clouds, what in many of its circumstances I saw frequently in sleep. The appearance, instantaneously disclosed, was of a mighty city, boldly say a wilderness of building, sinking far and self-withdrawn into a wondrous depth, far sinking into splendour without end. Fabric it seemed of diamond and of gold, with alabaster domes and silver spires, and blazing terrace upon terrace high uplifted. Here serene pavilions bright in avenues disposed, there towers beguert with battlements that on their restless fronts bore stars, illumination of all gems. By earthly nature had the effect been wrought upon the dark materials of the storm now pacified. On them and on the coves, and mountain steeps and summits, whereunto the vapours had receded, taking there their station under a cerulean sky, et cetera, et cetera. The sublime circumstance, battlements that on their restless fronts bore stars, might have been copied from my architectural dreams, for it often occurred. We hear it reported of Dryden and of Fuseli in modern times, that they thought it proper to eat raw meat for the sake of obtaining splendid dreams. How much better for such a purpose to have eaten opium, which yet I do not remember that any poet is recorded to have done except the dramatist Shadwell, and in ancient days Homer is, I think, rightly reputed to have known the virtues of opium. To my architecture succeeded dreams of lakes and silvery expanses of water. These haunted me so much that I feared, though possibly it will appear ludicrous to a medical man, that some dropsicle state or tendency of the brain might thus be making itself, to use a metaphysical word, objective, and the sentient organ project itself as its own object. For two months I suffered greatly in my head, a part of my bodily structure which had hitherto been so clear from all touch or taint of weakness, physically, I mean, that I used to say of it as the last Lord Orford said of his stomach, that it seemed likely to survive the rest of my person. Till now I had never felt a headache even, or any the slightest pain except rheumatic pains caused by my own folly. However I got over this attack, though it must have been verging on something very dangerous. The waters now changed their character, from translucent lakes shining like mirrors, they now became seas and oceans, and now came a tremendous change, which unfolding itself slowly like a scroll through many months promised an abiding torment, and in fact it never left me until the winding up of my case. Hitherto the human face had mixed often in my dreams, but not despotically, or with any special power of tormenting. But now that which I have called the tyranny of the human face began to unfold itself. Perhaps some part of my London life might be answerable for this. Be that as it may, now it was that upon the rocking waters of the ocean the human face began to appear. The sea appeared paved with innumerable faces upturned to the heavens, faces imploring, wrathful, despairing, surged upwards by thousands, by millions, by generations, by centuries. My agitation was infinite, my mind tossed and surged with the ocean, May 1818. The Malay has been a fearful enemy for months. I have been every night through his means, transported into Asiatic scenes. I know not whether others share in my feelings on this point, but I have often thought that if I were compelled to forgo England and to live in China, and amongst Chinese manners and modes of life and scenery, I should go mad. The causes of my horror lie deep, and some of them must be common to others. Southern Asia in general is the seat of awful images and associations. As the cradle of the human race, it would alone have a deep and reverential feeling connected with it. But there are other reasons. No man can pretend that the wild, barbarous and capricious superstitions of Africa, or of savage tribes elsewhere, affect him in the way that he is affected by the ancient, monumental, cruel and elaborate religions of Hindustan, etc. The mere antiquity of Asiatic things, of their institutions, histories, modes of faith, etc. is so impressive that to me the vast age of the race and name overpowers the sense of youth in the individual. A young Chinese seems to me an anti-Diluvian man renewed. Even Englishmen, though not bred in any knowledge of such institutions, cannot but shudder at the mystic sublimity of castes that have flowed apart and refused to mix through such immemorial tracts of time. Nor can any man fail to be awed by the names of the Ganges or the Euphrates. It contributes much to these feelings that Southern Asia is, and has been for thousands of years, the part of the earth most swarming with human life, the great Ofikina Gentium, workshop of the races. Man is a weed in those regions. The vast empires also, in which the enormous population of Asia has always been cast, give a further sublimity to the feelings associated with all the oriental names or images. In China, over and above what it has in common with the rest of Southern Asia, I am terrified by the modes of life, by the manners, and by the barrier of utter abhorrence and want of sympathy placed between us by feelings deeper than I can analyse. I could sooner live with lunatics or brute animals. All this and much more than I can say or have time to say, the reader must enter into before he can comprehend the unimaginable horror which these dreams of oriental imagery and mythological tortures impressed upon me. Under the connecting feeling of tropical heat and vertical sunlights, I brought together all creatures, birds, beasts, reptiles, all trees and plants, usages and appearances that are found in all tropical regions, and assembled them together in China or Hindustan. From kindred feelings I soon brought Egypt and all her gods under the same law. I was stared at, hooted at, grinned at, chattered at by monkeys, by paddockettes, by cockatoos. I ran into pagodas and was fixed for centuries at the summit or in secret rooms. I was the idol. I was the priest. I was worshipped. I was sacrificed. I fled from the wrath of Brahma through all the forests of Asia. Vishnu hated me. Shiva laid wait for me. I came suddenly upon Isis and Osiris. I had done a deed, they said, which the ibis and the crocodile trembled at. I was buried for a thousand years in stone coffins with mummies and sphinxes in narrow chambers at the heart of eternal pyramids. I was kissed with cancerous kisses by crocodiles, and laid confounded with all unutterable slimy things amongst reeds and nylotic mud. I thus give the reader some slight abstraction of my oriental dreams, which always filled me with such amazement at the monstrous scenery that horror seemed absorbed for a while in sheer astonishment. Sooner or later came a reflux of feeling that swallowed up the astonishment and left me not so much in terror as in hatred and abomination of what I saw. Over every form and threat and punishment and dim, sightless incarceration brooded a sense of eternity and infinity that drove me into an oppression as of madness. Into these dreams only it was, with one or two slight exceptions, that any circumstances of physical horror entered. All before had been moral and spiritual terrors, but here the main agents were ugly birds or snakes or crocodiles, especially the last. The cursed crocodile became to me the object of more horror than almost all the rest. I was compelled to live with him, and as was always the case almost in my dreams for centuries. I escaped sometimes and found myself in Chinese houses with cane tables, etc. All the feet of the tables, sofas, etc., soon became instinct with life. The abominable head of the crocodile and his leering