Thinking Styles Essay Example for Free

Thinking Styles Essay According to Harrison and Bramson, there are six thinking styles: analyst, synthesist, pragmatist, idealist, realist, and spiritually-guided. In this paper, I will analyze the last three. An idealist is typically concerned with value judgments. He looks at the world with inquiring eyes, asking about what is good for the people and society and believes in the good in people. The idealist is like Pollyanna – optimistic with his view of man, the idealist believes that conflict can be resolved by getting down to the basics. We are after all linked by the same humanity, and our similarities will help reconcile our differences. The realist, on the other hand, looks at the world as is. Facts are of utmost importance, as is observation and objectivity. The world as perceived through the senses is the real world, and hopes and value judgments should not cloud one’s view of reality. A realist sees a bleak landscape than an idealist because a realist chooses to look things as detachedly as possible, to make objective assessments and not make excuses or conjure reasoning to defend negative behavior. A realist insist on having reality, no matter how awful it could be. Â  A spiritually-guided thinking style is radically different from the first two because it is anchored on a belief in God. Faith plays a central role, a determining factor. A spiritually-guided person will see everything in relation to God’s will and its place in God’s great scheme of things. Spiritually-guided people tend to be more accepting and forgiving in the name of faith; however, authentic belief in the principles espoused by the religion can be suspicious. Focusing on God does not mean that the person truly understands the values of the faith, but simply that he is looking at the world and connecting what he sees with an idea of God. Â   Source: Bramson, Robert and Harrsion, Allen. The Art of Thinking. Berkley Publishing Group, 1987.

