CHAPTER 27 Mr. Carker the Manager rose with the lark and went out, walking in the summer day. His meditations, and he meditated with contracted brows while he strolled along, hardly seemed to soar as high as the lark, or to mount in that direction. Rather they kept close to their nest upon the earth and looked about among the dust and worms. But there was not a bird in the air singing unseen, farther beyond the reach of human eye than Mr. Carker's thoughts. He had his face so perfectly under control that few could say more in distinct terms of its expression than that it smiled or that it pondered. It pondered now intently. As the lark rose higher he sank deeper in thought. As the lark poured out her melody, clearer and stronger, he fell into a graver and profounder silence. At length when the lark came headlong down with an accumulating stream of song and dropped among the green wheat near him, rippling in the breath of the morning like a river, he sprang up from his reverie and looked round with a sudden smile, as courteous and as soft as if he had had numerous observers to propitiate. Nor did he relapse after being thus awakened, but clearing his face like one who bethought himself that it might otherwise wrinkle and tell tales went smiling on as if for practice. Perhaps with an eye to first impressions Mr. Carker was very carefully and trimly dressed that morning. Though always somewhat formal in his dress in imitation of the great man whom he served, he stopped short of the extent of Mr. Dombie's stiffness, at once perhaps because he knew it to be ludicrous, and because in doing so he found another means of expressing his sense of the difference and distance between them. Some people quoted him indeed in this respect as a pointed commentary and not a flattering one on his icy patron, but the world is prone to misconstruction and Mr. Carker was not accountable for its bad propensity. Clean and florid, with his light complexion fading as it were in the sun, and his dainty step enhancing the softness of the turf, Mr. Carker the manager strolled about meadows and green lanes and glided among avenues of trees until it was time to return to breakfast. Taking a nearer way back Mr. Carker pursued it, erring his teeth and said aloud as he did so, now to see the second Mrs. Dombie. He had strolled beyond the town and re-entered it by a pleasant walk, where there was a deep shade of leafy trees, where there were a few benches here and there for those who chose to rest, it not being a place of general resort at any hour and wearing at that time of the still morning the air of being quite deserted and retired. Mr. Carker had it or thought he had it all to himself. So with the whim of an idle man to whom there yet remained twenty minutes for reaching a destination easily accessible in ten Mr. Carker threaded the great bowls of the trees and went passing in and out before this one and behind that weaving a chain of footsteps on the dewy ground. But he found he was mistaken in supposing there was no one in the grove for as he softly rounded the trunk of one large tree on which the obdurate bark was knotted and overlapped like the height of a rhinoceros or some kindred monster of the ancient days before the flood, he saw an unexpected figure sitting on a bench near at hand about which in another moment he would have wound the chain he was making. It was that of a lady elegantly dressed and very handsome whose dark, proud eyes were fixed upon the ground and in whom some passion or struggle was raging. For as she sat looking down she held a corner of her underlip within her mouth, her bosom heaved, her nostril quivered, her head trembled, indignant tears were on her cheek, and her foot was set upon the moss as though she would have crushed it into nothing. And yet almost self-same glance that showed him this showed him the self-same lady rising with a scornful air of weariness and lassitude and turning away with nothing expressed in face or figure but careless beauty and imperious disdain. A withered and very ugly old woman dressed not so much like a gypsy as like any of that medley race of vagabonds who trump about the country begging and stealing and tinkering and weaving rushes by turns or altogether had been observing the lady too, for as she rose this second figure strangely confronting the first scrambled up from the ground out of it. It almost appeared and stood in the way. Let me tell your fortune, my pretty lady, said the old woman, munching with her jaws as if the death's head beneath her yellow skin were impatient to get out. I can tell it for myself was the reply. I, I, pretty lady, but not right. You didn't tell it right when you were sitting there. I see you. Give me a piece of silver, pretty lady, and I'll tell your fortune true. There's riches, pretty lady, in your face. I know, returned the lady, passing her with a dark smile and a proud step. I knew it before. What? You won't give me nothing, cried the old woman. You won't give me nothing to tell your fortune, pretty lady. How much will you give me not to tell it then? Give me something, or I'll call it after you, croaked the old woman passionately. Mr. Parker, whom the lady was about to pass close, slinking against his tree as she crossed to gain the path, advanced so as to meet her, and pulling off his hat as she went by, bade the old woman hold her peace. The lady acknowledged his interference with an inclination of the head and went her way. You give me something then, or I'll call it after her, screamed the old woman throwing up her arms and pressing forward against his outstretched hand. Or come, she added, dropping her voice suddenly, looking at him earnestly and seeming in a moment to forget the object of her wrath. Give me something, or I'll call it after you. After me, old lady, returned the manager, putting his hand in his pocket. Yes, said the old woman, steadfast in her scrutiny and holding out her shriveled hand. I know! What do you know? demanded Parker, throwing her a shilling. Do you know who the handsome lady is? Munching like that sailor's wife of yore, who had chestnuts in her lap and scowling like the witch who asked for some in vain, the old woman picked the shilling up and going backwards, like a crab or like a heap of crabs, for her alternately expanding and contracting hands might have represented two of that species. And her creeping face, some half a dozen more, crouched on the venous root of an old tree, pulled out a short black pipe from within the crown of her bonnet, lighted it with a match and smoked in silence, looking fixedly at her questioner. Mr. Parker laughed and turned upon his heel. Good, said the old woman, one child dead and one child living, one wife dead, one wife coming, go and meet her. In spite of himself the manager looked round again and stopped. The old woman who had not removed her pipe and was munching and mumbling while she smoked, as if in conversation with an invisible familiar, pointed with her finger in the direction he was going and laughed. What was that you said? Bell to meet, he demanded. The woman mumbled and chattered and smoked and still pointed before him, but remained silent. Clearing a farewell that was not complimentary, Mr. Parker pursued his way. But as he turned out of that place and looked over his shoulder at the root of the old tree, he could yet see the finger pointing before him and thought he heard the woman screeching. Go and meet her. Preparations for a choice repassed were completed, he found at the hotel, and Mr. Dombie and the major and the breakfast were awaiting the ladies. Individual constitution has much to do with the development of such facts, no doubt, but in this case appetite carried it hollow over the tender passion. Mr. Dombie being very cool and collected and the major fretting and fuming in a state of violent heat and irritation. At length the door was thrown open by the native, and after a pause, occupied by her languishing along the gallery, a very blooming but not very youthful lady appeared. My dear Mr. Dombie said the lady, I am afraid we are late, but Edith has been out already looking for a favorable point of view for a sketch and kept me waiting for her, falsest of majors, giving him her little finger. How do you do? Mrs. Skeuton said Mr. Dombie, let me gratify my friend Karkar. Mr. Dombie unconsciously emphasized the word friend as saying, no really, I do allow him to take credit for that distinction by presenting him to you. You have heard me mention Mr. Karkar. I am charmed, I am sure, said Mrs. Skeuton graciously. Mr. Karkar was charmed, of course. Would he have been more charmed on Mr. Dombie's behalf if Mrs. Skeuton had been, as he at first supposed her, the Edith whom they had toasted overnight? Why, where for heaven's sake is Edith, exclaimed Mrs. Skeuton looking round, still at the door, giving withers orders about the mounting of those drawings. My dear Mr. Dombie, will you have the kindness? Mr. Dombie was already gone to seek her. Next moment he returned, bearing on his arm the same elegantly dressed and very handsome lady whom Mr. Karkar had encountered underneath the trees. Karkar began Mr. Dombie, but their recognition of each other was so manifest that Mr. Dombie stopped surprised. I am obliged to this gentleman, said Edith, with a stately bend for sparing me some annoyance from an importunate beggar just now. I am obliged to my good fortune, said Mr. Karkar bowing low, for the opportunity of rendering so slight a service to one whose servant I am proud to be. As her eye rested on him for an instant, and then lighted on the ground, he saw, in its bright and searching glance, a suspicion that he had not come up at the moment of his interference, but had secretly observed her sooner. As he saw that, she saw in his eye that her distrust was not without foundation. Really! cried Mrs. Skuten, who had taken this opportunity of inspecting Mr. Karkar through her glass, and satisfying herself as she lisped audibly to the major, that he was all heart. Really now! this is one of the most enchanting coincidences that I have ever heard of. The idea, my dearest Edith, there is such an obvious destiny in it that really one might almost be induced to cross one's arm upon one's frock, and say, like those wicked turks, there is no what's his name but thingamy, and what you may call it is his profit. Edith deigned no revision of this extraordinary quotation from the Koran, but Mr. Dombie felt it necessary to offer a few polite remarks. It gives me great pleasure, said Mr. Dombie, with cumbrous gallantry, that a gentleman so nearly connected with myself as Karkar is, should have had the honor and happiness of rendering the least