eyes looked out at me, multiplied into a thousand repetitions, and I stood loathing and fascinated. And so often did this hideous reptile haunt my dreams that many times the very same dream was broken up in the very same way. I heard gentle voices speaking to me. I hear everything when I am sleeping, and instantly I awoke. It was broad noon, and my children were standing hand in hand at my bedside, come to show me their coloured shoes, or new frocks, or to let me see them dressed for going out. I protest that so awful was the transition from the damned crocodile and the other unutterable monsters and abortions of my dreams to the sight of innocent human natures and of infancy. But in the mighty and sudden revulsion of mind I wept, and could not forbear it as I kissed their faces. End of section 14 Recording by Martin Giesen in Hazelmere Surrey Section 15 of Confessions of an English Opium Eater This LibriVox recording is in the public domain. Recording by Martin Giesen Confessions of an English Opium Eater by Thomas DeQuincey Section 15 June 1819 I have had occasion to remark at various periods of my life that the deaths of those whom we love, and indeed the contemplation of death generally, is Keteris Paribus, other things being equal, more affecting in summer than in any other season of the year. And the reasons of these three, I think, first that the visible heavens in summer appear far higher, more distant, and if such a solicism may be excused, more infinite. The clouds by which chiefly the eye expounds the distance of the blue pavilion stretched over our heads are in summer more voluminous, massed, and accumulated in far grander and more towering piles. Secondly, the light and the appearances of the declining and the setting sun are much more fitted to be types and characters of the infinite. And thirdly, which is the main reason, the exuberant and riotous prodigality of life naturally forces the mind more powerfully upon the antagonist thought of death, and the wintry sterility of the grave. For it may be observed generally that wherever two thoughts stand related to each other by a law of antagonism, and exist as it were by mutual repulsion, they are apt to suggest each other. On these accounts it is that I find it impossible to banish the thought of death when I am walking alone in the endless days of summer. And any particular death, if not more affecting, at least haunts my mind more obstinately and besiegingly in that season. Perhaps this cause, and a slight incident which I omit, might have been the immediate occasions of the following dream, to which, however, a predisposition must always have existed in my mind. But having been once roused, it never left me, and split into a thousand fantastic varieties, which often suddenly reunited and composed again the original dream. I thought that it was a Sunday morning in May, that it was Easter Sunday, and as yet very early in the morning. I was standing, as it seemed to me, at the door of my own cottage. Right before me lay the very scene which could really be commanded from that situation, but exalted, as was usual, and solemnized by the power of dreams. They were the same mountains, and the same lovely valley at their feet. But the mountains were raised to more than alpine height, and there was interspace far larger between them of meadows and forest lawns. The hedges were rich with white roses, and no living creature was to be seen, accepting that in the green churchyard there were cattle, tranquilly reposing upon the verdant graves, and particularly about the grave of a child whom I had tenderly loved, just as I had really beheld them a little before sunrise in the same summer when that child died. I gazed upon the well known scene, and I said aloud as I thought to myself, it yet wants much of sunrise, and it is Easter Sunday, and that is the day on which they celebrate the first fruits of resurrection. I will walk abroad, old grief shall be forgotten today, for the air is cool and still, and the hills are high and stretch away to heaven, and the forest glades are as quiet as the churchyard, and with the dew I can wash the fever from my forehead, and then I shall be unhappy no longer. And I turned as if to open my garden gate, and immediately I saw upon the left a scene far different, but which yet the power of dreams had reconciled into harmony with the other. The scene was an oriental one, and there also it was Easter Sunday, and very early in the morning, and at a vast distance were visible as a stain upon the horizon, the domes and cupolas of a great city, an image or faint abstraction caught perhaps in childhood from some picture of Jerusalem. And not a bow shot from me, upon a stone and shaded by Judean palms, there sat a woman, and I looked, and it was Anne. She fixed her eyes upon me earnestly, and I said to her at length, So then I have found you at last. I waited, but she answered, I mean not a word. Her face was the same as when I saw it last, and yet again how different. Seventeen years ago when the lamp light fell upon her face, as for the last time I kissed her lips. Lips, Anne, that to me were not polluted. Her eyes were streaming with tears. The tears were now wiped away. She seemed more beautiful than she was at that time, but in all other points the same and not older. Her looks were tranquil, but with unusual solemnity of expression, and I now gazed upon her with some awe. But suddenly her countenance grew dim, and turning to the mountains I perceived vapours rolling between us. In a moment all had vanished, thick darkness came on, and in the twinkling of an eye I was far away from mountains, and by lamp light in Oxford Street, walking again with Anne just as we walked seventeen years before when we were both children. As a final specimen I cite one of a different character from eighteen hundred and twenty. The dream commenced with a music which now I often heard in dreams, a music of preparation and of awakening suspense, a music like the opening of the coronation anthem, and which like that gave the feeling of a vast march of infinite cavalcade filing off and the tread of innumerable armies. The morning was come of a mighty day, a day of crisis and of final hope for human nature, then suffering some mysterious eclipse and laboring in some dread extremity. Somewhere I knew not where, somehow I knew not how, by some beings I knew not whom. A battle, a strife, an agony was conducting, was evolving like a great drama or piece of music, with which my sympathy was the more insupportable from my confusion as to its place, its cause, its nature, and its possible issue. I, as is usual in dreams, whereof necessity we make ourselves central to every movement, had the power and yet had not the power to decide it. I had the power if I could raise myself to will it, and yet again had not the power for the weight of twenty Atlantics was upon me, or the oppression of inexpeable guilt. Deeper than ever plummet sounded, high lay inactive. Then, like a chorus, the passion deepened. Some greater interest was at stake, some mightier cause than ever yet the sword had pleaded, or trumpet had proclaimed. Then came sudden alarms, hurryings, to and fro, trepidations of innumerable fugitives. I knew not whether from the good cause or the bad, darkness and lights, tempest and human faces, and at last with the sense that all was lost, female forms, and the features that were worth all the world to me, and but a moment allowed, and clasped hands, and heart-breaking partings, and then everlasting farewells. And with a sigh, such as the caves of hell sighed, when the incestuous mother uttered the abhorred name of death, the sound