Application And Use Of Complex Numbers

Application And Use Of Complex Numbers HISTORY OF COMPLEX NUMBERS:- Complex numbers were first conceived and defined by the Italian mathematician Gerolamo Cardano, who called them fictitious, during his attempts to find solutions to cubic equations. This ultimately led to the fundamental theorem of algebra, which shows that with complex numbers, a solution exists to every polynomial equation of degree one or higher. Complex numbers thus form an algebraically closed field, where any polynomial equation has a root. The rules for addition, subtraction and multiplication of complex numbers were developed by the Italian mathematician Rafael Bombelli. A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton. COMPLEX NUMBER INTERPRETATION:- A number in the form of x+iy where x and y are real numbers and i = is called a complex number. Let z= x+iy X is called real part of z and is denoted by R (z) Y is called imaginary part of z and is denoted by I (z) CONJUGATE OF A COMPLEX NUMBER: A pair of complex numbers x+iy and x-iy are said to be conjugate of each other. PROPERTIES OF COMPLEX NUMBERS ARE:- 1) If + = + then = 2) Two complex numbers + and + are said to be equal If R (+) = R ( +) I (+) = I ( +) 3) Sum of the two complex numbers is ( +) +( + = (+ ) + (+) 4) Difference of two complex numbers is ( +) ( + = () + () 5) Product of two complex numbers is ( +) ( + = +( ) 6) Division of two complex numbers is = + 7) Every complex number can be expressed in terms of r (cosÃŽÂ ¸ + sinÃŽÂ ¸) R (x+) = r cosÃŽÂ ¸ I (x+) = r sinÃŽÂ ¸ r = and ÃŽÂ ¸ = REPRESENTATION OF COMPLEX NUMBERS IN PLANE The set of complex numbers is two-dimensional, and a coordinate plane is required to illustrate them graphically. This is in contrast to the real numbers, which are one-dimensional, and can be illustrated by a simple number line. The rectangular complex number plane is constructed by arranging the real numbers along the horizontal axis, and the imaginary numbers along the vertical axis. Each point in this plane can be assigned to a unique complex number, and each complex number can be assigned to a unique point in the plane. Modulus and Argument of a complex number: The number r = is called modulus of x+ and is written by mod (x+) or ÃŽÂ ¸ = is called amplitude or argument of x+ and is written by amp (x+) or arg (x+) Application of imaginary numbers: For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as à ¢Ã¢â‚¬ ¦Ã¢â‚¬  and à ¢Ã¢â‚¬ ¦Ã¢â‚¬ º are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as à ¢Ã‹â€ Ã¢â‚¬â„¢3 and à ¢Ã‹â€ Ã¢â‚¬â„¢5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits. Similarly, imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, cartography, vibration analysis, and many others. APPLICATION OF COMPLEX NO IN ENGINEERING:- Control Theory In control theory, systems are often transformed from the time domain to the frequency domain using the Laplace transform. The systems poles and zeros are then analyzed in the complex plane. The root locus, Nyquist plot, and Nichols plot techniques all make use of the complex plane. In the root locus method, it is especially important whether the poles and zeros are in the left or right half planes, i.e. have real part greater than or less than zero. If a system has poles that are in the right half plane, it will be unstable, all in the left half plane, it will be stable, on the imaginary axis, it will have marginal stability. If a system has zeros in the right half plane, it is a nonminimum phase system. Signal analysis Complex numbers are used in signal analysis and other fields for a convenient description for periodically varying signals. For given real functions representing actual physical quantities, often in terms of sines and cosines, corresponding complex functions are considered of which the real parts are the original quantities. For a sine wave of a given frequency, the absolute value |z| of the corresponding z is the amplitude and the argument arg(z) the phase. If Fourier analysis is employed to write a given real-valued signal as a sum of periodic functions, these periodic functions are often written as complex valued functions of the form where à Ã¢â‚¬ ° represents the angular frequency and the complex number z encodes the phase and amplitude as explained above. Improper integrals In applied fields, complex numbers are often used to compute certain real-valued improper integrals, by means of complex-valued functions. Several methods exist to do this; see methods of contour integration. Residue theorem The residue theorem in complex analysis is a powerful tool to evaluate path integrals of meromorphic functions over closed curves and can often be used to compute real integrals as well. It generalizes the Cauchy and Cauchys integral formula. The statement is as follows. Suppose U is a simply connected open subset of the complex plane C, a1,,an are finitely many points of U and f is a function which is defined and holomorphic on U \ {a1,,an}. If ÃŽÂ ³ is a rectifiable curve in U which doesnt meet any of the points ak and whose start point equals its endpoint, then Here, Res(f,ak) denotes the residue of f at ak, and n(ÃŽÂ ³,ak) is the winding number of the curve ÃŽÂ ³ about the point ak. This winding number is an integer which intuitively measures how often the curve ÃŽÂ ³ winds around the point ak; it is positive if ÃŽÂ ³ moves in a counter clockwise (mathematically positive) manner around ak and 0 if ÃŽÂ ³ doesnt move around ak at all. In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed (which is usually easy), and a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane. The integral over this curve can then be computed using the residue theorem. Often, the half-circle part of the integral will tend towards zero if it is large enough, leaving only the real-axis part of the integral, the one we were originally interested Quantum mechanics The complex number field is relevant in the mathematical formulation of quantum mechanics, where complex Hilbert spaces provide the context for one such formulation that is convenient and perhaps most standard. The original foundation formulas of quantum mechanics the Schrà ¶dinger equation and Heisenbergs matrix mechanics make use of complex numbers. The quantum theory provides a quantitative explanation for two types of phenomena that classical mechanics and classical electrodynamics cannot account for: Some observable physical quantities, such as the total energy of a blackbody, take on discrete rather than continuous values. This phenomenon is called quantization, and the smallest possible intervals between the discrete values are called quanta (singular: quantum, from the Latin word for quantity, hence the name quantum mechanics.) The size of the quanta typically varies from system to system. Under certain experimental conditions, microscopic objects like atoms or electrons exhibit wave-like behavior, such as interference. Under other conditions, the same species of objects exhibit particle-like behavior (particle meaning an object that can be localized to a particular region of space), such as scattering. This phenomenon is known as wave-particle duality. Application of complex number in Computer Science. 