assistance to Mrs. Granger. Mr. Dombie bowed to her, but it gives me some pain, and it occasions me to be really envious of Karkar. He unconsciously laid stress on these words as sensible that they must appear to involve a very surprising proposition, envious of Karkar, that I had not that honor and that happiness myself. Mr. Dombie bowed again. Edith, saving for a curl of her lip, was motionless. By the Lord, sir, cried the Major, bursting into speech at the sight of the waiter, who has come to announce breakfast. It's an extraordinary thing to me that no one can have the honor and happiness of shooting all such beggars through the head without being brought to book for it. But here's an arm for Mrs. Granger if she'll do JB the honor to accept it, and the greatest service Joe can render you, ma'am, just now is to lead you into table. With this the Major gave his arm to Edith. Mr. Dombie led the way with Mrs. Skeuten. Mr. Karkar went last, smiling on the party. I am quite rejoiced, Mr. Karkar, said the lady mother at breakfast, after another approving survey of him through her glass, that you have timed your visit so happily as to go with us today. It is the most enchanting expedition. Any expedition would be enchanting in such society, returned Karkar, but I believe it is in itself full of interest. Oh! cried Mrs. Skeuten, with a faded little scream of rapture. The castle is charming, associations of the Middle Ages, and all that, which is so truly exquisite. Don't you dot upon the Middle Ages, Mr. Karkar? Very much indeed, said Mr. Karkar, such charming times, cried Cleopatra, so full of faith, so vigorous and forcible, so picturesque, so perfectly removed from commonplace. Oh, dear, if they would only leave us a little more of the poetry of existence in these terrible days. Mrs. Skeuten was looking sharp after Mr. Dombie all the time she said this, who was looking at Edith, who was listening, but who never lifted up her eyes. We are dreadfully real, Mr. Karkar, said Mrs. Skeuten. Are we not? Few people had less reason to complain of their reality than Cleopatra, who had as much that was false about her as could well go to the composition of anybody with a real individual existence. But Mr. Karkar commiserated our reality nevertheless and agreed that we were very hardly used in that regard. Pictures at the castle quite divine, said Cleopatra. I hope you dot upon pictures. I assure you, Mrs. Skeuten, said Mr. Dombie, with solemn encouragement of his manager, that Karkar has a very good taste for pictures, quite a natural power of appreciating them. He is a very credible artist himself. He will be delighted, I am sure, with Mrs. Granger's taste and skill. Dammy, sir, cried Major Bagstock. My opinion is that you're the admirable Karkar and can do anything. Oh, smiled Karkar with humility, you are much too sanguine, Major Bagstock. I can do very little. But Mr. Dombie is so generous in his estimation of any trivial accomplishment a man like myself may find it almost necessary to acquire, and to which in his very different sphere he is far superior that Mr. Karkar shrugged his shoulders, deprecating further praise and said no more. All this time Edith never raised her eyes unless to glance toward her mother when that lady's fervent spirit shone forth in words. But as Karkar ceased, she looked at Mr. Dombie for a moment, for a moment only, but with a transient gleam of scornful wonder on her face, not lost on one observer who was smiling round the board. Mr. Dombie caught the dark eyelash in its descent and took the opportunity of arresting it. You have been to Warwick often, unfortunately, said Mr. Dombie. Several times. The visit will be tedious to you, I am afraid. Oh no, not at all. Ah, you are like your cousin, Phoenix, my dearest Edith, said Mrs. Scuton. He has been to Warwick Castle fifty times if he has been there once. Yet if he came to Leamington to-morrow, I wish he would, dear Angel, he would make his fifty-first visit next day. We are all enthusiastic, are we not, Mama? asked Edith with a cold smile. Too much so, for our peace, perhaps, my dear, returned her mother. But we won't complain.  The scabbard, perhaps, said Edith. Exactly. A little too fast.  Edith had turned her face towards Mr. Dombie when he first addressed her, and had remained in that attitude, while speaking to her mother, and while her mother spoke to her as though offering him her attention, if he had anything more to say. There was something in the manner of this simple courtesy, almost defiant, and giving it the character of being rendered on compulsion, or as a matter of traffic, to which she was a reluctant party, again not lost upon that same observer who was smiling round the board. It set him thinking of her as he had first seen her, when she had believed herself to be alone among the trees. Mr. Dombie, having nothing else to say, proposed the breakfast being now finished, and the major gorge like any boa constrictor, that they should start. A barouche being in waiting, according to the orders of that gentleman, the two ladies, the major, and himself, took their seats in it. The native and the wan page mounted the box, Mr. Townlinson being left behind, and Mr. Carker on horseback brought up the rear. Mr. Carker cantered behind the carriage, at the distance of a hundred yards or so, and watched it, during all of the ride, as if he were a cat, indeed, and its four occupants' mice. Whether he looked to one side of the road, or to the other, over distant landscape, with its smooth undulations, windmills, corn, grass, bean fields, wildflowers, farmyards, hayricks, and the spire among the wood, or upward in the sunny air, where butterflies were sporting round his head, and birds were pouring out their songs, or downward where the shadows of the branches interlaced, and made a trembling carpet on the road, or onward where the overhanging trees formed aisles and arches, dim with the softened light that steeped through leaves, one corner of his eye was ever on the formal head of Mr. Dombie, addressed towards him, and the feather in the bonnet drooping so neglectfully and scornfully between them, much as he had seen the haughty eyelids droop, not least so when the face met that now fronting it. Once, and once only, did his weary glance release these objects, and that was when a leap over a low hedge and a gallop across a field enabled him to anticipate the carriage coming by the road, and to be standing ready at the journey's end to hand the ladies out. Then, and but then, he met her glance for an instant in her first surprise, but when he touched her, in sliding with his soft white hand, it overlooked him altogether as before. Mrs. Skeuton was bent on taking charge of Mr. Carker herself and showing him the beauties of the castle. She was determined to have his arm and the majors, too. It would do that incorrigible creature, who was the most barbarous infidel in point of poetry, good to be in such company. This chance arrangement left Mr. Dombie at liberty to escort Edith, which he did, stalking before them through the apartments with a gentlemanly solemnity.  Yes, we have fallen off deplorably, said Mr. Carker. The peculiarity of their conversation was that Mrs. Skeuton, in spite of her ecstasies and Mr. Carker in spite of his urbanity, were both intent on watching Mr. Dombie and Edith. With all their conversational endowments, they spoke somewhat distractedly and at random in consequence. We have no faith left positively, said Mrs. Skeuton, advancing her shriveled ear, for Mr. Dombie was saying something to Edith. We have no faith in the dear old barons, who were the most delightful creatures, or in the dear old priests, who were the most warlike of men, or even in the days of that inestimable queen bests upon the wall there, which were so extremely golden, dear creature, she was all heart, and that charming father of hers, I hope you don't on Henry VIII. I admire him very much, said Carker. So bluff, cried Mrs. Skeuton.  Ah, ma'am, said Carker, stopping short. But if you speak of pictures, there's a composition. What gallery in the world can produce the counterpart of that? As the smiling gentleman thus spake, he pointed through a doorway to which Mr. Dombie and Edith were standing alone in the center of another room. They were not interchanging a word or a look. Standing together, arm in arm, they had the appearance of being more divided than if seas had rolled between them. There was a difference, even in the pride of the two, that removed them farther from each other, than if one had been the proudest and the other the humblest specimen of humanity in all creation. He, self-important, unbending, formal austere, she, lovely and graceful, in an uncommon degree, had totally, regardless of herself and him and everything around, and spurning her own attractions with her haughty brow and lip as if they were a badge or livery she hated. So unmatched were they, and opposed, so forced and linked together which adverse hazard and mischance had forged that fancy might have imagined the pictures on the walls around them, startled by the unnatural conjunction and observant of it in their several expressions. Grim knights and warriors looked scowling on them. A churchman, with his hand upraised, denounced the mockery of such a couple coming to God's altar. Quiet waters in landscapes, with the sun reflected in their depths, asked if better means of escape were not at hand, was there no drowning left? Ruins cried, look here and see what we are wedded to uncongenial time. Animals opposed by nature worried one another as a moral to them. Loves and cupids took to flight afraid and martyrdom had no such torment in its painted history of suffering. Nevertheless, Mrs. Skeuton was so charmed by the sight to which Mr. Carker invoked her attention that she could not refrain from saying, half aloud, how sweet, how very full of soul it was. Edith, overhearing, looked round and flushed indignant scarlet to her hair. My dearest Edith knows I was admiring her, said Cleopatra, tapping her almost timidly on the back with her parasol. Sweet pet! Again Mr. Carker saw the strife he had witnessed so unexpectedly among the trees. Again he saw the haughty languor and indifference come over it and hide it like a cloud. She did not raise her eyes to him, but with a slight peremptory motion of them seemed to bid her mother come near. Mrs. Skeuton thought it expedient to understand the hint, and advancing quickly with her two cavaliers kept near her daughter from that time. Mr. Carker now, having nothing to distract his attention, began to discourse upon the pictures and to select the best and point them out to Mr. Dombi, speaking with his