was reverberated, everlasting farewells. And again and yet again reverberated, everlasting farewells. And I awoke in struggles, and cried aloud, I will sleep no more. But I am now called upon to wind up a narrative which has already extended to an unreasonable length. Within more spacious limits the materials which I have used might have been better unfolded, and much which I have not used might have been added with effect. Perhaps, however, enough has been given. It now remains that I should say something of the way in which this conflict of horrors was finally brought to a crisis. The reader is already aware, from a passage near the beginning of the introduction to the first part, that the opiometer has in some way or other unwound almost to its final links the accursed chain which bound him. By what means? To have narrated this according to the original intention would have far exceeded the space which can now be allowed. It is fortunate, as such a cogent reason exists for abridging it, that I should, on a matureer view of the case, have been exceedingly unwilling to injure, by any such unaffecting details, the impression of the history itself as an appeal to the prudence and the conscience of the yet unconfirmed opiometer, or even though a very inferior consideration to injure its effect as a composition. The interest of the judicious reader will not attach itself chiefly to the subject of the fascinating spells, but the fascinating power. Not the opiometer, but the opium is the true hero of the tale, and the legitimate centre on which the interest revolves. The object was to display the marvellous agency of opium, whether for pleasure or for pain. If that is done, the action of the piece has closed. However, as some people, in spite of all laws to the contrary, will persist in asking what became of the opium eater, and in what state he now is, I will answer for him thus. The reader is aware that opium had long ceased to found its empire on spells of pleasure. It was solely by the tortures connected with the attempt to abjure it that it kept its hold. Yet, as other tortures, no less it may be thought, attended the non-abjuration of such a tyrant, a choice only of evils was left. And that might as well have been attempted, which, however terrific in itself, held out a prospect of final restoration to happiness. This appears true, but good logic gave the author no strength to act upon it. However, a crisis arrived for the author's life, and a crisis for other objects still dearer to him, and which will always be far dearer to him than his life, even now that it is again a happy one. I saw that I must die if I continued the opium. I determined, therefore, if that should be required, to die in throwing it off. How much I was at that time taking, I cannot say, for the opium which I used had been purchased for me by a friend, who afterwards refused to let me pay him, so that I could not ascertain even what quantity I had used within the year. I apprehend, however, that I took it very irregularly, and that I varied from about fifty or sixty grains to one hundred and fifty a day. My first task was to reduce it to forty to thirty, and as fast as I could to twelve grains. I triumphed. But think not, reader, that therefore my sufferings were ended, nor think of me as one sitting in a dejected state. Think of me as one even when four months had passed, still agitated, writhing, throbbing, palpitating, shattered, and much perhaps in the situation of him who has been wracked, as I collect the torments of that state from the effecting account of them left by a most innocent sufferer of the times of James I. Meantime I derived no benefit from any medicine, except one prescribed to me by an Edinburgh surgeon of great eminence, Viz, a moniated tincture of the Lyrian. Medical account, therefore, of my emancipation I have not much to give.  At all events it would be misplaced in this situation. The moral of the narrative is addressed to the opiometer, and therefore of necessity limited in its application. If he is taught to fear and tremble, enough has been effected. But he may say that the issue of my case is at least a proof that opium, after a seventeen years use, and an eight years abuse of its powers, may still be renounced, and that he may chance to bring to the task greater energy than I did, or that with a stronger constitution than mine he may obtain the same results with less. This may be true. I would not presume to measure the efforts of other men by my own. I heartily wish him more energy. I wish him the same success. Nevertheless, I had motives external to myself which he may unfortunately want, and these supplied me with conscientious supports, which mere personal interests might fail to supply to a mind debilitated by opium. Jeremy Taylor conjectures that it may be as painful to be born as to die. I think it probable, and during the whole period of diminishing the opium I had the torments of a man passing out of one mode of existence into another. The issue was not death, but a sort of physical regeneration, and I may add that ever since, at intervals, I have had a restoration of more than youthful spirits, though under the pressure of difficulties which in a less happy state of mind I should have called misfortunes. One memorial of my former condition still remains. My dreams are not yet perfectly calm. The dread swell and agitation of the storm have not wholly subsided. The legions that encamped in them are drawing off, but not all departed. My sleep is still too molt to us, and like the gates of paradise to our first parents when looking back from afar, it is still in the tremendous line of Milton, with dreadful faces thronged and fiery arms. End of Section 15 Recording by Martin Giesen in Hazelmere Surrey Section 16 of Confessions of an English Opium Eater This LibriVox recording is in the public domain. Recording by Martin Giesen Confessions of an English Opium Eater by Thomas DeQuincey Section 16 Appendix from the London Magazine for December 1822 The interest excited by the two papers bearing this title in our numbers for September and October 1821 will have kept our promise of a third part fresh in the remembrance of our readers. That we are still unable to fulfil our engagement in its original meaning will, we are sure, be matter of regret to them as to ourselves, especially when they have perused the following affecting narrative. It was composed for the purpose of being appended to an addition of the Confessions in a separate volume, which is already before the public, and we have reprinted it entire, that our subscribers may be in possession of the whole of this extraordinary history. The proprietors of this little work, having determined on reprinting it, some explanation seems called for to account for the non-appearance of a third part promised in the London Magazine of December last, and the more so because the proprietors under whose guarantee that promise was issued might otherwise be implicated in the blame little or much attached to its non-fulfillment. This blame in mere justice the author takes wholly upon himself. What may be the exact amount of the guilt which he thus appropriates is a very dark question to his own judgment, and not much illuminated by any of the masters in casuistry whom he has consulted on the occasion. On the one hand it seems generally agreed that a promise is binding in the inverse ratio of the numbers to whom it is made, for which reason it is that we see many persons break promises without scruple that are made to a whole nation, who keep their faith religiously in all private engagements, breaches of promise towards the stronger party being committed at a man's own peril. On the other hand the only parties interested in the promises of an author are his readers, and these it is a point of modesty in any author to believe as few as possible, or perhaps only one, in which case any promise imposes a sanctity of moral obligation which it is shocking to think of. Casuistry dismissed, however, the author throws himself on the indulgent consideration of all who may conceive themselves aggrieved by his delay in the following account of his own condition from the end of last year, when the engagement was made up nearly to the present time. For any purpose of self-excuse it might be sufficient to say that intolerable bodily suffering had totally disabled him for almost any exertion of mind. More especially for such as demands and presupposes a pleasurable and genial state of feeling. But as a case that may by possibility contribute a trifle to the medical history of opium in a further stage of its action than can often have been brought under the notice of professional men, he has judged that it might be acceptable to some readers to have it described more at length.  