1) Arithmetic and logic in computer system Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. 2) Recticing Software engineering in 21st century This technological manual explores how software engineering principles can be used in tandem with software development tools to produce economical and reliable software that is faster and more accurate. Tools and techniques provided include the Unified Process for GIS application development, service-based approaches to business and information technology alignment, and an integrated model of application and software security. Current methods and future possibilities for software design are covered. In Electrical Engineering: The voltage produced by a battery is characterized by one real number (called potential), such as +12 volts or à ¢Ã‹â€ Ã¢â‚¬â„¢12 volts. But the AC voltage in a home requires two parameters. One is a potential, such as 120 volts, and the other is an angle (called phase). The voltage is said to have two dimensions. A 2-dimensional quantity can be represented mathematically as either a vector or as a complex number (known in the engineering context as phasor). In the vector representation, the rectangular coordinates are typically referred to simply as X and Y. But in the complex number representation, the same components are referred to as real and imaginary. When the complex number is purely imaginary, such as a real part of 0 and an imaginary part of 120, it means the voltage has a potential of 120 volts and a phase of 90 °, which is physically very real. Application in electronics engineering Information that expresses a single dimension, such as linear distance, is called a scalar quantity in mathematics. Scalar numbers are the kind of numbers students use most often. In relation to science, the voltage produced by a battery, the resistance of a piece of wire (ohms), and current through a wire (amps) are scalar quantities. When electrical engineers analyzed alternating current circuits, they found that quantities of voltage, current and resistance (called impedance in AC) were not the familiar one-dimensional scalar quantities that are used when measuring DC circuits. These quantities which now alternate in direction and amplitude possess other dimensions (frequency and phase shift) that must be taken into account. In order to analyze AC circuits, it became necessary to represent multi-dimensional quantities. In order to accomplish this task, scalar numbers were abandoned and complex numbers were used to express the two dimensions of frequency and phase shift at one time. In mathematics, i is used to represent imaginary numbers. In the study of electricity and electronics, j is used to represent imaginary numbers so that there is no confusion with i, which in electronics represents current. It is also customary for scientists to write the complex number in the form a + jb. In electrical engineering, the Fourier transform is used to analyze varying voltages and currents. The treatment of resistors, capacitors, and inductors can then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. (Electrical engineers and some physicists use the letter j for the imaginary unit since i is typically reserved for varying currents and may come into conflict with i.) This approach is called phasor calculus. This use is also extended into digital signal processing and digital image processing, which utilize digital versions of Fourier analysis (and wavelet analysis) to transmit, compress, restore, and otherwise process digital audio signals, still images, and video signals. Introduce the formula E = I à ¢Ã¢â€š ¬Ã‚ ¢ Z where E is voltage, I is current, and Z is impedance. Complex numbers are used a great deal in electronics. The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. This seems odd at first, as the concept of using a mix of real and imaginary numbers to explain things in the real world seem crazy!. . To help you get a clear picture of how theyre used and what they mean we can look at a mechanical example We can now reverse the above argument when considering a.c. (sine wave) oscillations in electronic circuits. Here we can regard the oscillating voltages and currents as side views of something which is actually rotating at a steady rate. We can only see the real part of this, of course, so we have to imagine the changes in the other direction. This leads us to the idea that what the oscillation voltage or current that we see is just the real portion of a complex quantity that also has an imaginary part. At any instant what we see is determined by a phase angle which varies smoothly with time. We can now consider oscillating currents and voltages as being complex values that have a real part we can measure and an imaginary part which we cant. At first it seems pointless to create something we cant see or measure, but it turns out to be useful in a number of ways. 1) It helps us understand the behaviour of circuits which contain reactance (produced by capacitors or inductors) when we apply a.c. signals. 2) It gives us a new way to think about oscillations. This is useful when we want to apply concepts like the conservation of energy to understanding the behaviour of systems which range from simple a mechanical pendulums to a quartz-crystal oscillator. Applications in Fluid Dynamics In fluid dynamics, complex functions are used to describe potential flow in two dimensions. Fractals. Certain fractals are plotted in the complex plane, e.g. the Mandelbrot set Fluid Dynamics and its sub disciplines aerodynamics, hydrodynamics, and hydraulics have a wide range of applications. For example, they are used in calculating forces and moments on aircraft, the mass flow of petroleum through pipelines, and prediction of weather patterns. The concept of a fluid is surprisingly general. For example, some of the basic mathematical concepts in traffic engineering are derived from considering traffic as a continuous fluids. Relativity In special and general relativity, some formulas for the metric on spacetime become simpler if one takes the time variable to be imaginary. (This is no longer standard in classical relativity, but is used in an essential way in quantum field theory.) Complex numbers are essential to spinors, which are a generalization of the tensors used in relativity. Applied mathematics In differential equations, it is common to first find all complex roots r of the characteristic equation of a linear differential equation and then attempt to solve the system in terms of base functions of the form f(t) = ert. In Electromagnetism: Instead of taking electrical and magnetic part as a two different real numbers, we can represent it as in one complex number IN Civil and Mechanical Engineering: The concept of complex geometry and Argand plane is very much useful in constructing buildings and cars. This concept is used in 2-D designing of buildings and cars. It is also very useful in cutting of tools. Another possibility to use complex numbers in simple mechanics might be to use them to represent rotations.