usual familiar recognition of Mr. Dombi's greatness and rendering homage by adjusting his eyeglass for him, or finding out the right place in his catalogue, or holding his stick or the like. These services did not so much originate with Mr. Carker in truth as with Mr. Dombi himself, who was apt to assert his chieftainship by saying with subdued authority and in an easy way for him, Here, Carker, have the goodness to assist me, will you, which the smiling gentleman always did with pleasure. They made the tour of the pictures, the walls, crow's nest, and so forth, and as they were still one little party, and the major was rather in the shade being sleepy during the process of digestion, Mr. Carker became communicative and agreeable. At first he addressed himself for the most part to Mrs. Skeuton, but as that sensitive lady was in such ecstasies with the works of art, after the first quarter of an hour that she could do nothing but yawn, they were such perfect inspirations she observed as a reason for that mark of rapture. He transferred his attention to Mr. Dombi. Mr. Dombi said little beyond an occasional very true Carker or indeed Carker, but he tacitly encouraged Carker to proceed and inwardly approved of his behavior very much, deeming it as well that somebody should talk, and thinking that his remarks, which were, as one might say, a branch of the parent establishment, might amuse Mrs. Granger. Mr. Carker, who possessed an excellent discretion, never took the liberty of addressing that lady direct, but she seemed to listen, though she never looked at him, and once or twice, when he was emphatic in his peculiar humility, the twilight smile stole over her face, not as a light, but as a deep black shadow. Warwick Castle, being at length pretty well exhausted and the major very much so, to say nothing of Mrs. Scuton, whose peculiar demonstrations of delight had become very frequent indeed, the carriage was again put in requisition, and they rode to several admired points of view in the neighborhood. Mr. Dombi ceremoniously observed of one of these, that a sketch, however slight, from the fair hand of Mrs. Granger, would be a remembrance to him of that agreeable day, though he wanted no artificial remembrance. He was sure, here Mr. Dombi made another of his bows, which he must always highly value. Withers the lean, having Edith's sketchbook under his arm, was immediately called upon by Mrs. Scuton to produce the same, and the carriage stopped, that Edith might make the drawing, which Mr. Dombi was to put away among his treasures. But I am afraid I trouble you too much, said Mr. Dombi. By no means. Where would you wish it taken from? she answered, turning to him with the same enforced attention as before. Mr. Dombi, with another bow, which cracked the starch in his cravat, would beg to leave that to the artist. I would rather you choose for yourself, said Edith. Suppose then, said Mr. Dombi, we say from here. It appears a good spot for the purpose. Or, Corker, what do you think? There happened to be, in the foreground, at some little distance, a grove of trees, not unlike that in which Mr. Corker had made his chain of footsteps in the morning, and, with a seat under one tree greatly resembling in the general character of its situation, the point where his chain had broken. Might I venture to suggest to Mrs. Granger, said Corker, that that is an interesting, almost a curious point of view. She followed the direction of his riding whip with her eyes, and raised them quickly to his face. It was the second glance they had exchanged since their introduction, and would have been exactly like the first, but that its expression was plainer. Will you like that? said Edith to Mr. Dombi. I shall be charmed, said Mr. Dombi to Edith. Therefore the carriage was driven to the spot where Mr. Dombi was to be charmed, and Edith, without moving from her seat, and opening her sketchbook with her usual proud indifference, began to sketch. My pencils are all pointless, she said, stopping and turning them over. Pray allow me, said Mr. Dombi, or Corker will do it better, for he understands these things. Corker, have the goodness to see to these pencils for Mrs. Granger. Mr. Corker rode up close to the carriage door on Mrs. Granger's side, and, letting the rain fall on his horse's neck, took the pencils from her hand with a smile and a bow, and sat in the saddle, leisurely mending them. Having done so, he begged to be allowed to hold them, and to hand them to her as they were required, and thus Mr. Corker, with many commendations of Mrs. Granger's extraordinary skill, especially in trees, remained close at her side, looking over the drawing as she made it. Mr. Dombi, in the meantime, stood bolt upright in the carriage like a highly respectable ghost, looking on, too, while Cleopatra and the Major dallyed as two ancient doves might do. Are you satisfied with that, or shall I finish it a little more? said Edith, showing the sketch to Mr. Dombi. Mr. Dombi begged that it might not be touched. It was perfection. It is most extraordinary, said Corker, bringing every one of his red gums to bear upon his praise. I was not prepared for anything so beautiful and so unusual altogether. This might have applied to the sketcher no less than to the sketch, but Mr. Corker's manner was openness itself, not as to his mouth alone, but as to his whole spirit. So it continued to be, while the drawing was laid aside for Mr. Dombi, and while the sketching materials were put up. Then he handed in the pencils, which were received with a distant acknowledgement of his help, but without a look, and tightening his reign fell back and followed the carriage again. Thinking perhaps as he rode, that even this trivial sketch had been made and delivered to its owner as if it had been bargained for and bought. Thinking perhaps that although she had assented with such perfect readiness to his request, her haughty face bent over the drawing or glancing at the distant objects represented in it had been the face of a proud woman engaged in assorted and miserable transaction. Thinking perhaps of such things, but smiling certainly, and while he seemed to look about him freely in enjoyment of the air and exercise, keeping always that sharp corner of his eye upon the carriage. A stroll along the haunted ruins of Kenilworth, and more rides to more points of view, most of which Mrs. Skeuton reminded Mr. Dombi Edith had already sketched as he had seen in looking over her drawings, brought the day's expedition to a close. Mrs. Skeuton and Edith were driven to their own lodgings. Mr. Carker was graciously invited by Cleopatra to return thither with Mr. Dombi and the Major in the evening to hear some of Edith's music, and the three gentlemen repaired to their hotel to dinner. The dinner was the counterpart of yesterday's, except that the Major was twenty-four hours more triumphant and less mysterious. Edith was toasted again, Mr. Dombi was again agreeably embarrassed, and Mr. Carker was full of interest and praise. There were no other visitors at Mrs. Skeuton's. Edith's drawings were strewn about the room, a little more abundantly than usual perhaps, and withers the wan page handed round a little stronger tea. The harp was there, the piano was there, and Edith sang and played, but even the music was played by Edith to Mr. Dombi's order, as it were in the same uncompromising way, as thus. Edith, my dearest love, said Mrs. Skeuton half an hour after tea, Mr. Dombi is dying to hear you, I know. Mr. Dombi has life enough left to say so for himself, mama, I have no doubt. I shall be immensely obliged, said Mr. Dombi. What do you wish? Piano? Hesitated Mr. Dombi? Whatever you please, you have only to choose. Accordingly, she began with the piano. It was the same with the harp, the same with her singing, the same with the selection of the pieces that she sang and played, such frigid and constrained, yet prompt and pointed acquiescence with the wishes he imposed upon her and no one else, was sufficiently remarkable to penetrate through all the mysteries of Piquet and impress itself on Mr. Karker's keen attention. Nor did he lose sight of the fact that Mr. Dombi was evidently proud of his power and liked to show it. Nevertheless Mr. Karker played so well, some games with the major and some with Cleopatra, whose vigilance of eye in respect of Mr. Dombi and Edith no links could have surpassed, that he even heightened his position in the lady mother's good graces, and when, on taking leave, he regretted that he would be obliged to return to London next morning, Cleopatra trusted community of feeling not being met with every day, that it was far from being the last time they would meet. I hope so said Mr. Karker with an expressive look at the couple in the distance as he drew towards the door following the major. I think so. Mr. Dombi, who had taken a stately leave of Edith, bent or made some approach to a bend over Cleopatra's couch and said in a low voice, I have requested Mrs. Granger's permission to call on her tomorrow morning for a purpose, and she has appointed twelve o'clock. May I hope to have the pleasure of finding you at home, madam, afterwards?  