What the benefit may be will admit of a doubt, but there can be none as to the value of the body. For a more worthless body than his own, the author is free to confess cannot be. It is his pride to believe that it is the very ideal of a base, crazy, despicable human system, that hardly ever could have been meant to be seaworthy for two days under the ordinary storms and wear and tear of life. And indeed, if that were the creditable way of disposing of human bodies, he must own that he should almost be ashamed to bequeath his wretched structure to any respectable dog. But now to the case, which for the sake of avoiding the constant recurrence of a cumbersome peripheresis, the author will take the liberty of giving in the first person. Those who have read the confessions will have closed them with the impression that I had wholly renounced the use of opium. This impression I meant to convey, and that for two reasons. First, because the very act of deliberately recording such a state of suffering necessarily presumes in the recorder a power of surveying his own case as a cool spectator, and a degree of spirits for adequately describing it, which it would be inconsistent to suppose in any person speaking from the station of an actual sufferer. Secondly, because I, who had descended from so large a quantity as eight thousand drops, to so smaller one comparatively speaking, as a quantity ranging between three hundred and one hundred and sixty drops, might well suppose that the victory was in effect achieved. In suffering my readers, therefore, to think of me as a reformed opium eater, I left no impression but what I shared myself. And as may be seen, even this impression was left to be collected from the general tone of the conclusion, and not from any specific words, which are in no instance at variance with the literal truth. In no long time after that paper was written, I became sensible that the effort which remained would cost me far more energy than I had anticipated, and the necessity for making it was more apparent every month. In particular, I became aware of an increasing callousness or defect of sensibility in the stomach, and this I imagined might imply a cirrus state of that organ, either formed or forming. An eminent physician, to whose kindness I was at that time deeply indebted, informed me that such a termination of my case was not impossible, though likely to be forestalled by a different termination in the event of my continuing the use of opium. Opium, therefore, I resolved wholly to abjure, as soon as I should find myself at liberty to bend my undivided attention and energy to this purpose. It was not, however, until the 24th of June last that any tolerable concurrence of facilities for such an attempt arrived. On that day I began my experiment, having previously settled in my own mind that I would not flinch but would stand up to the scratch under any possible punishment. I must premise that about 170 or 180 drops had been my ordinary allowance for many months. Occasionally I had run up as high as 500 and once nearly to 700. In repeated preludes to my final experiment I had also gone as low as 100 drops, but had found it impossible to stand it beyond the fourth day, which, by the way, I have always found more difficult to get over than any of the preceding three. I went off under easy sale, 130 drops a day for three days. On the fourth I plunged at once to 80. The misery which I now suffered took the conceit out of me at once, and for about a month I continued off and on about this mark, then I sunk to 60, and the next day to none at all. This was the first day for nearly ten years that I had existed without opium. I persevered in my abstinence for ninety hours, i.e. upwards of half a week. Then I took, ask me not how much, say ye severest, what would ye have done? Then I abstained again. Then took about 25 drops, then abstained, and so on. Meantime the symptoms which attended my case for the first six weeks of my experiment were these. Enormous irritability and excitement of the whole system. The stomach in particular restored to a full feeling of vitality and sensibility, but often in great pain. Unceasing restlessness night and day. Sleep! I scarcely knew what it was. Three hours out of the twenty-four was the utmost I had, and that so agitated and shallow that I heard every sound that was near me. Lower jaw constantly swelling, mouth ulcerated, and many other distressing symptoms that would be tedious to repeat. Amongst which, however, I must mention one, because it had never failed to accompany any attempt to renounce opium. Viz, violent sternutation. This now became exceedingly troublesome, sometimes lasting for two hours at once, and recurring at least twice or three times a day. I was not much surprised at this on recollecting what I had somewhere heard or read, that the membrane which lines the nostrils is a prolongation of that which lines the stomach. Hence, I believe, are explained the inflammatory appearances about the nostrils of dram-drinkers. The sudden restoration of its original sensibility to the stomach expressed itself, I suppose, in this way. It is remarkable also that during the whole period of years through which I had taken opium, I had never once caught cold, as the phrase is, or even the slightest cough. But now a violent cold attacked me, and a cough soon after. In an unfinished fragment of a letter begun about this time to, I find these words. You ask me to write the, do you know Beaumont and Fletcher's play of Thierry and Theodore. There you will see my case as to sleep, nor is it much of an exaggeration in other features. I protest to you that I have a greater influx of thoughts in one hour at present than in a whole year under the reign of opium. It seems as though all the thoughts which had been frozen up for a decade of years by opium had now, according to the old fable, been thawed at once. Such a multitude stream in upon me from all quarters. Yet such is my impatience and hideous irritability, but for one which I detain and write down, fifty escape me. In spite of my weariness from suffering and want of sleep, I cannot stand still or sit for two minutes together. Inunc et versus teicum meditare canoros. Go now and compose your melodies. At this stage of my experiment I sent to a neighbouring surgeon, requesting that he would come over to see me. In the evening he came, and after briefly stating the case to him, I asked this question. Whether he did not think that the opium might have acted as a stimulus