Feminism in Pop Culture

Many myths and misconceptions float around the term ‘Feminism’. It is a movement that is frequently projected as being violent, aggressive, and full of ‘bra burning’ extremists. The word alone often evokes reactions among people that are negative, uncomplimentary and stereotypical. The disturbing of the patriarchal paradigm was a phenomenon that became prominent only in the Twentieth Century. Historically speaking women have always numerically outnumbered men, but through the system of patriarchy they have been suppressed by political, economic and social machinery. The difference between Gender and Sex When trying to examine feminism we must keep in mind the subtle difference between ‘gender’ and ‘sex’. For example, if a man were to dress or behave like a woman, it would not change the fact that he is still biologically a man, and here is where the difference lies. When we use the term ‘gender’, we are referring to a social construct, a store knowledge that has developed over generations that helps us in our identification of a person as a man or a woman. A person’s sex on the other hand is purely biological. A primary argument of feminist theory is that arbitrary allocations such as this that are constructs of society are completely devoid of any genuine value. Thus the duty of feminism, in one sense, involves the subversion of existing patriarchal paradigms by questioning phallocentric, or penis-centred, sources of power. Patriarchy and the Woman The term ‘Patriarchy’ itself can be broadly defined as an ideological system of belief that privileges males over females. This is a complex system that employs androcentric values, rituals and practices in order to maintain status quo. Another means of control involves patriarchy passing itself off as the so-called ‘norm’ or the ‘right’ way in which a society must divide itself, and regards the Female as a departure from this ‘norm’ and treats her as ‘the other’, a notion that only reinforces the sharp cleavage between the two sexes. As a result of this treatment, the decisions of a society are based on whatever the man decides, whereas everything else is lumped together as ‘the other’, the Female. It is however ironic that patriarchy itself requires the co-operation of the Female in order to subjugate her, making her a willing participant in her own suppression. As the French feminist Simone de Beauvoir put it so aptly in her seminal book, ‘The Second Sex’, published in 1949, ‘One is not born, but rather becomes a woman. ’, a statement that raises our consciousness to the disparity between the male ‘norm’ and the female ‘other’. It was indeed French Feminism that first brought to light the fact that all western languages are irredeemably male-engendered, male constituted and male-dominated. Discourse itself is phallocentric as seen in its vocabulary, syntax, rules of logic and its tendency for classification and opposition as well as the need for objective knowledge. Definitions of Feminist Literary Criticism There are multiple definitions that can be applied to Feminist Literary criticism. It differs from other schools of critical theory in that it does not derive its literary principles from a single authoritative figure or from a body of sacred texts. This is quite unlike other approaches such as Psychoanalysis, Marxism or Deconstruction, which can all be attributed to their primary exponents, Freud, Marx and Derrida respectively. Feminist theory has evolved from several sources, with several feminist thinkers contributing to the canon. Moreover, critical theory used in readings of Woman’s literature borrows from other disciplines such as History, Anthropology, Linguistics, Psychoanalysis and Marxism. It was a form of criticism created by literary and academic women who participated in the women’s liberation movement in the late 1960s. Kate Millet’s book, ‘Sexual Politics’ (1870) was the first major treatise on feminist criticism, and also represented a strong political argument for women’s rights. The Dictionary of Concepts in Literary Criticism and Theory defines Feminist Criticism as ‘The understanding and analysis of and response to literary works, and/or language and/or the institution of literary study or theory from the point of view of women’s experience. ’ â€Å"Feminist Criticism†, says Elaine Showalter, in her book ‘New Feminist Criticism’, â€Å"has established gender as a fundamental category of literary analysis. † Her article, ‘Dancing through the Minefield’ has also made some observations on the politics and practice of feminist criticism. She also points out that the earlier groups of feminist critics were preoccupied with the gender bias in writing, whereas the later group of gynocritics studied women as writers. Another columnist, Annette Kolodny, defines feminist criticism as â€Å"An acute and impassioned attentiveness to the ways in which primarily male structures of power are encoded within our literary inheritance, and the consequences of that encoding for women†¦ not only for a better understanding of the past but also for an improved recording of the present and the future. This form of criticism, as a self-aware and concerted approach to literature came into being in the late 1960s, as a part of the international woman’s movement. One of the first areas it looked into and challenged was literature, where it was always assumed that the representative reader, writer and critic were all male. The historical background and watershed marks in Feminist Criticism Behind the movement in the 1960s, however, lay two centuries of struggle, represented only by a few texts such as Mary Wollstonecraft’s ‘The vindication of the Rights of Women’ (1792). A later book, this time by John Stuart Mill, ‘The Subjection of Women’ (1869) was also brought to the fore. It suggested that the Wife was a family’s source of sustenance, and therefore the empowerment of the generations could be achieved only by empowering The Woman. The next seminal work in Feminist Criticism was penned by Virginia Woolf in 1929. Called ‘A Room of One’s Own’, the book talked about the major directions in which feminist explorations of literature needed to develop. The book is rich with insights about the absence of women writers and readers, and the probable fate to which the hypothetical ‘Sister of Shakespeare’, blessed with equal or greater genius, would have been consigned to thanks to socio-cultural obstacles of the age. In it, Woolf’s contention is that ‘A woman must have money and a room (referring to space, privilege and opportunity) of her own if she is to write [fiction]. † Other significant books include Toril Moi’s ‘Sexual/Textual Politics’ (1985) and Sandra Gilbert and Susan Gubar’s ‘No Mans Land: The Place of the Woman Writer in the 20th Century’. These texts introduced the principles of feminist literary theory to the world. Their purpose was to offer feminist readings of texts that looked at the images and the stereotypes of women in literature as well as the omissions and misconceptions about women in criticism and ‘women-as-sign’ in semiotic systems. This kind of criticism concerns itself with developing a specifically female framework for dealing with works written by women, in all aspects of their production, including analysis and interpretation in ll literary forms and expressions, including journalism and popular culture, like Patricia Mayers-Spack’s ‘The Female Imagination’, Ellen Moer’s ‘Literary Women’, Elaine Showalter’s ‘A Literature of their Own: British Women Novelists from Bronte to Lessing’, or Gilbert and Gubar’s ‘The Mad Woman in the Attic’, a reference to Bertha Mason, who is ‘usually in some sense the author ’s double, (the other) an image of her own anxiety and rage. ’ Through the women’ liberation movement, literary criticism drew a connection between the lived lives of thousands of women who studied and taught literature. An important area of research was the limited secondary roles of fictional heroines and other feminine stereotypes in canonical literature. The Role of Feminist Criticism Feminist criticism, developing in tandem with the women’s liberation movement brought in a dual perspective that brought about a reappraisal of texts, looked at the construction of gender through language and the gendering of text, and examined the representation of women in literature and the exclusion of women as fictional characters, authors and readers. As far as literature is concerned, the role of Feminist criticism was to look at canonical literary works and the manner in which they represent women as stereotypes, and to develop theories for sexual differences in reading, writing and literary interpretation. It brings to the fore and establishes ‘gender’ as a fundamental category of literary analysis, and takes into account the fact that the vast majority of what is conceded to be the ‘literary canon’ is by and large authored by men, based on masculine norms and values, and women’s writing therefore is either excluded or undervalued in canonical literature, criticism and theory. Feminist critics also look at the representation of female experiences in literature. They reason that because a major aspect of literature is the reporting of our biological sense experiences, it would be impossible for the male to authentically capture an entirely feminine experience such as menstruation or childbirth. Feminist criticism also bases itself on two other primary assumptions: That gender is constructed through language (by way of political incorrect words and phrases such as ‘chairman’, ‘male nurse’ or ‘actor and actress’), and that writing strategies are sex-related and therefore misogynistic. Feminist criticism also shows that women readers, critics and writers bring different perceptions and expectations to their literary experiences, and insist that women have important stories to tell of their own culture. This kind of criticism opened space that now extended beyond the study of only women writers and now included the reappraisal of all literature that makes up our heritage. Feminist critics look at literary representation of sexual differences, and how literature shapes masculine and feminine values, privileging one set over another. The aim of feminist criticism therefore becomes to re-examine male texts, emphasize writing by women by charting a new literary history that includes neglected texts, a female tradition created by a sub-community of women writers who found support from their literary foremothers and so become role models for younger female writers. They also look at the oral tradition and other extra-literary expressions. Another aim involves the creation of new reading and writing collectives, libraries, publishing houses, social centres, colleges and so on. Feminist criticism confronts the problem of the feminist reader by offering new methods and fresh critical evaluation of issues, such as the mother-daughter cultural and relational aspect. Another major concern of Gynocritics is to identify what is taken to be distinctly feminine subject matter in literature written by women, the idea of sisterhood and female bonding, domesticity, gestation, birth, motherhood, mother-daughter or woman-woman relationships, etc. They also undertake to show that there is a distinctive feminine mode of experience or subjectivity in thinking, feeling, valuing and perceiving the self and others. French Feminism Related to this is the specification of the traits of women’s language and its distinctive style of speech and writing. Women must write in a way in which they can avoid the pitfalls of phallocentric language mentioned earlier, in a style represented by the term ‘ecriture feminine’ or writing in the feminine, a concept that was a product of French feminism. Helene Cixous, its main exponent, credited with authoring its manifesto, ‘The Laugh of Medusa’ (1975), stated that ecriture feminine is to be found in metaphors of female sexuality and women’s libidinal differences. Another critic, Luce Irigary, talks about women’s writing and its evasion of the male monopoly by replacing the monolithic phallus by the diversity, fluidity and multiple possibilities represented by female sexuality. These critics believe that women must try to resurrect the ‘feminine-feminine’ which possibly lies in the unconscious of all women. Julia Kristeva speaks of a pre-natal, pre-linguistic, pre-oedipal and unsystematic signifying language between the mother and the infant centred on the mother that she labels as semiotic and abstract, as opposed to the symbolic or letter based language of the father. Semiotic writing disrupts phallocentric writing because it is free from oppressive order and rationality. Both men and women can write in this mode, which deconstructs masculine structures of knowledge and attacks patriarchy and its language. The overall aim of ecriture feminine is therefore to allow a woman to write of, from and about their bodies. French feminist theory has contributed significantly to feminist literary criticism by studying the relationship between women, psychology and language. Currently feminist criticism employs a wide range of approaches and addresses a variety of issues of feminist interest. This is called ‘Playful Pluralism’. The oft-asserted goal of feminist critics has been to enlarge and re-order, or in some cases entirely displace the (patriarchal) literary canon. Feminist studies have served to raise the stakes of many female authors who were erstwhile neglected or even overlooked.