Dombi, come along, cried the major, looking in at the door. Damme, sir, old Joe has a great mind to propose an alteration in the name of the Royal Hotel, and that it should be called the Three Jolly Bachelors in honor of ourselves and Karker. With this the major slapped Mr. Dombi on the back, and, winking over his shoulder at the ladies with a frightful tendency of blood for the head, carried him off. Mrs. Skeuten reposed on her sofa, and Edith sat apart by her harp in silence. The mother, trifling with her fan, looked stealthily at the daughter more than once. But the daughter, brooding gloomily with downcast eyes, was not to be disturbed. Thus they remained for a long time without a word, until Mrs. Skeuten's maid appeared, according to custom, to prepare her gradually for night. At night she should have been a skeleton with dart and hourglass, rather than a woman, this intended, for her touch was as the touch of death. The painted object shriveled underneath her hand, the form collapsed, the hair dropped off, the arched dark eyebrows changed to scanty tufts of gray, the pale lips shrunk, the skin became cadaverous and loose, an old worn yellow nodding woman with red eyes, alone remained in Cleopatra's place, huddled up like a slovenly bundle in a greasy flannel gown. The very voice was changed as it addressed Edith when they were alone again. Why don't you tell me, it said sharply, that he is coming here tomorrow by appointment. Because you know it, returned Edith, mother, the mocking emphasis she laid on that one word. You know he has bought me, she resumed, or that he will, tomorrow. He has considered of his bargain, he has shown it to his friend, he is even rather proud of it, he thinks that it will suit him and may be had sufficiently cheap, and he will buy tomorrow, God, that I have lived for this and that I feel it. Compress into one handsome face the conscious self abasement and the burning indignation of a hundred women strong in passion and in pride, and there it hit itself with two white shuddering arms. What do you mean, returned the angry mother? Haven't you from a child? A child, said Edith looking at her, when I was a child, what childhood did you ever leave to me? I was a woman, artful, designing, mercenary, laying snares for men, before I knew myself or you or even understood the base and wretched aim of every new display I learned. You gave birth to a woman, look upon her, she is in her pride tonight. And as she spoke she struck her head upon her beautiful bosom, as though she would have beaten down herself. Look at me, she said, who have never known what it is to have an honest heart and love. Look at me, taught to scheme and plot when children play and married in my youth, an old age of design to one for whom I had no feeling but indifference. Look at me, whom he left a widow dying before his inheritance descended to him, a judgment on you, well deserved, and tell me what has been my life for ten years since. We have been making every effort to endeavor to secure you to a good establishment. Rejoined her mother, that has been your life and now you have got it. There is no slave in a market, there is no horse in a fair, so shown and offered and examined and paraded mother, as I have been for ten shameful years, cried Edith with a burning brow. And the same bitter emphasis on the one word. Is it not so? Have I been made the byword of all kinds of men?  The license of look and touch, she said with flashing eyes. Have I submitted to it in half the places of resort upon the map of England? Have I been hawked and vented here and there until the last grain of self-respect is dead within me and I loathe myself? Has this been my late childhood? I had none before.  You might have been well married, said her mother, twenty times at least Edith, if you had given encouragement enough. Know who takes me, refuse that I am, and as I well deserve to be, she answered, raising her head and trembling in her energy of shame and stormy pride. Shall take me as this man does, with no art of mine put forth to lure him. He sees me at the auction, and he thinks it well to buy me. Let him, when he came to view me, perhaps to bid. He required to see the role of my accomplishments, I gave it to him. When he would have me show one of them to justify his purchase to his men, I require of him to say which he demands, and I exhibit it. I will do no more. He makes the purchase of his own will, and with his own sense of its worth, and the power of his money, and I hope it may never disappoint him. I have not flaunted and pressed the bargain, neither have you, so far as I have been able to prevent you. You talk strangely, tonight, Edith, to your own mother. It seems so to me, stranger to me than you, said Edith. But my education was completed long ago. I am too old now, and have fallen too low by degrees, to take a new course and to stop yours, and to help myself. The germ of all that purifies a woman's breast, and makes it true and good, has never stirred in mind, and I have nothing else to sustain me when I despise myself. There had been a touching sadness in her voice, but it was gone, when she went on to say with a curled lip. So, as we are genteel and poor, I am content that we should be made rich by these means. All I say is, I have kept the only purpose I have had the strength to form. I had almost said the power with you at my side, mother, and have not tempted this man on. This man, you speak, said her mother, as if you hated him. And you thought I loved him, did you not? She answered, stopping on her way across the room and looking round. Shall I tell you? She continued, with her eyes fixed on her mother, who already knows us thoroughly, and reads us right, and before whom I have even less of self-respect or confidence than before my own inward self, being so much degraded by his knowledge of me. This is an attack, I suppose, returned her mother coldly, on poor, unfortunate, what's his name, Mr. Carker. Your want of self-respect and confidence, my dear, in reference to that person who is very agreeable, it strikes me, is not likely to have much effect on your establishment.  Edith suddenly let fall her face, as if it had been stung, and while she pressed her hands upon it, a terrible tremble crept over her whole frame. It was quickly gone, and with her usual step she passed out of the room. The maid, who should have been a skeleton, then reappeared, and giving one arm to her mistress, who appeared to have taken off her manner with her charms, and to have put on paralysis with her flannel gown, collected the ashes of Cleopatra, and carried them away in the other, ready for tomorrow's revivification. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. So the day has come at length, Susan said Florence to the excellent Nipper, when we are going back to our quiet home. Susan drew in her breath with an amount of expression, not easily described, and further relieving her feelings with a smart cough answered, Very quiet indeed, Miss Floyd, no doubt, excessive so. When I was a child, said Florence thoughtfully, and after musing from some moments, did you ever see that gentleman who has taken the trouble to ride down here to speak to me?  Three times, Miss returned the Nipper. Once, when you was out, a walking with them skit, Florence gently looked at her, and Miss Nipper checked herself. With Sir Barnett and his lady, I mean to say Miss, and the young gentleman, and two evenings since then, when I was a child, and when company used to come to visit papa, did you ever see that gentleman at home, Susan, asked Florence? Well, Miss, returned her maid after considering. I really couldn't say I ever did. When your poor dear ma died, Miss Floyd, I was very new in the family you see and my element. The Nipper bridled, as a pining that her merits had been always designedly extinguished by Mr. Donby. Was the floor below the attics? To be sure, said Florence, still thoughtfully, you are not likely to have known who came to the house. I quite forgot. Not, Miss, but what we talked about the family and visitors, said Susan, and but what I heard much said, although the nurse before Mrs. Richards did make unpleasant remarks when I was in company, and hint at little pictures. But that could only be attributed, poor thing, observed Susan, with composed forbearance to habits of intoxication for which she was required to leave and did. Florence, who was seated at her chamber window, with her face resting on her hand, sat looking out and hardly seemed to hear what Susan said. She was so lost in thought. At all events, Miss, said Susan, I remember very well that this same gentleman, Mr. Cawker, was almost, if not quite, as great a gentleman with your paw then as he is now. It used to be said in the house then, Miss, that he was at the head of all your pa's of theirs in the city, and managed the whole, and that your pa minded him more than anybody, which, begging your pardon, Miss Fly, he might easy do, for he never minded anybody else. I know that, picture as I might have been. Susan Nipper, with an injured remembrance of the nurse before Mrs. Richards, emphasized, picture strongly. And that Mr. Cawker has not fallen off, Miss, she pursued, but has stood his ground and kept his credit with your pa. I know from what is always said among our people by that perch, whenever he comes to the house, and though he's the weakest weed in the world, Miss Fly, and no one can have a moment's patience with the man, he knows what goes on in this city tolerable well, and says that your pa does nothing without Mr. Cawker, and leaves all to Mr. Cawker, and acts according to Mr. Cawker, and has Mr. Cawker always at his elbow, and I do believe that he believes that washiest of perches, that after your pa, the Emperor of India, is the child unborn to Mr. Cawker. Not a word of this was lost on Florence, who, with an awakened interest in Susan's speech, no longer gazed abstractedly on the prospect without, but looked at her and listened with attention. Yes, Susan, she said, when that young lady had concluded, he is in papa's confidence, and is his friend, I am sure. Florence's mind ran high on this theme, and had done for some days. Mr. Cawker, in the two visits with which he had followed up his first one, had assumed a confidence between himself and her, a right on his part to be mysterious and stealthy, in telling her that the ship was still unheard of, a kind of mildly restrained power and authority over her, that made her wonder, and caused her great uneasiness. She had no means of repelling it, or of freeing herself from the web he was gradually winding about her, for that would have required some art and knowledge of the world, opposed to such address as his, and Florence had none. True, he had said no more to her than that there was no news of the ship, and that he feared the worst, but how he came to know that she was interested in the ship, and why he had the right to signify his knowledge to her so insidiously and darkly, troubled Florence very much. This conduct on the part of Mr. Cawker, and her habit of often considering it with wonder and uneasiness, began to invest him with an uncomfortable fascination in Florence's thoughts, a more distinct remembrance of his features, voice, and manner, which she sometimes courted as a means of reducing him to the level of a real personage capable of exerting no greater charm over her than another, did not remove the vague impression, and yet he never frowned or looked upon her with an air of dislike or animosity, but was always smiling and serene. Again Florence, in pursuit of her strong purpose with reference to her father, and her steady resolution to believe that she was herself unwittingly to blame for their so cold and distant relations, would recall to mind that this gentleman was his confidential friend, and would think with an anxious heart could her struggling tendency to dislike and fear him to be a part of that misfortune in her which had turned her father's love adrift and left her so alone. She dreaded that it might be, sometimes believed it was, then she resolved that she would try to conquer this wrong feeling, persuaded herself that she was honored and encouraged by the notice of her father's friend, and hoped that patient observation of him and trust in him would lead her bleeding feet along the stony road which ended in her father's heart. Thus with no one to advise her, for she could advise with no one without seeming to complain against him, gentle Florence tossed on an uneasy sea of doubt and hope, and Mr. Corker, like a scaly monster of the deep, swam down below and kept his shining eye upon her. Florence had a new reason in all this for wishing to be at home again. Her lonely life was better suited to her course of timid hope and doubt, and she feared sometimes that in her absence she might miss some hopeful chance of testifying her affection for her father. Heaven knows she might have set her mind at rest, poor child, on this last point.  