to the digestive organs, and that the present state of suffering in the stomach, which manifestly was the cause of the inability to sleep, might arise from indigestion? His answer was no. On the contrary, he thought that the suffering was caused by digestion itself, which should naturally go on below the consciousness, but which from the unnatural state of the stomach vitiated by so long a use of opium, was become distinctly perceptible. This opinion was plausible, and the unintermitting nature of the suffering disposes me to think that it was true. For if it had been any mere irregular affection of the stomach, it should naturally have intermitted occasionally, and constantly fluctuated as to degree. The intention of nature, as manifested in the healthy state, obviously is to withdraw from our notice all the vital motions, such as the circulation of the blood, the expansion and contraction of the lungs, the peristaltic action of the stomach, etc. And opium, and opium, it seems, is able in this, as in other instances to counteract her purposes. By the advice of the surgeon, I tried bitters. For a short time these greatly mitigated the feelings under which I laboured. But about the 42nd day of the experiment, the symptoms already noticed began to retire, and new ones to arise of a different and far more tormenting class. Under these, but with a few intervals of remission, I have since continued to suffer. But I dismiss them undescribed for two reasons. First, because the mind revolts from retracing circumstantially any sufferings from which it is removed by too short or by no interval. To do this with minuteness enough to make the review of any use would be infandom renoire dolorem, reader's translation, to renew unspeakable grief, and possibly without a sufficient motive. But secondly, I doubt whether this latter state be anyway referable to opium, positively considered, or even negatively, that is whether it is to be numbered among the last evils from the direct action of opium, or even amongst the earliest evils consequent upon a want of opium in a system long deranged by its use. Certainly one part of the symptoms might be accounted for from the time of year, August. For though the summer was not a hot one, yet in any case the sum of all the heat funded, if one may say so during the previous months, added to the existing heat of that month, naturally renders August in its better half the hottest part of the year. And it so happened that the excessive perspiration, which even at Christmas attends any great reduction in the daily quantum of opium, and which in July was so violent as to oblige me to use a bath five or six times a day, had about the setting in of the hottest season wholly retired, on which account any bad effect of the heat might be the more unmitigated. Another symptom is what in my ignorance I call internal rheumatism, sometimes affecting the shoulders etc., but more often appearing to be seated in the stomach, seemed again less probably attributable to the opium, or the want of opium, than to the dampness of the house which I inhabit, which had about this time attained its maximum, July having been as usual a month of incessant rain in our most rainy part of England. Under these reasons for doubting whether opium had any connection with the latter stage of my bodily wretchedness, except indeed as an occasional cause, as having left the body weaker and more crazy, and thus predisposed to any mal-influence whatever, I willingly spare my reader all description of it. Let it perish to him and would that I could as easily say let it perish to my own remembrances, that any future hours of tranquility may not be disturbed by too vivid an ideal of possible human misery. So much for the sequel of my experiment. As to the former stage, in which probably lies the experiment and its application to other cases, I must request my reader not to forget the reasons for which I have recorded it. These were two. First, a belief that I might add some trifle to the history of opium as a medical agent. In this I am aware that I have not at all fulfilled my own intentions, in consequence of the torpor of mind, pain of body, and extreme disgust to the subject which besieged me whilst writing that part of my paper, which part being immediately sent off to the press, distant about five degrees of latitude, cannot be corrected or improved. But from this account, rambling as it may be, it is evident that thus much benefit may arise to the person's most interested in such a history of opium, vis to opiumeeters in general, that it establishes for their consolation and encouragement the fact that opium may be renounced, and without greater sufferings than an ordinary resolution may support, and by a pretty rapid course of descent. To communicate this result of my experiment was my foremost purpose. Secondly, as a purpose collateral to this, I wish to explain how it had become impossible for me to compose a third part in time to accompany this republication. But during the time of this experiment the proof sheets of this reprint were sent to me from London, and such was my inability to expand or to improve them that I could not even bear to read them over with attention enough to notice the press errors or to correct any verbal inaccuracies. These were my reasons for troubling my reader with any record, long or short, of experiments relating to so truly base a subject as my own body. And I am earnest with the reader that he will not forget them, or so far misapprehend me as to believe it possible that I would condescend to so rascally a subject for its own sake, or indeed for any less object than that of general benefit to others. Such an animal as the self-observing valetudinarian I know there is. I have met him myself occasionally, and I know that he is the worst imaginable chayartondimoruminos, self-tormentor, aggravating and sustaining by calling to distinct consciousness every symptom that would else perhaps, under a different direction given to the thoughts, become evennessant. But as to myself, so profound is my contempt for this undignified and selfish habit that I could as little condescend to it as I could to spend my time in watching a poor servant-girl, to whom at this moment I hear some lad or other making love at the back of my house. Is it for a transcendental philosopher to feel any curiosity on such an occasion? Or can I, whose life is worth only eight and a half years' purchase, be supposed to have leisure for such trivial employments? However, to put this out of question, I shall say one thing, which will perhaps shock some readers, but I am sure it ought not to do so, considering the motives on which I say it. No man, I suppose, employs much of his time on the phenomena of his own body without some regard for it. Whereas the reader sees that so far from looking upon mine with any complacency or regard, I hate it, and make it the object of my bitter ridicule and contempt. And I should not be displeased to know that the last indignities which the law inflicts upon the bodies of the worst malefactors might hereafter fall upon it. And in testification of my sincerity in saying this, I shall make the following offer. Like other men, I have particular fancies about the place of my burial. Having lived chiefly in a mountainous region, I rather cleave to the conceit that a grave in a green churchyard amongst the ancient and solitary hills will be a sublimer and more tranquil place of repose for a philosopher than in any of the hideous Golgothers of London. Yet if the gentlemen of Surgeon's Hall think that any benefit can redound to their science from inspecting the appearances in the body of an opium eater, let them speak but a word, and I will take care that mine shall be legally secured to them. i.e., as soon as I have done with it myself, let them not hesitate to express their wishes upon any scruples of false delicacy and consideration for my feelings.  