The Twilight Saga 5: Midnight Sun 20. Tracker

Each vampire strode out of the forest with a wild expression on their face while their brilliant bright red eyes glittered. The three of them came closer together once they saw how many of us there were. The female had long red curly hair and a catlike appearance. The two males were both tall and built. As they came closer to my family I could understand their chaotic thoughts – our family was large for our kind and civilized compared to most other nomads. I knew what these kind of vampires looked like already, so their torn clothes, disheveled hair and bare feet were not something that would take me off guard. All of their thoughts were thinking in sync with each other. How many vampires are there? They were all shocked as they made their way towards us. Our numbers were an unpleasant surprise to them. They drifted ever closer to us with extreme caution. Carlisle, Emmett and Jasper walked toward the approaching vampires to greet them, leaving only a short distance between us. I stationed myself securely in front of Bella. The visitors were cautiously looking around, mentally tabulating their chances of winning if a fight were to ensue. Once they began closing ranks with my family I began to listen carefully to their thoughts, making sure none of them sensed Bella for what she was ?C a human. Their eyes aren't red†¦ but†¦ How weird. The vampire named Laurent thought. As they descended upon us I had already figured out their names. Each one of them was thinking about the other in turn. The vampire named Victoria was looking anxiously between Laurent and the other male vampire, James. She didn't like the idea that James had to put Laurent in the front ?C to seem the leader of their coven but she was also grateful that he did because if there was an attack Laurent would be killed first and not her precious James. Her eyes darted in our direction. Why are they huddled around that one girl? Victoria thought. As she continued to look in our direction I concentrated on her thoughts alone. She was unknowingly absorbing the signs of the subtle differences between our kind and Bella's. Bella was the only human in a sea of vampires. The scent had not hit her yet. I began concentrating on the others thoughts also. James was a particularly vicious vampire. He was constantly gloating about how superior he was in his mind. James had caught sight of the many scars on Jaspers skin. Look at all of those battle scars. I'll keep my eye on him. He is the real danger of this coven. James was thinking strategy. I just don't understand why so many would gather together like this. Laurent thought. My family and the visitors finally met. â€Å"We thought we heard a game,† Laurent said lazily. â€Å"I'm Laurent, these are Victoria and James.† He gestured toward the others. Carlisle looked completely at ease as he spoke. â€Å"I'm Carlisle,† he began in a hollow voice. â€Å"This is my family, Emmett and Jasper, Rosalie, Esme and Alice, Edward and Bella.† He pointed to each grouping as he spoke. The new comers still hadn't caught scent of Bella but James was peering around me to her. He was noticing that her cheeks were tinged lightly with a pinkish glow and how her eyes were a dark chocolate brown. He stepped closer, unintentionally, to get a better look. â€Å"Do you have room for a few more players?† Laurent asked cordially. â€Å"Actually, we were just finishing up. But we'd certainly be interested another time. Are you planning to stay in the area for long?† Carlisle said in faux enthusiasm, though Laurent hadn't noticed. How long do they plan to be in the area? It's doubtful they would be able to stay here for long. Victoria looked at us incredulously. â€Å"We're headed north, in fact, but we were curious to see who was in the neighborhood. We haven't run into any company in a long time.† Laurent replied amicably. There is something about the dark haired girl. James continued to look at her. His eyes wondered to mine as he continued to think strategically. He doesn't seem like too much for a threat. He thought scathingly. I didn't let my expression change ?C the less he knew about me and my ability, the better. Jasper could feel the extreme hostility emitting from James so he used his gift to calm him down, along with sending waves of calm to the other vampires. James' thoughts returned to the conversation once he heard Carlisle's response. â€Å"No, this region is usually empty except for us and the occasional visitor, like yourselves.† Carlisle explained. Except for them? All three thought simultaneously. Jasper was truly talented. His continuous calm had changed the atmosphere into a more controllable situation. â€Å"What's your hunting range?† Laurent inquired. â€Å"The Olympic Range here, up and down the Coast Ranges on occasion. We keep a permanent residence nearby. There's another permanent settlement like ours up near Denali.† Carlisle explained. A permanent residence? They all thought together. They never leave? How is that possible? Laurent thought in astonishment before voicing his question. â€Å"Permanent? How do you manage that?† he asked, intrigued. This could be our opportunity to get Bella away from here. Be ready to move her away from them. Carlisle directed his thoughts to me. â€Å"Why don't you come back to our home with us and we can talk comfortably?† Carlisle invited. â€Å"It's a rather long story,† he explained. Home? Victoria and James thought together and then exchanged incredulous looks. â€Å"That sounds very interesting, and welcome.† Laurent smiled while choosing his words carefully. â€Å"We've been on the hunt all the way down from Ontario, and we haven't had the chance to clean up in a while.† I wonder what it is like to be so clean and dressed so nicely all the time, Laurent wondered. â€Å"Please don't take offense, but we'd appreciate it if you'd refrain from hunting in this immediate area. We have to stay inconspicuous, you understand.† Carlisle asked politely. â€Å"Of course,† Laurent nodded. â€Å"We certainly won't encroach on your territory. We just ate outside of Seattle, anyway,† he laughed while picturing his last prey and the kill. What? You idiot! Why would you agree to that? James roared in apparent displeasure. I could feel Bella shaking and I tried to hide her obvious human tendencies from the visitors. The constant deluge of thoughts had me struggling trying to keep up with everything. I focused on the threat and Carlisle. Get ready to get her out of here! Carlisle ordered me. â€Å"We'll show you the way if you'd like to run with us ?C Emmett and Alice, you can go with Edward and Bella to get the Jeep,† Carlisle said as casually as possible while inconspicuously directing Emmett and Alice of what to do. I could hear the wind from a mile away before it hit us. Alice looked at me frantically for a fraction of a second as she realized this, too, and her vision of us escaping unscathed shifted abruptly. I saw it flash and in that second I realized what was going to happen. The wind was only a second away and I was prepared. Suddenly the wind blew Bella's hair off her neck and sent her fragrance soaring towards the other vampires. James turned to face her as many thoughts went running through his head. I was preparing to protect Bella. Her scent had been punctuated by the moisture in the air, just like always. A howling rush of anxious thoughts came flowing out of my families minds as they realized the danger. Ummm†¦what a delicious scent, he thought hungrily. His nostrils flared to bring her scent deeper into his lungs, he crouched down, preparing to spring. His eyes narrowed while coming closer to Bella. I was a step ahead of him and so was my family because they had caught her scent strongly on the wind before he did. He was not going to lay a single finger on Bella. My protective side took over and a ferocious snarl ripped up my throat menacingly towards James. I met his gaze unflinchingly and he was suddenly very still like a dog who's hunting a rabbit, ready to attack. â€Å"What's this?