Of Walter she thought often, ah, how often, when the night was gloomy and the wind was blowing round the house, but hope was strong in her breast. It is so difficult for the young and ardent, even with such experience as hers, to imagine youth and ardor quenched like a weak flame, and the bright day of life merging in tonight, at noon, that hope was strong yet. Her tears fell frequently for Walter's sufferings, but rarely for his supposed death, and never long. She had written to the old instrument-maker, but had received no answer to her note, which indeed required none. Thus matters stood with Florence on the morning when she was going home, gladly to her old secluded life. Dr. and Mrs. Blimber, accompanied much against his will, by their valued charge Master Barnett, were already gone back to Brighton, where that young gentleman and his fellow pilgrims to Parnassus were then, no doubt, in the continual resumption of their studies. The holiday time was past and over. Most of the juvenile guests at the villa had taken their departure, and Florence's long visit was come to an end. There was one guest, however, albeit not resident within the house, who had been very constant in his attention to the family, and who still remained devoted to them. This was Mr. Toots, who, after renewing, some weeks ago, the acquaintance he had had the happiness of forming with Skeettles, Jr., on the night when he burst the blimberian bonds and soared into freedom with his ring on, called regularly every other day, and left a perfect pack of cards at the hall door, so many indeed that the ceremony was quite a deal on the part of Mr. Toots, and a hand at whisk on the part of the servant. Mr. Toots likewise, with the bold and happy idea of preventing the family from forgetting him, but there is reason to suppose that this expedient originated in the teeming brain of the chicken, had established a six-ord cutter, managed by aquatic friends of the chickens, and steered by that illustrious character in person, who wore a bright red fireman's coat for the purpose, and concealed the perpetual black eye with which he was afflicted beneath a green shade. Previous to the institution of this equipage, Mr. Toots sounded the chicken on a hypothetical case, as supposing the chicken to be enamored of a young lady named Mary, and to have conceived the intention of starting a boat of his own. What would he call the boat? The chicken replied with diverse strong asservations that he would either christen it pole or the chicken's delight. Improving on this idea, Mr. Toots, after deep study and the exercise of much invention, resolved to call his boat the Toots's Joy, as a delicate compliment to Florence, of which no man knowing the parties could possibly miss the appreciation. Stretched on a crimson cushion in his gallant bark with his shoes in the air, Mr. Toots, in the exercise of his project, had come up the river day after day and week after week, and had flitted to and fro near Sir Barnett's garden, and had caused his crew to cut across and across the river at sharp angles, for his better exhibition to any lookers on, from Sir Barnett's windows, and had had such evolution performed by the Toots's Joy as had filled all the neighboring part of the waterside with astonishment. But whenever he saw anyone in Sir Barnett's garden on the brink of the river, Mr. Toots always feigned to be passing there by a combination of coincidences of the most singular and unlikely description. How are you, Toots, Sir Barnett would say, waving his hand from the lawn, while the artful chicken steered close inshore. How did you, Sir Barnett? Mr. Toots would answer. What a surprising thing that I should see you here! Mr. Toots, in his sagacity, always said this as if, instead of that being Sir Barnett's house, it were some deserted edifice on the banks of the Nile Organges. I never was so surprised, Mr. Toots would exclaim, Is Miss Domby there? Whereupon Florence would appear, perhaps. Oh, Diogenes is quite well, Miss Domby, Mr. Toots would cry. I called to ask this morning. Thank you very much, the pleasant voice of Florence would reply. Won't you come ashore, Toots? Sir Barnett would say then. Come, you're in no hurry. Come and see us. Oh, it's of no consequence, thank you, Mr. Toots would blushingly rejoin. I thought Miss Domby might like to know, that's all. Goodbye! And poor Mr. Toots, who was dying to accept the invitation, but hadn't the courage to do it, signed to the chicken with an aching heart and away went the joy, cleaving the water like an arrow. The joy was lying in a state of extraordinary splendor at the garden steps on the morning of Florence's departure. When she went downstairs to take leave after her talk with Susan, she found Mr. Toots awaiting her in the drawing room. Oh, how did you, Miss Domby? Said the stricken Toots, always dreadfully disconcerted when the desire of his heart was gained. And he was speaking to her. Thank you, I'm very well indeed. I hope you're the same. So was Diogenes yesterday. You are very kind, said Florence. Thank you, it's of no consequence, retorted Mr. Toots. I thought perhaps you wouldn't mind, in this fine weather, coming home by water, Miss Domby. There's plenty of room in the boat for your maid. I am very much obliged to you, said Florence, hesitating. I really am, but I would rather not. Oh, it's of no consequence, retorted Mr. Toots. Good morning. Won't you wait and see Lady Sketl's? Asked Florence kindly. Oh no, thank you, return Mr. Toots, it's of no consequence at all. So shy was Mr. Toots on such occasions, and so flurried. But, Lady Sketl's, entering at the moment, Mr. Toots was suddenly seized with a passion for asking her how she did, and hoping she was very well. Nor could Mr. Toots, by any possibility, leave off shaking hands with her, until Sir Barnett appeared, to whom he immediately clung with the tenacity of desperation. We are losing today, Toots, said Sir Barnett, turning towards Florence. The light of our house, I assure you. Oh, it's of no consequence. I mean, yes, to be sure, faltered the embarrassed Toots. Good morning. Notwithstanding the emphatic nature of this farewell, Mr. Toots, instead of going away, stood leering about him vacantly. Florence, to relieve him, bade adieu, with many thanks to Lady Sketl's, and gave her arm to Sir Barnett. May I beg of you, my dear Miss Domby, said her host, as he conducted her to the carriage, to present my best compliments to your dear papa. It was distressing to Florence to receive the commission, for she felt as if she were imposing on Sir Barnett, by allowing him to believe that a kindness rendered to her was rendered to her father. As she could not explain, however, she bowed her head and thanked him, and again she thought that the dull home free from such embarrassments and such reminders of her sorrow was her natural and best retreat. Such of her late friends and companions, as were yet remaining at the villa, came running from within, and from the garden, to say goodbye. They were all attached to her, and very earnest in taking leave of her. Even the household were sorry for her going, and the servants came nodding and curtsying round the carriage door, as Florence looked round on the kind faces, and saw among them those of Sir Barnett and his lady, and of Mr. Toots, who was chuckling and staring at her from a distance. She was reminded of the night when Paul and she had come from Dr. Blimbers, and when the carriage drove away, her face was wet with tears. Soreful tears, but tears of consolation too, for all the softer memories connected with the dull old house to which she was returning, made it dear to her, and they rose up. How long it seemed since she had wandered through the silent rooms, since she had last crept softly and afraid into those her father occupied, since she had felt the solemn but yet soothing influence of the beloved dead in every action of her daily life. This new farewell reminded her, besides of her parting with poor Walter, of his looks and words that night, and of the gracious blending she had noticed in him, of tenderness for those he left behind with courage and high spirit. His little history was associated with the old house too, and gave it a new claim and hold upon her heart. Even Susan Nipper softened toward the home of so many years as they were on their way toward it. Gloomy as it was, and rigid justice as she rendered to its gloom, she forgave it a great deal. I shall be glad to see it again. I don't deny, Miss, said the Nipper. There ain't much in it to boast of, but I wouldn't have it burnt or pulled down neither. You'll be glad to go through the old rooms, won't you, Susan? said Florence, smiling. Well, Miss, returned the Nipper, softening more and more towards the house as they approached it nearer. I won't deny but what I shall, though I shall hate him again, tomorrow very likely. Florence felt that, for her, there was greater peace within it than elsewhere. It was better and easier to keep her secret shut up there among the tall dark walls than to carry it abroad into the light and try to hide it from a crowd of happy eyes. It was better to pursue the study of her loving heart alone and find no new discouragements in loving hearts about her. It was easier to hope and pray and love on, all uncared for, yet with constancy and patience in the tranquil sanctuary of such remembrances, although it moldered, rusty and decayed about her, then in a new scene let its gaity be what it would. She welcomed back her old enchanted dream of life and longed for the old dark door to close upon her once again. Full of such thoughts they turned into the long and somber street. Florence was not on that side of the carriage which was nearest to her home, and as the distance lessened between them and it she looked out of her window for the children over the way. She was thus engaged when an exclamation from Susan caused her