Such bequests are not common. Reversionary benefits contingent upon the death of the testator are indeed dangerous to announce in many cases. Of this we have a remarkable instance in the habits of a Roman prince who used upon any notification made to him by rich persons that they had left him a handsome estate in their wills to express his entire satisfaction at such arrangements and his gracious acceptance of those loyal legacies. But then, if the testators neglected to give him immediate possession of the property, if they traitorously persisted in living, see, we were a perseverarent, as Suetonius expresses it, he was highly provoked and took his measures accordingly. In those times, and from one of the worst of the Caesars, we might expect such conduct, but I am sure that from English surgeons at this day I need look for no expressions of impatience or of any other feelings but such as are answerable to that pure love of science and all its interests which induces me to make such an offer. September 30th, 1822 End of Section 16 Recording by Martin Giesen in Hazelmere Surrey End of Confessions of an English Opium Eater by Thomas De Quincey


In this lecture, I will continue with the inelastic scattering of neutrons by phonons. As I told you earlier that we have discussed elastic neutron scattering for all structures at various length scales and now we have come to inelastic neutron scattering in which phonons form a very important part of the experimental studies for understanding collective oscillations in crystalline solids known as phonons. I will discuss phonons and later I will also discuss stochastic motions and towards the end I will come to molecular vibrations and also extremely slow motions but now we will continue our discussion on phonons. Now phonons are collective oscillations in a solid when you consider the solid atoms are coupled by springs. So, here basically if there are two atoms we assume that they have a spring connecting them or rather the force behaves like a spring that means the energy force is proportional to displacement in the first order and the simple harmonic oscillator. So, here the this is a picture I borrowed from internet from this source where it is a lithium fluoride crystal which actually has shown as the springs connecting the ions in this crystal and this picture remains valid for all crystalline materials in which we will discuss the phonons. Now the force equation or the equation of motion for the sth part at ion let us say this is the sth ion will given by the force as second differential of the displacement and the sum over all the nearest not nearest all neighbors where p are the neighbors. So, basically the Newtonian equation of d 2 x by dt 2 equal to force that translates here as m into d 2 u s by dt 2 m is the mass of the ion is force is a spring constant. So, it is basically c of p plus s minus c of p depends on that there is a force constant between the two atoms and then sorry I am sorry here I am sorry this is I made a mistake here c p of p plus s into u of s plus p minus u of s summation over p p are the neighbors neighbors of the sth atom. So, this is a simple harmonic force which depends on the displacement of the s plus pth or rather the pth neighbor that means we have just let me just take a linear chain and go to second order force. So, there is a spring here there is also a spring here between the term there is a spring here there is also a spring between the next nearest neighbors. So, if this is the sth atom this is minus 1 this is minus 2 this is plus 1 this is plus 2 and in ideal case I should sum up over all the neighbors and this is the equation of motion for the sth atom and then we get this equation I have to start with I have started with a monatomic lattice c p is the spring constant and then if the sum is over all the neighbors of the sth atom. So, now for this particular case this is the concept of phonon is that I consider a wave like solution where the displacement of u of s plus p is given in terms of a prefactor p k a sum over p please note this here I am the there is a wave vector associated with the displacement which is k a is a lattice constant and I have taken the the displacement as a traveling wave in space and then this is a very general solution that u s plus p in terms of the number u is given by a this is nothing, but a wave like solution and here. So, this is given by a wave like solution and what are the solutions let us get into that now here. So, now in time also I consider dependence of e to the power minus i omega t this is a temporal frequency and this is a spatial frequency and now the displacement I write in terms of u e to the power i s k a is for the sth atom and it is given by a sum over the neighbors you can see I have just use it use the displacement term which is e to the power i s plus p k a minus e to the power minus s k a and sum over neighbors. So, this sum actually here when I do I divide by e to the power i s k plus a what I get is the equation of motion for the atom in this lattice and p is the summation over the nearest neighbors. Now, we know that if I have if these are the atom positions I am showing it as a linear chain, but it can be easily translated into three dimensional that is also. So, fact is that if this is the central atom then if I consider the neighbor here I also have a neighbor at minus p neighbor at or plus p plus 1 also have a neighbor at minus p plus 1. So, they are symmetric the c p and the force constants are symmetric because the force between these two are same as force between these two. Similarly, the force between this and this one is same as force between this and the next nearest neighbor. So, c p equal to minus c minus p not minus c p c of minus p force is the same and then this summation series I can write in terms of because it is e to the power i p k a minus 1 instead of going only for the positive numbers I can sum it over p is greater than 0 and i p k plus e to the power minus i p k because this is minus direction this is a plus direction and p is a number neighbor number which is greater than 0. So, I can write it as e to the power i p k a plus e to the power minus i p k minus 2 and this is equal to cos of 2 cos of p k a. So, 2 cos of p k minus 2 negative. So, ultimately I get this equation is cleaning. So, I have got this equation m omega square equal to c p 2 minus 2 cos p k a. So, that 2 comes out and this is the equation for omega square and if I consider a special case actually often this works well if I consider only nearest neighbor interaction then of all the p's you know only the nearest neighbor only the nearest neighbors they survive and then I have omega square equal to 2 by m c p into 1 minus cos p k a where it is p is equal to 1. So, I can call it c. So, this will be equal to 2 by m 1 only. So, it is c into 1 minus cos k a and cos k a equal to cos k by 2 plus k a by sorry let me write it here and cos a plus b is cos square k by 2 sin square k by 2 omega square and finally, it is very easy to show that the solution is omega equal to 4 c by m to the power half it is a free factor sin k by 2. Now, let us look at this solution. Now, this sin k by 2 as k goes to 0 k goes to 0 sin k by 2 goes as k by 2 you know sin x equal to x and when I consider this then this solution gives me k going to 0 omega equal to 4 c by m to the power half k by 2 which comes