† Laurent exclaimed in surprise. Why are they protecting her? She is just a human and an exceptionally frail one at that! This is going to be harder than my last hunt. James thought in a sinister way, determined to seize her at the first opportunity. His thoughts continued on a visual basis as I saw that he would pick victims who were harder to catch and track them down – delighting in the hunt. He continued to dwell on his satisfying memories of his obsession. The harder the kill, the more thrilling he found it. A sickening jolt ran through my stomach as I realized that if we didn't kill him now that he would continue to hunt Bella until she was dead. I shifted simultaneously with each movement he was planning to make. â€Å"She's with us,† Carlisle claimed quickly, almost in a threat. The scent didn't register with Laurent or Victoria for a few seconds longer. When it finally registered with them the scent was obviously not as strong to them as it was to James. â€Å"You brought a snack?† Laurent had a smile spread across his face as he took a step forward, ignoring everyone's protective stance. He was resisting the temptation much easier than James. A small horrified gasp exited Bella's lips. Another growl ripped up my throat, harsher than before. My teeth were showing and it sent a jolt of unease down Laurent's spine. He stepped back. â€Å"I said she's with us,† Carlisle looked tense and protective. â€Å"But she's human,† Laurent protested with a quizzical look on his face, slightly taken aback. Maybe this is how they stay inconspicuous†¦keeping a human as a pet? â€Å"Yes,† Emmett replied while stepping towards James. Laurent knew better than to become aggressive when there were so many vampires protecting Bella. He caught sight of Jasper who had his hands clenched so tightly that his scars shown pearly white. He looked quickly away and towards James while giving him a dark look. What the hell are you doing? Are you trying to get us killed? He thought. James slowly pulled out of his crouch but his thoughts and eyes were still on Bella. No matter what happened now, he was going to hunt her. Tonight ?C she will be mine, James thought excitedly. This should make for a much more interesting sport, he continued and it was obvious that our presence made the hunt considerably more interesting. I refused to move from my protective stance, remaining forcibly in his way. Jasper's waves of calm were working on the other two vampires but not on James. He seemed completely unaffected, like his body overrode it for the mere thought of a hunt as intriguing as this one would be. This one should be fun; I bet James is already making plans. Victoria thought while failing extravagantly to hide the excitement of the hunt on her face. â€Å"It appears we have a lot to learn about each other,† Laurent spoke smoothly, trying to placate the situation. â€Å"Indeed,† Carlisle's voice was relatively calm. I don't understand the fascination. â€Å"But we'd like to accept your invitation.† Laurent's eyes darted toward Bella and me and then quickly away. Good†¦Good, keep talking. This should help me out, James thought while his face lit up with a feverous fanatical glow. â€Å"And, of course, we will not harm the human girl. We won't hunt in your range, as I said.† Laurent added. James threw him a disgruntled look. Well that doesn't help me out at all, he thought angrily. Or†¦maybe this will bring them into a false sense of security and they will let their guard down, James continued to plan in his head. Carlisle studied Laurent's expression for several seconds. He seems to be handling this relatively well. I don't think inviting them over will hurt anything, Carlisle contemplated. â€Å"We'll show you the way. Jasper, Rosalie, Esme?† he called. All three of them moved forward blocking Bella from their view. Alice bounded up next to Bella while Emmett walked backwards to us, never letting James out of his sight, knowing that I could see everything he saw. I'm coming with you, Edward. I won't let anything happen to Bella, Emmett thought protectively. We need to leave now, Alice thought urgently. â€Å"Let's go, Bella.† I commanded. Bella didn't move; her eyes were wide in terror and shock. I grabbed her by the elbow and pulled her towards the jeep. Emmett and Alice stayed behind me, protecting both of us from any form of attack they might try to come at us with, all of us working as a seamless team. We don't have much time, Edward. James will be after Bella shortly. Carlisle won't be able to stall them for long. Alice looked upset. My impatience of her slow human pace was unbearable so by the time we reached the forest edge I threw Bella on my back as gentle as I could without slowing down and then I ran for it. Emmett and Alice were struggling to keep up with me; I was flying through the forest in a fury trying to get Bella away from the danger. I knew that this whole experience was jarring for Bella but the most important thing right now was for her to be safe. When we arrived next to the jeep I opened the door to the backseat and practically threw her in as the rest of us hurried into the Jeep. The key was protruding from the ignition already and I turned it quickly while the engine roared to life. â€Å"Strap her in,† I ordered Emmett who was already in the backseat. We have to go ?C now! Alice shouted from her head. She was already sitting in the passenger's seat looking extremely anxious. Her thoughts were unnecessary because I was already spinning the Jeep around to face the mountain road. Hurry, he's close. Alice's eyes were wide with terror for Bella. I was muttering ferociously while several profanities come through my lips, words that I would never use in front of a lady. Emmett and Alice were on full alert, constantly updating me in their thoughts at what was going on around us. I can't hear or see anything. Emmett informed me urgently. He lost Bella's scent once we took off in the Jeep, she explained to me, relaxing slightly. I watched Bella in the review mirror and through Emmett's eyes. She was bouncing up and down on the seat, her eyes wide. I suddenly wished Jasper had come along with us to keep her calm. Go south, they will split up but the prospects of them finding us are slim. Oh, she paused in thought, looks like they aren't planning to leave so quickly after everything after all. I wonder what they are going to do, Alice tried to look further in the future but there were too many decisions that hadn't been decided yet. I turned south on the main road. â€Å"Where are we going?† Bella finally spoke with a squeak. No one answered her. Just tell her, Alice commanded. I shook my head slightly. Emmett realized we were having one of our private conversations and understood what I was answering. â€Å"Dammit, Edward! Where are you taking me?