to turn quickly round. Why gracious me! cried Susan, breathless. Where's our house? Our house! said Florence. Susan, drawing in her head from the window, thrust it out again and drew it in again as the carriage stopped and stared at her mistress in amazement. There was a labyrinth of scaffolding raised all round the house from the basement to the roof. Loads of bricks and stones and heaps of mortar and piles of wood blocked up half the width and length of the broad street at the side. Ladders were raised against the walls, laborers were climbing up and down, men were at work upon the steps of the scaffolding, painters and decorators were busy inside, great rolls of ornamental paper were being delivered from a cart at the door, an upholsterer's wagon also stopped the way no furniture was to be seen through the gaping and broken windows in any of the rooms, nothing but workmen and the implements of their several trades. Swarming from the kitchen to the garret, inside and outside alike brick layers, painters, carpenters, masons, hammer, hod, brush, pickaxe, saw and trowel all at work together in full chorus, Florence descended from the coach half doubting if it were or could be the right house until she recognized Talenson with a sunburned face standing at the door to receive her. There is nothing the matter, inquired Florence. Oh no miss, there are great alterations going on. Yes miss, great alterations, said Talenson. Florence passed him as if she were in a dream and hurried upstairs. The garish light was in the long darkened drawing room and there were steps and platforms and men in paper caps in the high places. Her mother's picture was gone with the rest of the moveables and on the mark where it had been was scrawled in chalk. This room in panel, green and gold. The staircase was a labyrinth of posts and planks like the outside of the house and a whole olympus of plumbers and glazers was reclining in various attitudes on the skylight. Her own room was not yet touched within but there were beams and boards raised against it without balking the daylight.  It was here that Susan Nipper who had been in quest of Florence found her and said would she go downstairs to her papa who wished to speak to her. At home and wishing to speak to me cried Florence trembling. Susan who was infinitely more distraught than Florence herself repeated her errand and Florence pale and agitated hurried down again without a moment's hesitation. She thought upon the way down would she dare to kiss him? The longing of her heart resolved her and she thought she would. Her father might have heard that heartbeat when it came into his presence. One instant and it would have beat against his breast but he was not alone. There were two ladies there and Florence stopped striving so hard with her emotion that if her brute friend Dai had not burst in and overwhelmed her with his caresses as a welcome home at which one of the ladies gave a little scream and that diverted her attention from herself she would have swooned upon the floor.  How do you do? Florence took the hand between her own and putting it timidly to her lips yielded to its withdrawal. It touched the door in shutting it with quite as much endearment as it had touched her. What dog is that? said Mr. Domby displeased. It is a dog papa from Brighton. Well said Mr. Domby and a cloud passed over his face for he understood her. He is very good tempered said Florence addressing herself with her natural grace and sweetness to the two lady strangers. He is only glad to see me. Pray forgive him. She saw in the glance they interchanged that the lady who had screamed and who was seated was old and that the other lady who stood near her papa was very beautiful and of an elegant figure. Mrs. Skeuton said her father turning to the first and holding out his hand. This is my daughter Florence. Charming I am sure observed the lady putting up her glass. So natural my dear Florence you must kiss me if you please. Florence having done so turned towards the other lady by whom her father stood waiting. Edith said Mr. Domby this is my daughter Florence. Florence this lady will soon be your mama. Florence started and looked up at the beautiful face in a conflict of emotions among which the tears that name awakened struggled for a moment with surprise interest admiration and an indefinable sort of fear. Then she cried out oh papa may you be happy may you be very very happy all your life and then fell weeping on the ladies bosom. There was a short silence the beautiful lady who at first had seemed to hesitate whether or no she should advance to Florence held her to her breast and pressed the hand with which she clasped her close about her waist as if to reassure and comfort her. Not one word passed the lady's lips she bent her head down over Florence and she kissed her on the cheek but she said no word. Shall we go on through the rooms said Mr. Domby and see how our workmen are doing pray allow me my dear madam. He said this in offering his arm to Mrs. Scuton who had been looking at Florence through her glass as though picturing to herself what she might be made by the infusion from our own copious storehouse no doubt of a little more heart and nature. Florence was still sobbing on the ladies breast and holding to her when Mr. Domby was heard to say from the conservatory let us ask Edith dear me where is she Edith my dear cried Mrs. Scuton where are you looking for Mr. Domby somewhere I know we are here my love the beautiful lady released her hold of Florence and pressing her lips once more upon her face withdrew hurriedly and joined them Florence remained standing in the same place happy sorry joyful and in tears she knew not how or how long but all at once when her new mama came back and took her in her arms again Florence said the lady hurriedly and looking into her face with great earnestness you will not begin by hating me by hating you mama cried Florence winding her arm round her neck and returning the look hush begin by thinking well of me said the beautiful lady begin by believing that I will try to make you happy and that I am prepared to love you Florence goodbye we shall meet again soon goodbye don't stay here now again she pressed her to her breast she had spoken in a rapid manner but firmly and Florence saw her rejoin them in the other room and now Florence began to hope that she would learn from her new and beautiful mama how to gain her father's love and in her sleep that night in her lost old home her own mama smiled radiantly upon the hope and blessed it dreaming Florence end of chapter 28


Hello and welcome to the session. In this session we will discuss the method for integration by parts. This method is basically very useful in integrating products of functions. For given functions f1 and f2 integral of the product of these two functions would be equal to the first function f1x into integral of the second function f2x minus integral of the differential coefficient of the first function multiplied by the integral of the second function. We have to be very careful in choosing the first function and the second function. The second function would be that function whose integral is well known to us and if any function is the power of x or a polynomial in x then we take that function as the first function and if in some cases if one function is inverse trigonometric function logarithmic function then these functions would be taken as the first function. Let's try and find out the value of the integral i equal to integral of x into e to the power x dx. Here the two functions are x and e to the power x. We know that if a function is a power of x or a polynomial in x then we take it as the first function. So in this case this x would be taken as the first function and e to the power x is taken as the second function. Now we integrate this by parts. On doing this we get the first function that is x into integral of the second function minus integral of the differential coefficient of the first function into integral of the second function. This gives us x into now integral of e to the power x is e to the power x itself minus integral of differential coefficient of x would be 1 into integral of e to the power x is e to the power x dx which further is equal to x into e to the power x minus e to the power x plus c. Remember that we do not add the constant of integration to the integral of the second function. So this is the final value for i. Here c is the constant of integration. If we have the integral of the type integral of e to the power x multiplied by fx plus f dash x dx this would be equal to e to the power x into fx plus c. Consider the integral i equal to integral of e to the power x into 1 upon x minus 1 upon x square dx. Now as you can see this integral is of this form integral of e to the power x into fx plus f dash x dx. Here we have fx is the function 1 upon x and its f dash x is equal to minus 1 upon x square. So from this we see that the value of this integral i is equal to e to the power x into fx that is 1 upon x plus c where the c is the constant of integration. Now we discuss some special types of integrals. The first one here is integral of square root x square minus a square dx is equal to x upon 2 square root x square minus a square minus a square upon 2 log modulus x plus square root x square minus a square plus c. The next one is integral square root of x square plus a square dx this is equal to x upon 2 square root x square plus a square plus a square upon 2 log modulus x plus square root x square plus a square plus c. Then integral square root a square minus x square dx is equal to x upon 2 square root a square minus x square plus a square upon 2 sin inverse x upon a plus c. Let's try and find the value of the integral i equal to integral of square root 4 minus x square dx. This is written in the form integral of square root 2 square minus x square dx. Now if you look at this function you can very well see that we can use this formula according to which we have integral of square root a square minus x square dx is equal to x upon 2 multiplied by square root a square minus x square plus a square upon 2 sin inverse x upon a plus c. In this case we will take a as 2 and we will substitute this value of a in this formula we get this is equal to x upon 2 square root of a square minus x square plus a square upon 2 sin inverse x upon a plus c. This is equal to x upon 2 square root of 4 minus x square plus 2 sin inverse x upon 2 plus c. This is the value for i. This c is the constant of integration. This is how we use this formulae to find the value of the integrants. This completes the session. Hope you understood the method of integration by parts.