to c by m k. So, omega is proportional to k as a linear relationship and that means, when I go to center of the zone which is at k equal to 0 then the solution rather omega k relationship it goes down to 0 as 0 linearly. So, this is similar to let us say a sound wave propagating in a continuum media we know that sound wave velocity of 330 meters per second per second and in this range there is no dispersion when I mean dispersion let me just mean it here that omega versus k for sound wave it goes like this goes like this for our case which is phonons it is going like this. So, when k goes to 0 it behaves like a sound wave or a or rather continuum media and the wave propagating and mechanical wave propagating in that and that is why omega is proportional to k this branch is called acoustic branch because as omega k goes to 0 omega also goes to 0 like sound wave and actually speaking when you tend towards k equal to 0 the acoustic wave or the acoustic phonon goes into sound wave. This is basically an elastic wave in an elastic medium where we have the microscopic structure of atoms sitting at various sides, but when you go to k equal to 0 or long wavelength limit the whole medium behaves like a continuum because again as we had discussed earlier when the wavelength is so large it cannot distinguish between the sides and it acts like a continuum the medium acts like a continuum and what we get is sound wave. Now, another interesting thing is that let us consider the relative displacements of the neighbors.  So, that is what we wrote earlier oh sorry here it instead of that we read u this was what we wrote earlier. So, now when I do that s plus 1 and u s the ratio is e to the power i k a and when we use this value consider the boundary of the first Brillouin zone. What is the Brillouin zone? If let me just consider a linear lattice of spacing a or spacing a real space its reciprocal space is again a linear lattice of spacing twice pi by a. So, because this is a here the spacing will be twice pi by a that is how we make the reciprocal lattice. And now the Brillouin zone is nothing but we check connect the nearest neighbors and perpendicular to them at half the position and that is the Wigner side cell we call it the Wigner side cell in reciprocal space. So, it is pi by a here and minus pi by a in the negative direction and this is known as first Brillouin zone this is the first Brillouin zone. So, first Brillouin boundary comes at pi by a for more complicated for example, if I have other kinds of lattices then the Brillouin zone shapes will be different, but Brillouin zone at Brillouin zone boundary we will have special properties of the phonon. So, here let me see when in this chain where k is equal to pi by a what we find now u s plus 1 the neighbors and u s at the zone boundary k equal to pi by a it becomes e to the power i pi equal to minus 1 that means, at the zone boundary the neighbors the nearest neighbors are exactly pi phase apart in their movement. Now, once they are pi phase away any further difference will not give us a new independent displacement set because already they are pi away after that they can only repeat something which has happened less than pi by a. So, this is one reason we plot phonon dispersion curves in the range of 0 to pi by a for phonons also minus pi by a this I mentioned earlier today I mentioned it let me just do it. So, this is the zone center this is pi by a minus pi by a we try to evaluate the phonons up to the zone boundary. Now, because any k beyond zone boundary let us say zone boundary is pi by a if I goes marginally outside then this can be if this is the phonon dispersion curve in the second zone it will look like this I will come to again later it will come like this. So, this is same as a point if I move it by minus twice pi by a and get back to the first drill war zone. So, all phonons by all phonons I mean that all the displacement patterns if I can call it pattern all the displacement vectors all the possible displacements are contained inside the first drill war zone and outside the first drill war zone whatever we find can be brought back to the first drill war zone. That is why I try to get the phonon dispersion curve within the first drill war zone where this is the phonon wave vector please remember again and again this is the phonon wave vector this is the phonon frequency and this is the dispersion curve. So, because at the zone boundary we complete the set where u s plus 1 any two neighboring atoms are pi phase apart and after that we cannot have any new motion new motion pattern that will give us a new phonon. So, this is already contained in the first drill war zone now. So, in the first drill war zone so now that is why one thing is that I will find out the motions at the first drill here the solution for a monatomic lattice I have showed that as k goes to 0 the k omega was proportional to k which is acoustic, but now when k equal to pi by a the frequency is given by here you can see I had written a sine k a by 2 when k equal to pi by a it is sine pi by 2 1. So, omega is equal to 4 c by m to the power half and the relation is sine. So, that means for a monatomic case let me just plot the 0 to pi by a. So, this is the phonon dispersion curve. So, here it is 4 c by m to the power half 4 c by m to the power half and here it is 0 and for this simple case it is a sinusoidal curve, but now this is a movement now there is one atom in the unit cell unit cell. So, this has got three degrees of freedom three degrees of freedom. So, of these three I have shown you the dispersion relation for one now basically when you have particles or planes of particles this wave which I wrote as e to the power i s plus p a. So, this displacement can be longitudinal or transverse. So, first let me point out one by one we have phonons only in the first Brillois zone we need to do a measurement where the q the phonon wave vector goes from 0 to pi by a and maybe negative side. Second if I have a monatomic crystal monatomic crystal that means one atom per unit cell then I have three degrees of freedom and then these three are one can be longitudinal and two can have the two transverse motion transverse motions. So, this makes it three waves or these all three are called acoustic waves why I have come to it shortly. Now, suppose there are two atoms. So, if there are two atoms per unit cell an example let us say CSCL. So, let me just let me just go. So, what is the CSCL structure let me just try to draw it for you as an example sample. So, you have chlorine at the end edges. So, eight edges gives me one chlorine per unit cell and one body centered rescission. Now, that means if I consider let us say a propagation in this direction which is 1 0 0 direction in reciprocal please remember in reciprocal space then or in real space this will have planes like this I will have planes of chlorine followed by planes of cesium then again planes of chlorine. So, this is how if I go in 1 0 0 direction I will get the planes which now I am showing as a chain basically the planes these chains are actually let me see I can make something back on you this is basically a plane plane of atoms moving. So, now there are two movements say here in CSCL case one is CS one is CL in general there are two atoms of different mass, but they are also part of a traveling wave like solution this traveling like wave like solution this concept was brought in I think by Chris Igor Tom, but this is a basic concept of phonons these are the frequency pattern or the displacement pattern is a wave and actually when there are a number of atoms in a unit cell we can find out what are the number of waves that are possible which you can consider as independent of each other that means we can break down all the frequencies and all the displacement in terms of eigenvalues and eigenvectors I will complete shortly. So, now one is that let us consider this atom we are considering nearest number interaction. So, when you have a nearest number interaction that motion of equation of motion is given its mass is m 1 so m 1 into dt us by dt 2 which is the time derivative is equal to the force which is the nearest number is v s minus 1 and v s.  