† Bella shouted this time, looking horrified. I looked in the review mirror at her slightly crest fallen face and it broke my resolve. â€Å"We have to get you away from here ?C far away ?C now.† I said hastily. I pressed the accelerator down harder at my words while the Jeep's speed reached a hundred and five miles an hour. â€Å"Turn around! You have to take me home!† she vehemently exclaimed. This is exactly why I didn't want to tell her where we were going because I knew that she would demand what I couldn't give her. I looked in the review mirror again to see her face. She was fighting with the harness, tearing at the straps with tears welling up in her eyes. â€Å"Emmett,† I called. Emmett looked down at her while she was angrily grasping at the straps. Jeez, she is in a fury. Emmett thought. He brought his hands to her wrists and held them tightly in his grasp. Bella looked in the review mirror with pure anguish in her eyes. â€Å"No! Edward! No, you can't do this,† she cried out. When she begged and pleaded with me like this it broke my heart. I returned her gaze in the mirror. â€Å"I have to, Bella, now please be quiet.† I implored. She was stubborn, as always. â€Å"I won't! You have to take me back ?C Charlie will call the FBI! They'll be all over your family ?C Carlisle and Esme! They'll have to leave, to hide forever!† She shouted with a tragic expression displayed on her face. Of course Bella was being selfless. It was just in her nature to care about everyone else when her life was in danger. This was nothing to our family – the FBI ?C it's happened before with Jasper and Emmett. â€Å"Calm down, Bella.† I commanded. â€Å"We've been there before,† I was almost crying with exasperation. â€Å"Not over me, you don't! You're not ruining everything over me!† she began struggling under Emmett's hold. Edward, what do you want me to do? I don't want to hurt her but she is going to hurt herself with all of her struggling. Emmett thoughts became worried immediately. â€Å"Edward, pull over,† Alice directed. Bella has a good plan if you will just listen to her. I gave Alice a grave look while pressing the gas down even harder, showing her that I wasn't even going to slow down, let alone pull over. â€Å"Edward, let's just talk this through,† she continued. He's not following us; he actually has no idea where we went. Now pull over, she inclined her head toward the roads shoulder. â€Å"You don't understand,† I yelled in frustration. Alice had no idea that James was a tracker – that when he hunted his prey he never gave up and always conquered. I couldn't bring Bella back to Forks, he would find her and she would be in danger again. If she were to die, I would too. â€Å"He's a tracker, Alice, did you see that? He's a tracker!† I shouted. Crap! Emmett looked grim. â€Å"Pull over, Edward.† Do it now! We have to talk about this now! We are in this together and we all have to make the decisions together. That includes Bella! Alice raised her eyebrows like she was daring me to disagree with her. I looked down at the speedometer as the Jeep had reached one-twenty. â€Å"Do it, Edward,† Alice said to me in a bossy disapproving voice while glaring at me. She needed to understand, I had to explain to her but I didn't want to say this in front of Bella. I didn't want her to be more terrorized than she already was. I looked into the review mirror again as I saw Bella's encouraging eyes telling me to pull over. Her heart was hammering loudly in her chest and her scent was circling all of us in the Jeep, emphasizing her human frailness. I closed my eyes for a fraction of a second, hoping when I opened them again that this would all be over with. I couldn't stop, I must keep going! â€Å"Listen to me, Alice,† I gave her a reproachful look. â€Å"I saw his mind. Tracking is his passion, his obsession ?C and he wants her, Alice ?C her, specifically. He begins the hunt tonight.† â€Å"He doesn't know where ?C† Alice began but I cut her off. â€Å"How long do you think it will take him to cross her scent in town? His plan was already set before the words were out of Laurent's mouth.† I heard a faint gasp come from Bella's lips and I looked quickly in the review mirror to see her lips parted in pure horror. â€Å"Charlie! You can't leave him there! You can't leave him!† she shouted and began thrashing against Emmett and the harness with nothing but pure worry in her expression. â€Å"She's right,† Alice said while she looked to the future and then she looked at me in horror. I quickly dived into her mind, her vision was devastating. Bella! She will be so hurt and broken I don't know if we could fix her if Charlie is killed. We have to stop him ?C now! At the thought of what this could do to her I automatically slowed down. I didn't want her to die, but I could protect her from him†¦ but I couldn't protect her from the agony, the grief that she would have to suffer if her father was killed. It would be torture to see her in such pain or worse, if she finally took the blame off herself and realized it was entirely my fault and refused to let me comfort her. Alice could almost see my brain hard at work. â€Å"Let's just look at our options for a minute,† she said coaxingly, knowing that I was deep in thought about our options. The Jeep slowed as I took my foot off the accelerator slowly and the speedometer showed the Jeep slowing down to ninety miles an hour. In Alice's vision James would give Victoria the first kill ?C Charlie. Victoria was his mate and they were extremely vicious together, feeding off of each other's ruthlessness. She would display Charlie's dead body to try and coax us back ?C and it would work! I slammed the brakes while pulling into the shoulder. I felt horribly powerless. The car behind me screeched to a halt too and honked their horn. I saw Bella slam back into the seat and I was instantly nervous I had done something to hurt her but she looked unscathed. I turned to look at Alice. â€Å"There are no options,† I howled. To bring her back when that monster was hunting her ?C I just couldn't bare it if something were to happen. My brain was in limbo. â€Å"I'm not leaving Charlie!† Bella yelled louder than I had ever heard but I ignored her. â€Å"We have to take her back,† Emmett said quietly. â€Å"No,† I said with authority. â€Å"He's no match for us, Edward. He won't be able to touch her,† Emmett promised. â€Å"He'll wait,† I explained. We'll beat him at his own game then! â€Å"I can wait, too.† Emmett said while grinning widely. â€Å"You didn't see ?C you don't understand. Once he commits to a hunt, he's unshakeable. We'd have to kill him.† I shouted. And this is a problem because? â€Å"That's an option,† he replied unperturbed. I was becoming angrier because I knew I was going to lose this argument. â€Å"And the female. She's with him. If it turns into a fight, the leader will go with them, too.† Three against seven? Please! â€Å"There are enough of us.† â€Å"There's another option,† Alice replied quietly. She saw what Bella was planning in her head and the only way she saw this plan was if it was a possibility. This made me angrier than before. â€Å"There ?C is ?C no ?C other ?C option!