of Square with the Program of Fuscation by Boas Barak, Tzvika Brackersky, and Ilan Komogotsky, and Prava Skotari, and Ilan is going to give the talk. Hi, thanks for having me. I'm Ilan, and I'll talk about limits on low-degree Surrounding Generators. This is a joint work with Boas, Tzvika, and Provesh. So even though this talk is in the Fuscation session, I will barely talk about Fuscation. I won't even define it, but I'll mostly talk about Surrounding Generators. So what is a Surrounding Generator, or in short, a PRG? So a PRG is a function that expands n bits to n bits. We will denote it by G. So G goes from n to m. And it's convenient for this talk to think about each output bit as a function. So G sub i will just be the function that gets the x bits in the input, the n bits in the input, and outputs a single bit, 0 or 1. So G sub i goes from n to 1, and G goes from n to m. And it's a collection of m functions, G sub i. The Surrandleness of PRG, or the security of this primitive, is defined by saying that any computationally bounded adversary cannot distinguish a G on a random seed versus a really uniform string of length n. This is the security definition. It's a basic primitive in cryptography. It's the basic building block in constructing Surrounding functions and GGM construction. And we also know that, assuming one-way functions, we can build a PRG with arbitrary polynomial stretch by the hill construction. So this is really one of the basic photographic primitives that's used everywhere. And a natural question, given that this is such a basic primitive, is how simple can this primitive be? What do I mean by simple? So there are many ways to define simplicity of a primitive. Specifically for a PRG, one way to think about it is just saying, what's the circuit size that computes it? Second one, what's the depth of the circuit? And there may be more. So one central notion of simplicity that was considered in the past two decades is something called locality. What is a local Surrounding generator? So it's the same thing. It's a function that maps from n bits to n bits. But it's simple, in what sense? Each output bit, so each such function G sub i is a local function. So G sub i doesn't really look at all the n input bits, but it only looks at these specific ones. So there is some mapping that we'll call i sub i that maps the indices that are relevant for G sub i in order to compute G in the i sub bit. So this is a local Surrounding generator. What do we know about them? Do they exist? Maybe they don't exist. What's the trade-offs? Can we get an arbitrarily small d with an arbitrarily large expansion? All of these questions are of central interest, both due to practical implications because these are really easier to design pure Gs and they have lots of theoretical applications that we'll discuss. So we have positive and negative results about this primitive. The positive results are summarized as follows. If you assume that one way functions are in NC1, namely, there exists a one-way function computable in bounded depth, then there is a local Surrounding generator with constant locality that expands from n bits to n plus n to the epsilon, or some small constant epsilon. This is up about metal from 2006. The second result is actually not a real construction, but it's a candidate, a very generic approach towards constructing local Surrounding generators. It was initiated by Goldwright in 2000, and it's a family of assumptions or candidates saying that, look, maybe it's plausible that there is a construction that maps n to some specific polynomial. Think about it like n squared that has only constant locality and it is a pure G. So Goldwright suggested that this function may be one way, but follow-up work suggests that actually it even might be Surrounding. We also have negative results. The negative results are the following. If you want locality two, there's actually nothing you can do. There's not a pure G that expands even by a single bit. If you want locality three, Cri-Milterson showed that you can have only linear stretch, namely you can stretch n bits to maybe two n bits, but not much more than that. For D equals four, same thing. That's mostly done. And most surprisingly, for general D, they gave an upper bound on how much the pure G can stretch. They show that it's at most something like n to the D, n to the D over two. That's the best you can hope for for a local pure G with locality D. And as I said, this primitive has tons of applications. So here are just three of them. One application is very efficient constructions of public encryption schemes. That's upper bound in 2010. Later, they were also used to construct efficient MPC protocols. And most relevant to this work is the recent work, is the recent line of works of constructing indistinguishability of this case from this primitive. So I won't really tell you what IO is. All you need to know is the following bit. It's our dream. If we can get it, we will solve all of our problems and we can all go home. So the theorem that Lin proved, Lin and Nantens are high, roughly two years ago, is that this magical primitive that we all hope exists can be based on the following two assumptions. The first assumption is that there is a local pseudo-random generator with locality D that maps n bits to n to the one plus epsilon. The second assumption is another creature that we'll call degree D multiliner maps. I will not define that, but just remember that for D equals two, this is what we all know and love called bilinear maps. So let's see what's the implication of this theorem. So first, let's plug in D equals two and see what happens. So on the one hand, we have bilinear maps. We have candidates. We believe that they're secure in some sense. We're fine. Unfortunately, as we saw, there's no PRG with such stretch. What about D equals three or four? The situation is even worse. Not only there's no such PRG, but we also don't have satisfying candidate multiliner maps, three or four multiliner maps. So we'd have to go for the equals five. But even there, we don't have candidate multiliner maps, but we do have PRGs. So that's that. So the situation is not so good. So this is where you think things end, but luckily we have the beautiful work of Lina Dussaro from last year showing the following result. It's actually the same thing as the previous one. There's an extra word, bloc, localize, DD. So they show that IO exists based on the following two assumptions. Again, degree D multiliner maps and a PRG with the stretches and bits to enter the one plus epsilon with the property that is D bloc local. What is bloc locality? So it's the same thing as locality, except now the inputs to the PRG are not bits, but are actually, you can think about it as coming from a large alphabet, sigma. So now the PRG maps from sigma to the n to zero one to the m. And one convenient way to think about it is that each bloc is not a symbol in an alphabet, but actually b bits. So the alphabet is of size two to the b and each bloc is of size b bits and the locality means that each output bit depends only on few blocks, but inside the bloc it can do whatever it wants. So in terms of locality, the locality of this thing is pretty big because you can touch two to the two b inputs on every output. So what B and the sorrow needed is a PRG with bloc locality two that or D in general that maps n times b bits because this is the size of your input now, two to the three b times n to the one plus epsilon. This is what they need for their construction in order for it to work. And their observation is that all the lower bounds that we had of most of the tar and crying milters and do not apply as far as we know when they wrote the paper, this primitive might even exist for D equals two, which is kind of spectacular because it will imply IO from bilinear maps. So our results in natural are that the discriminative does not exist for D equals two. So you need a different approach to construct IO from bilinear maps. And we also have maybe a positive result that we believe that this primitive actually exists for D equals three, meaning that the only thing between us and IO is the three linear map, which sounds not so hard. So here's our results in slightly more details. So we have a couple of attacks depending on the model. The strongest result or the hardest model is the first line in this table, saying that if your PRG stretches from n times b bits to two to the two b times n bits, then no matter what predicates you use, no matter what underlying graph you have, and no matter if the predicates are different or equal, this PRG will be broken. We have an algorithm that distinguishes random from the output of the PRG. If you relax the predicates to be the same on all output bits, so these GIs are the same for every I, then we can even have a better attack and rule out such a PRG even with stretch two to the b. And if you think that the predicate will be random, the graph will be random, and you allow different predicates, then we can also rule out two to the b. Two to the b stretch. So these are the results. So all of these results are, the first one already breaks the assumption of linear to the linear to the sorrow, and the second ones are with better parameters, but we don't know how to get IO from this range of parameters. I'll talk about it in the summary. So as a bonus, we also give a candidate a very simple and appealing candidate for three block local PRG with very small block sides, just off one, and polynomial stretch. So you can look at the paper for more details about that. So these are our results. In the rest of this talk, I'll give you an overview of how we achieved the first result, but not with two b, but with three b. This will be enough to show you the main ideas. I should also mention that the second result was also obtained independently by Lombardi and Lakutanathan in DCC last year. So we're going to break PRG, right? So what's the game in a PRG? There's an adversary that gets G to the random or uniform, and it's to distinguish. What does it mean to distinguish? It should output the probability that it outputs one on the image of a PRG. It should be noticeably different than the probability that it outputs one if you sample the input from the PRG and not from uniform. So this is the game, the Surand in this game. We will actually do something even harder than that. We'll break it even stronger, even in a more strong sense, in a stronger sense. We'll do something we call image refutation. What is image refutation? We will require the adversary, or this is what we'll actually achieve, to on inputs from the image of the PRG. We'll always say one. We'll just always say one by default on all images of the PRG. But if the input comes from the uniform distribution, we'll say one only with a very small probability. You can think about it as sort of one sided analog of Surand in this. So this is what we're actually going to do. And as I said, this is stronger than distinguishing because just think of Z as the uniform distribution. This is much stronger. We