So, for the two terms and that is how it comes v s plus v s 1 minus 2 us similarly for so, this is what we wrote here and we take solutions for us and v s again earlier I had chosen a travel even solution like this now I have chosen two solutions here us equal to u and then this is the wave vector that dictates the wavelength of the motion and this is for the second atom.  So, it comes like this and similarly for the other one the second atom also it will be minus omega square m 2 v equal to c u into 1 minus i k. So, now, I have got two equations in u and v and I can write down the coefficient form the determinant for a real solution this determinant should be zero. You can see from here I can take u on this side. So, it becomes c minus e to the power i k and 2c minus m 1 omega square here 2c minus m 1 omega square and this is c into e to the power i k.    So, that is why I said u v into this determinant should be solved and then for this to have real solutions it should be the determinant of the coefficient should go to zero and then this is the equation which I obtained for the motion of the two particles. Interestingly now I have got six degrees of freedom six degrees of freedom. Now, I know that out of which three will be acoustic acoustic because that will mean one longitudinal I will show you structurally and two transverse wave longitudinal means the particle displacement and the wave propagation direction they are parallel k and particle displacement they are parallel in case of transverse k and the particle displacements they are perpendicular to each other and that can happen in two planes. Now, for this equation I have got two solutions one is when k goes to zero let us discuss this solutions then omega square is equal to 2c 1 by m 1 plus 1 by m 2 and omega square equal to because there it is a equation in omega to the power 4 I can put that equal to some say some I do not know alpha square where alpha equal to omega square. So, it becomes a binary equation second order equation in omega square and these are the two solutions when k goes to zero and when k goes to pi I have got the solutions 2c by m 1 2c by m 2 m 1 is greater than m 2. So, this will be the solution when I have two atoms per unit cell. So, how does the displacement they look like when I said longitudinal waves please note that the k vector this is the k vector and this is the because in this direction the wave is propagating and I show the displacement of this plane this plane of atoms. So, you can see that the second plane of atom is displaced this much the third plane may be displaced a little more the fourth plane little more then again it keeps reducing and finally it comes to a plane after the wavelength that I get back to the central plane which I have assumed the central plane. So, that is a longitudinal wave. So, here the displacements follow a sine curve whereas in this case also here the second plane is transverse if this is the k direction the displacement is in this direction. So, the second plane you can see this is displaced upward little more little less and ultimately it comes down to the displacement here. So, that means, the sinusoidal wave here I can draw like this. So, here if I consider this as a direction then I have got two particular direction because there are planes of atom in this direction also. So, there are two transverse waves in this case and there is a longitudinal wave and in case of only one atom these two things together longitudinal and transverse acoustic waves they make up for the total degrees of freedom which is free. When we have two atoms then also the number of acoustic waves should be free. So, this is a acoustic waves which will be free and also there will be optical waves optical waves why optical I will complete shortly why call them optical. You can see that that k equal to pi by a because m1 is greater than m2 2c by m1 is smaller than m2 this is the solution and this is the solution for the optical branch. But at k equal to 0 you can see this is the optical branch and this part because omega square is proportional to k square and omega is proportional to k barring a constant factor. So, it goes to 0. So, now we have got three optical branches and three acoustic branches for two atoms. So, I hope now I have able to make you understand the displacement patterns in case of monatomic and diatomic lattice and this can be further generalized for any kind of lattice structures. Now, this I called acoustic because I said earlier that they the omega goes to 0 as k goes to 0 and as k goes to 0 the medium behaves like a continuum. So, what about optical part? Here I show you the displacement model of the acoustic mode and the optical mode borrowed from here. So, here please see this is the acoustic mode. The atoms they move in the same direction and the amplitude of their oscillation varies as per the wave vector k which is the wavelength of this oscillation, but they are all they all are falling on the same wave pattern. So, when this is one atom going down the other one also going down when it is going up all of them go up and this is the displacement pattern in case of optic mode optic mode. You please see the same pattern here I have got the wavelength remains same, but the nearest atoms they are moving in opposite direction. When this one is moving in this direction the next nearest neighbor is moving in this direction this is in this direction and the next to next nearest neighbor again in goes in this direction. So, the atoms are moving moving against each other each other. This part this part of my description I borrowed from Kittel's introduction to solid state physics the phonons. So, now I have talked to you about acoustic modes and when atoms are moving against each other when they are moving against each other if the center of mass is fixed and if there are ions like as I showed you incisium chloride then this when this ions are moving against each other it looks like a dipole oscillation dipole oscillating oscillation and this dipole oscillation is able to couple with the electric field of an electromagnetic wave and can absorb or emit electromagnetic waves and that is why these are called the optical modes when the atoms are moving against each other with the center of mass fixed. So, acoustic mode go in the low K continuum limit goes to sound wave and optical mode because they are capable of absorbing or releasing electromagnetic radiation because in case of ionic solids they will be like oscillating dipoles with this I stop in the next part I will go into more generalized description of phonons and then how to talk about various measurements in the next part.


Hello everybody, welcome back to the Premiere Pro 2023 tutorial. In this one, I'm going to show you how to close all the gaps on your timeline with just one click. Normally you'll go through them and you just right click and ripple delete and it's a very tedious process and it's also tricky because you've gotten multiple tracks here.  That actually means close all gaps. When you do that, all the gaps are closed. That's all there is to it. Thanks for watching.