† I shouted. I could see the shock on Bella and Emmett's face in the mirror. I turned to look at Alice. She has a good plan and you know it! Alice barked in her head. I continued to stare at her with deepest dislike. If she doesn't convince James that she is no longer in Forks than he will let Victoria kill Charlie. You can't let that happen. What would Carlisle say? I continued to glare at her and her logic. â€Å"Does anyone want to hear my plan?† Bella asked. â€Å"No,† I growled because I already knew her plan and disagreed with it. I've had enough of this! Alice glared at me so menacingly I almost thought she was going to burn holes through me. â€Å"Listen,† Bella pleaded desperately. â€Å"You take me back.† â€Å"No,† I cut in. I turned to look at her and now she was glaring at me. â€Å"You take me back,† she continued anyway. â€Å"I tell my dad I want to go home to Phoenix. I pack my bags. We wait till this tracker is watching, and then we run. He'll follow us and leave Charlie alone. Charlie won't call the FBI on your family. Then you can take me any damned place you want.† Wow! I like her style. She fights dirty! Emmett looked surprised. Just let her do this, Edward. Alice continued to glare at me. â€Å"It's not a bad idea, really.† Emmett allowed. â€Å"It might work ?C and we simply can't leave her father unprotected. You know that,† Alice replied in a I told you so tone. Everyone's eyes were on me. I took in a deep breath. â€Å"It's too dangerous ?C I don't want him within a hundred miles of her.† â€Å"Edward, he's not getting through us,† Emmett said confidently. I wish I were as confident as he was. I looked at Alice because she started flitting through the future again. Ah, yes, the future is getting clearer. I see†¦ â€Å"I don't see him attacking. He'll try to wait for us to leave her alone.† â€Å"It won't take long for him to realize that's not going to happen,† Emmett said. â€Å"I demand that you take me home.† Bella said firmly. My brain was swelling with the onslaught of information ?C the past events, the present and the future. Bringing my fingers to my temples and squeezing my eyes shut while trying to dispel all thoughts was useless but I tried anyway. â€Å"Please,† Bella whispered a cry. I knew I had to do what was best for Bella all around, not what was just best for me. I decided a compromise would be the best I could deal with. â€Å"You're leaving tonight, whether the tracker sees or not. You tell Charlie that you can't stand another minute in Forks. Tell him whatever story works. Pack the first things your hands touch, and then get in your truck. I don't care what he says to you. You have fifteen minutes. Do you hear me? Fifteen minutes from the time you cross the doorstep.† I conceded. The engine roared to life as I turned the key. I whipped the truck around while listening to everyone's thoughts. I knew this was going to happen, Alice thought smugly. Yes! We get to fight! Hell yes! Emmett rejoiced. â€Å"Emmett?† Bella said. I looked in the mirror and she was looking down at her hands. â€Å"Oh, sorry.† Emmett said while letting go of her wrists. This is the most exciting thing since mine and Jasper's trip to Africa. I hope Edward always keeps Bella around, everything is always so interesting! Emmett continued to think happy thoughts the whole way back to Forks. While everyone else was silent I was working plans in my head. â€Å"This is how it's going to happen,† I began to explain our strategy. â€Å"When we get to the house, if the tracker is not there, I will walk her to the door. Then she has fifteen minutes.† I gave Bella a dark look in the mirror to let her know I wasn't going to change my mind on this point. â€Å"Emmett, you take the outside of the house. Alice, you get the truck. I'll be inside as long as she is. After she's out, you two can take the Jeep home and tell Carlisle.† What? No fight! â€Å"No way,† Emmett interrupted. â€Å"I'm with you.† I sighed. â€Å"Think it through, Emmett. I don't know how long I'll be gone.† I explained. You aren't going to ruin this for me. â€Å"Until we know how far this is going to go, I'm with you,† Emmett said with authority. A growl almost escaped my lips. â€Å"If the tracker is there,† I frowned, â€Å"we keep driving.† No worries! â€Å"We're going to make it there before him,† Alice said with confidence. Oh no you don't, Edward, I'm staying with her. She thought when I planned to send her home.†What are we going to do with the Jeep?† Alice asked to provoke me. I gritted my teeth as I spoke. â€Å"You're driving it home.† No way! â€Å"No, I'm not!† she said coolly. Tonight I just couldn't help myself, a stream of profanities come through my lips, but low enough I was sure Bella couldn't hear them. Would she think of me as a gentleman after this? What a dumb thing to be thinking about in such a crucial moment, I thought to myself. â€Å"We can all fit in my truck,† Bella said quietly. I ignored her, she wasn't helping my cause. â€Å"I think you should let me go alone,† Bella said even more quietly, purposely provoking me. I clenched my teeth and breathed through them slowly. â€Å"Bella, please just do this my way, just this once.† â€Å"Listen, Charlie's not an imbecile,† she continued like she hadn't heard me. â€Å"If you're not in town tomorrow, he's going to get suspicious.† Why does she continually worry about me when she should be worried about herself? Beautiful, selfless, warm, trusting human†¦why do you do this to me? I roared internally. â€Å"That's irrelevant. We'll make sure he's safe, and that's all that matters.† I told her. I could see her rebuttal churning in her eyes before she spoke. â€Å"Then what about this tracker? He saw the way you acted tonight. He's going to think you're with me, wherever you are.† Where on earth did this creature come from? Emmett wondered. â€Å"Edward, listen to her,† he urged. â€Å"I think she's right,† Emmett said, positively delighted. Hum, she has a point. â€Å"Yes, she is,† Alice agreed. They already convinced me to come back to Forks and bring her back to the vampire who hunted her and now they expect me to stay behind! â€Å"I can't do that.† I barked. It was true, it was almost physically impossible for me to leave her now. â€Å"Emmett should stay, too. He definitely got an eyeful of Emmett.† She continued. You have got to be kidding me! She's turning on me now! â€Å"What?† Emmett's eyes narrowed in her direction. I'll placate him. Don't worry. â€Å"You'll get a better crack at him if you stay,† Alice suggested. The way they were planning was driving me insane. I had to put my foot down at some point. â€Å"You think I should let her go alone?† I said incredulously. Do you think I'm an idiot? â€Å"Of course not. Jasper and I will take her.† Duh. I felt like I was being beaten down. They were making sense and I knew it, but I just couldn't stand the pain if something was to happen to her and I wasn't there to protect her. â€Å"I can't do that.† I repeated. Bella spoke up, â€Å"Hang out here for a week ?C† I looked at her in the mirror and she could see my I don't think so expression and amended â€Å"- a few days. Let Charlie see you haven't kidnapped me, and lead this James on a wild-goose chase. Make sure he's completely off my trail. Then come and meet me. Take a roundabout route, of course, and then Jasper and Alice can go home.† It will work. Really. Alice thought to me. â€Å"Meet you where?† I conceded, curiosity getting the best of me. â€Å"Phoenix.