identify the elements that are not in the image. And another upside is that we can actually handle preprocessing on the inputs because we're doing image refutation. This is actually useful for Lin and Sauer's paper. They actually used it. So it's actually another advantage for us. So here's the proof idea. We'll work in two steps. The first step, what we're going to do, we are going to take our local PRG and we're going to massage it to get a sparse low degree polynomial where we think of it as an algebraic polynomial and not as a function, as a Boolean function. So we'll take a local PRG, we're going to massage it and get a sparse algebraic polynomial with low degree. That's what we're going to do. Once we do that, we have a polynomial which is sparse. It has only S monomials, let's say. And this is just a collection P1 to Pm of polynomials. Each of them has low degree and this is the polynomial that we get. What we're going to do, we're going to compute this program. We're going to compute value which is the maximum over, you go over all inputs X and you look at the sum XI, Zi given an input Z. This is the input you want to decide whether it's in the image of the PRG or just random. You're going to compute the following program. You're going to find the maximum X, the X that maximizes the sum of Zi, this is the i to the b to the z, times the polynomial, that's polynomial Bi on the input X. We're just going to maximize this computation. Let's assume for a second we can do it in polynomial time. I will explain how we do it in a second. A priori it seems like it takes exponential time because we have to go over all x's. But we can actually do it in polynomial time. I'll show you in a minute how. Assume that we do these two steps. I claim that we're done. Y, Z is in the image of the PRG. It's going to be the case that value is large. If we're not in the image of the PRG with high probability, it's going to be small. So we'll only look at the value of val if it's high we'll output one, if it's low we'll output zero. This is the algorithm, super simple. So let's see first step two. So we're given an input Z and we need to decide whether the value of val is large or small. Let's see why this is enough. So assume for a second that the polynomial is sparse because we said we'll have a transformation that will result with the sparse polynomial. So the first observation, if Z is indeed the image of the PRG there is some x that maps to it, right? That x will satisfy the following. If you plug in this x, pi of x is equal to Zi. So you get that this sum is just the sum of Zi squares which is m because Z is plus minus one, just for simplicity. Instead of writing things in the exponent. So the sum will be m if this is in the image of the PRG. If it's not in the image of the PRG what we have is a sum that we can use concentration in the qualities to prove that it has good concentration namely we have a sum of random values plus minus ones times this pi of x if Z is random. If Z is random some sum of them are plus some of them are minus. Most of them will cancel out. And you can use Chernoff to show that this sum is bounded by the square root of n times s times m. So n is the input size, m is the output size and s is the number of monomials which is just used to bound the highest value of pi. This is a Hoeffding bound for non-pullian random variables. So you see when Z is in the image of the PRG we get m when Z is not in the image of the PRG and in sum of random we'll get with high probability something like square root of n times s times m. So this is enough for us because if m is bigger than n times s we'll have a gap and we'll just check and decide. So this is step number two. How do we compute this program? So let's see. This is where we use SOS sum of squares. We're just using it in the black box. We're using a result of Charcot and Weirth, the Charcot and Weirth that says that you can take any degree to polynomial and look at this value which is the maximum of a piece of x. You can approximate it up to a logarithmic factor. This is a generic result that you can efficiently approximate any such degree to polynomial up to a log n factor. So this is what we're going to use. I'm not going to talk about this logarithmic factor, it just goes into a stretch of the PRG. I'll just ignore that in the rest of the talk. So this is how we do step two. How do we do step one? So remember what we're trying to do is to take a local PRG and translate it into a sparse polynomial with low algebraic degree. A priori, as I said, you might think it seems like it won't work because if you take a two-block local PRG, any function, any two-block local function, when you look at it as a polynomial, the degree of the polynomial is huge. It's two to the two b. So what we're going to do, we're going to preprocess x. That's why I said preprocessing is important for us. We're going to preprocess x in the following way. We're going to look at any block size b and just expand it out, tensor it out, and define a new x prime on two to the b times n variables where you can think of each variable as like an indicator function of which b bits you had in the input. So we will take x, which is of size n, we'll expand it to x, which is of size two to the b times n, and we'll work with this PRG, with this modified PRG. So this is what we're doing. And now you can say that it's easy to observe that if you started with block locality L, then you'll end up with algebraic degree L, not more. And the number of monomials is g in g is not too big. It's only two to the two b. You might think there's a caveat. We preprocessed the input. So maybe the new PRG, right, is not really a PRG, because once you feed g prime with random input, it's not like applying g on a random input. But this is where our image refutation kicks in. The image of g prime, if you think about it for a second, is contained in the image of g. And our refutation says that on strings which are in the image, we will always output one. Only on the outside, we will output zero with high probability. This is where we use the fact that we are doing image refutation. So overall, what we got, plugging in the parameters that I just described in construction. So if you remember, it was n times s times m. So it's two to the two b, which is the sparsity. And the new n is two to the b times n. So we show that n must be at least two to the three b times n. Let me summarize. And leave me with two open questions. So to summarize, it seems like we ruled out plausible constructions of IO from degree two, block local exchanges. There are two very nice questions. The first one, we didn't really get the tightest result we hoped for. We didn't really get two to the b times n. In the worst case, worst case, different case. This is open. And it also leaves some room for playing in the constructions of IO, if you can construct IO from this small stretch. And the second question, which I find really interesting is come up with new ways of constructing IO. It seems like we're almost exhausted. One path, let's find new ideas. These subjects that you come up with at the end is polynomials that you said that maybe they're not a PRG. But actually the image of the PRG is included in them. So what are they exactly? Maybe they are interesting objects in their cells. They could be used maybe instead of a PRG. I don't know, do you have an idea? Can you repeat the question? Like these polynomials that you constructed at the end, you said they might not be a PRG. Yes. But what they are, maybe they are interesting in their cells, like for some other. Maybe. Okay, and my question is about this block size PRG. So what are they, for example, can the blocks be overlapped? Would that make sense or is it like in the end? So for the construction from IO, we need a real locality in not overlapping blocks. So we need real locality like I defined it. If you can do it from a relaxed notion of PRGs that have some sort of, that would be great. So in terms of the original, did you have a question? So it depends how you define overlapping blocks. What's overlapping, how much they overlap. So we didn't analyze it. I think it's a good way maybe to overcome our lower bounds. Yes. In terms of the original motivation for locality, so I'm just wondering like, okay, locality was supposed to have few to some, like for the implementation of the PRG. I don't know, like intuitively, like we go from locality to deep block locality to block locality that has become different assumptions. So I don't, it depends on the size of the block. So I don't know, like if this notion of deep block locality for example, could be used in the same type of applications as normal locality. I assume it could. Okay, another quick question. Yeah.


Hi everyone and welcome to the Stock Swoosh Play of the Day for July 20th 2016 presented by thestockswoosh.com and this is Paul Lang. This is the daily chart of DFS and these charts you're looking at are e-signal charts. The daily chart of DFS had a gap down to right here on this particular morning. This was mildly bearish on the daily chart and also very bearish on the intraday pattern and it gave a really wonderful entry that allowed for very nice profit to donate on this over just a 7 to 8 minute time period. Most of our plays we try and get done during the first 30 minutes of the day and this was one that was perfect for that. If you take a look at that daily chart, I'm going to switch over to the one minute chart and right there is the gap down. And then as the stock rallied up to here, right as it rolled over, this is my favorite type of entry here, rallies up initially and then rolls over. I shorted right up near the top of that roll over with a fairly tight stop that was available and the stock fell like a rock in the next 5, 6, 7 minutes. I got not all of that move because after that first drop it went so quick. I took a first target, took a second target, but the stop allowed a 2,500 share allotment which would be a $1,050 risk. And the drop that occurred over that, that really I took it only over about a 4 minute period, produced a profit of $1,675. The stock actually went about 40 cents lower than where I got out so there was some more profit left in there. That did end up being the low of the day as the stock spent the rest of the day rallying back, but nevertheless that's all you need to make your money and this all occurred during the first 7 or 8 minutes of the trading day. If you'd like to know how to find plays like this, how to execute plays like this, how to do this all during the first 30 minutes of the day, you want to take a look at the Golden Gap course, which is the strategy that we teach here at the Stock Swish. If you're interested in this class, it's going to be taught Saturday and Sunday July 31st. You can see the advantages of this particular strategy. It's a great one to learn. And if you are available, you can email or call at the number on your screen. Thanks everybody. Until next time, this is Paul Lang for the StockSwish.com.


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