† She said matter-of-factly. â€Å"No. He'll hear that's where you're going,† I said impatiently. Oh! Great plan†¦Alice thought seeing what Bella would say before she spoke again. â€Å"And you'll make it look like that's a ruse, obviously. He'll know that we'll know that he's listening. He'll never believe I'm actually going where I say I am going.† Interesting, always interesting. â€Å"She's diabolical,† Emmett began to chuckle and I ignored him. â€Å"And if that doesn't work?† I muttered. â€Å"There are several million people in Phoenix,† she informed me like that settled it. How did our conversation end up like this ?C here, in Forks embracing danger? We should be a hundred miles away by now! â€Å"It's not that hard to find a phone book,† I said grimly. â€Å"I won't go home,† she said happily. This is entertaining, really. Emmett thought with another chuckle in his head. I wanted to roll my eyes at her or shake some sense into her. Maybe she had lost her mind with the stress of the ordeal. â€Å"Oh?† I asked, utterly perplexed. â€Å"I'm quite old enough to get my own place,† she smiled at me in the mirror. It won't come to that. Don't worry. â€Å"Edward, we'll be with her,† Alice winked at me. Everyone had lost their minds. A sadistic vampire was hunting Bella and everyone had turned it into a big joke! â€Å"What are you going to do in Phoenix?† I rebuked. If I have time, shop. She thought but pretended that she didn't think that when she looked at me and replied, â€Å"Stay indoors.† I threw her a disgruntled look. With Jasper gone Edward and I can track this James down and kill him! â€Å"I kind of like it.† Emmett grinned stupidly. I glared at him. â€Å"Shut up, Emmett,† I commanded and I meant that for his thoughts too. It didn't stop him. â€Å"Look, if we try to take him down while she's still around, there's a much better chance that someone will get hurt ?C she'll get hurt, or you will, trying to protect her. Now, if we get him alone†¦Ã¢â‚¬  we can hack him up into little pieces and burn him! Emmett finished in his thoughts with another wide grin spreading across his face at the thought. I saw the bright orange streetlights as they grew brighter and larger as Forks loomed into view. We had finally arrived back in town and I was suddenly anxious that our plan won't work. The streets were empty and it felt like it was an ominous sign. Alice could see the grim expression on my face. She'll be fine, Edward, I've seen it. Alice thought calmy. â€Å"Bella,† I began while Alice and Emmett became alert immediately, gazing raptly out the windows. â€Å"If you let anything happen to yourself ?C anything at all ?C I'm holding you personally responsible. Do you understand that?† I said softly. I heard her loud gulp. â€Å"Yes,† she whispered. I looked at Alice who turned back to me. â€Å"Can Jasper handle this?† He cares for Bella, too. â€Å"Give him some credit, Edward. He's been doing very, very well, all things considered.† I raised an eyebrow. â€Å"Can you handle this?† I asked. I have fewer problems handling it then you do. I'd never hurt Bella. How dare you. Alice thought while a growl ripped up her throat and she pulled back her lips to show her gleaming teeth. Coming from Alice, the very tiny Alice, made me smile despite the events of this evening. â€Å"But keep your opinions to yourself,† I said harshly, knowing that the knowledge of her visions would be too much for Bella to handle. You mean the one where I think you should change her into a vampire so she can live with us forever? She thought with great smugness. I grimaced while pulling into Bella's driveway, looking out at the dark grounds surrounding her house. A lump formed in my throat at the thought of what had to happen next.

A History of the Horn, Better Known as the French Horn

Throughout the last six centuries, the evolution of horns has gone from the most basic of instruments used for hunting and announcements to more sophisticated musical versions designed to elicit the most melodious sounds. The First Horns The history of horns starts with the use of actual animal horns, hollowed out of the marrow, and blown into to create loud sounds announcing celebrations and the start of feasts, as well as for sharing warnings, such as the approach of enemies and threats. The Hebrew shofar is a classic example of an animal horn that was, and still is, widely used in celebrations. These culturally significant rams horns are used to announce major holidays and celebrations, such as Rosh Hashanah and Yom Kippur. However, the basic animal horn does not allow for much manipulation of sound other than what the user can do with his mouth. Rafael Ben-Ari/Getty Images Transitioning From Communication Tool to Musical Instrument Making the transition from a method of communication to a way to create music, horns were first formally seen being used as musical instruments during 16th-century operas. They were made from brass and mimicked the structure of the animal horn. Unfortunately, they provided a challenge for adjusting notes and tones. As such, horns of different lengths were introduced, and players had to switch between them throughout a performance. While this did provide some added flexibility, it wasnt an ideal solution, and horns werent widely used. During the 17th century, additional modifications to the horn were seen, including the enhancement of the bell end (larger and flared bells) of the horn. After this alteration was made, the cor de chasse, or French horn as the English called it, was born. The first horns were monotone instruments. But in 1753, a German musician called Hampel invented the means of applying movable slides (crooks) of various length that changed the key of the horn. In 1760, it was discovered rather than invented that placing a hand over the bell of the French horn lowered the tone, called stopping. Devices for stopping were later invented, which further enhanced the sound that performers could create. In the early 19th century, pistons and valves, instead of crooks, were used, giving birth to the modern French horn and eventually the double French horn. This new design allowed for an easier transition from note to note, without having to switch instruments, which meant performers could keep a smooth and uninterrupted sound. It also allowed for players to have a wider range of tones, which created more complex and harmonic sound. Despite the fact that the term French horn has been widely accepted as the proper name of this instrument, its modern design was actually developed by German builders and is most frequently manufactured in Germany. As such, many experts assert that the proper name for this instrument should simply be a horn. Who Invented the French Horn? Tracing the invention of the French horn to one person is tricky. However, two inventors are named as the first to invent a valve for the horn. According to the Brass Society, Heinrich Stoelzel (1777–1844), a member of the band of the Prince of Pless, invented a valve that he applied to the horn by July 1814 (considered the first French horn) and Friedrich Blà ¼hmel (fl. 1808–before 1845), a miner who played trumpet and horn in a band in Waldenburg, is also associated with the invention of the valve. Edmund Gumpert and Fritz Kruspe are both credited with inventing double French horns in the late 1800s. German Fritz Kruspe, who has been noted most often as the inventor of the modern double French horn, combined the pitches of the horn in F with the horn in B-flat in 1900.