Pv Value in a Seal Questions and Answers

Pv Value in a Seal Questions and Answers Question 1 (4 marks) List 4 important parameters (not the equation parameters) that are determined by the Pv value in a seal. The suitability of material combinations for the seal faces. The amount of heat generated at the face It also follows that at a given rotational speed An increase in shaft diameter since implies an increase in the Pv value. Assessor Feedback Question 2 (4 marks) The contact property of the interface is influenced by which component in a seal unit? What is the need for seal balance? The fluid pressure in the axial direction is the only pressure component influencing the contact property of the interface. The fluid pressure in the axial direction is the only pressure component influencing the contact property of the interface. Thus, only this component is considered for seal balance and further used to compute the resulting contact force acting on the face. Assessor Feedback Question 3(8 marks) Given the following data, calculate the face area, spring pressure and balance ratios (external and internal) of a seal, for both externally acting and internally acting pressures. Is this Balanced or Unbalanced and why? Seal face contact outer diameter, D = 61.8 mm Effective seal balance diameter, B = 52.6 mm Deal face contact inner diameter, d = 49.2 mm Spring force at working length, F =188 N Calculate the face area of the seal: Α=à Ã¢â€š ¬(D_0^2-D_1^2 )/4 Α=à Ã¢â€š ¬(à £Ã¢â€š ¬-68.2à £Ã¢â€š ¬-^2-à £Ã¢â€š ¬-49.2à £Ã¢â€š ¬-^2 )/4 =1098.46 à £Ã¢â€š ¬-mmà £Ã¢â€š ¬-^2 A=0.001098à £Ã¢â€š ¬- mà £Ã¢â€š ¬-^2 Calculate the spring pressure: P_sp=F_sp/A =188/0.00109846 =171148.7 à £Ã¢â€š ¬-N/à £Ã¢â€š ¬-_(m^2 ) =P_sp 0.17115 MPa Calculate the balance ratio for the external loading: B=(D_0^2-D_b^2)/(D_0^2-D_t^2 ) Α=(à £Ã¢â€š ¬-61.8à £Ã¢â€š ¬-^2-à £Ã¢â€š ¬-52.6à £Ã¢â€š ¬-^2)/(à £Ã¢â€š ¬-61.8à £Ã¢â€š ¬-^2-à £Ã¢â€š ¬-49.2à £Ã¢â€š ¬-^2 ) =1052.48/1398.6 B=0.753 (B Calculate the balance ration for the internal loading B=(D_b^2-D_t^2)/(D_0^2-D_t^2 ) Α=(à £Ã¢â€š ¬-52.6à £Ã¢â€š ¬-^2-à £Ã¢â€š ¬-49.2à £Ã¢â€š ¬-^2)/(à £Ã¢â€š ¬-61.8à £Ã¢â€š ¬-^2-à £Ã¢â€š ¬-49.2à £Ã¢â€š ¬-^2 ) =346.12/1398.6 B=0.25 (B Assessor Feedback Question 4 (4 marks) From the following single mechanical seals, identify the 7 sealing components and other mechanical components, briefly describing their functions? 1)Mating Ring. 2)Primary Sealing Ring. 3) O-ring. 4) O-Ring. 5) Disc. 6) Spring. 7) Retainer. Fluid is to be kept from escaping where the shaft extends through the housing, especially as the shaft rotates. A ring, part 1, with an O-ring, part 4, is sealed against the housing of the container. It is called the mating ring. Another ring, part 2, with an O-ring, part 3, is mounted onto the shaft. It is called the primary sealing ring. The contacting faces of these rings are lapped flat, within light bands. Initial contact between the faces is maintained by a spring, part 6, which pushes them together. The spring reacts against a retainer, part 7 Assessor Feedback Question 5 (4 marks) What difference do you notice between the two mechanical seals shown below. Name them and describe their application. Shows of an outside balanced seal. The shaft packing is forced against the retainer, leaving an area under the seal ring exposed to stuffing box pressure. The closing force exerted by the stuffing box pressure, acting against the shoulder of the seal ring, is slightly greater than the opening force exerted by the liquid film between the faces, thereby keeping the faces in contact at all times. Inside balanced seal illustrates a conventional inside seal that has been balanced. Notice that a step in the shaft has allowed the sealing face of the mating ring to be moved radially inward without decreasing the width of the face itself. The primary sealing ring remains mounted on the original shaft diameter, which means that the closing force remains unchanged. Because we have successfully exposed more of the primary sealing ring face to hydraulic pressure working to open the seal, the design is considered balanced. Assessor Feedback Question 6 (4 marks) Name the primary sealing elements in a single mechanical seal. 1) Primary sealing surfaces. 2) Secondary sealing surfaces. 3) a means of actuation. 4) a means of drive. Assessor Feedback Question 7 (4 marks) While its accepted that solid alumina ceramic seal rings will be considerably more expensive than ceramic coated steel rings, why should they be the preferred choice between the two types of seal ring? When handling corrosive fluids at moderate pressures and velocities: alumina ceramics may be employed as thin coatings or solid rings (preferred!!) For highly corrosive fluids: high purity ceramic alumina can be used. Alumina ceramics have: Relatively low tensile strength Poor resistance to thermal shock Low thermal conductivity High elasticity modulus Assessor Feedback Question 8 (4 marks) Which dynamic secondary sealing element is the preferred type to handle axial movement? Give reasons for your answer. What type of damage does a wedge type secondary seal do to pump shafts/sleeves? Explain how this mechanism works. The pusher type of mechanical seals move axially along the rotating shaft or the sleeve to maintain the contact with the faces of the seal. This feature of these seals helps compensate for the wearing that may occur at the seal face, and wobbling due to misalignment. The pusher types of mechanical seals are used commonly, are less expensive and are easily available in the market in wide range of sizes and designs. The only disadvantage of these seals is that they tend to hang up and sometimes there is fretting of the shaft. Pusher seals utilize a dynamic secondary seal which moves axially with the major seal face. which is either an O-ring, wedge or other type of equipment, across the shaft as a means of compensation for face wear and/or shaft movement. For high temperature (up to 500 deg F) or aggressive chemicals a Teflon wedge ring may be used. Since Teflon is plastic and does not rebound like elastomer, it has to be pushed by spring force into the wedge shaped opening to maintain a seal on the shaft. Non-Pusher type or Bellow seals have no dynamic secondary seal under the movable seal ring. Check Which dynamic secondary sealing element is for axial movement. Operation does not cause shaft wear pusher type seals can handle bi-directional shaft rotation, large pressure, temperature and speed excursions. Assuming a spring-loaded Teflon wedge can also be used as a dynamic shaft seal behind the rotating primary seal ring. The spring and process pressures keep the wedge in contact with the shaft. Like chevrons and U-cups, wedges can only seal in one direction. Because of the tendency for Teflon to cold flow, almost all wedges need to be loaded by one or more springs along with the process pressure. Wedge seals often cause shaft damage by fretting. Assessor Feedback Question 9 (4 marks) What is the distinct advantage offered by a bellows seal? How can the design be improved to accommodate higher pressures? Which bellows material offers the best corrosion resistance? One of the most frequent and serious problems valves face is gland leakage, results in wasted and increased plant downtime. Apart from the high cost of energy losses, Gland leakages can also cause serious environmental, ecological and health hazards to plant workers and personnel. Leakage of sensitive material can also constitute to a fire hazard, explosion, or damage to equipment by corrosive material. Air entering the pipeline could produce inflammable explosive or poisonous mixtures. Gland packed valves often demand continual maintenance in accessibility creating particular difficulties. The bellows comply to conditions at high temperatures and are capable of withstanding over 10,000 cycles without failure. Bellow Seals are also known as Zero Leak Valves or Emission Free Valves The multi-ply bellow design is preferred for handling higher pressure fluids (generally two or three plies of the metal wall). A two ply bellow can increase its pressure rating by 80% to 100% as compared to a single ply bellow of the same thickness. Alternatively, if a single ply bellow of a thickness equivalent to a pressure rating of a two ply bellow is used, the stroke length is reduced. Thus, a multi-ply bellow design offers a distinct advantage over a single ply bellow. The stainless steel bellow material AISI 316Ti which contains Titanium to withstand high temperatures. Alternatively, Inconel 600 or Inconel 625 improve fatigue strength and corrosion resistance as compared with stainless steel bellows. Similarly, Hastalloy C-276 offers greater corrosion resistance and fatigue strength than Inconel 625. Fatigue resistance can be improved by using a multiply bellows system and reducing the stroke length; this can significantly increase the bellow service life. Assessor Feedback Question 10 (6 marks) Do a comparative analysis of inboard and outboard mounting of seals. Inside-mounted seal is the most common in the industry and the most energy-efficient when compared with other sealing methods, such as packing and seal less equipment. They are used in all industries with respect to fluid types and the seals property ranges, pressure speed, diameter and temperature. Inside seals are mounted within the equipment seal chamber the advantages of this design include: The seal can be cooled by the pumped fluid in an enlarged dead-ended chamber, by a product bypass flush or by a clean external flush. Depending on the seal chamber design, the rotary action of the seal assembly may help keep debris away from the seal faces. With proper hydraulic balancing, the product pressure helps keep the seal faces closed. Catastrophic leakage is usually avoided during seal failure. Leakage can be restricted by the stationary elements in the gland. Inside seals are available in many materials and designs. Environmental controls are easily included in the design. Centrifugal forces tend to reduce leakage. Outside seals are mounted external of the equipment housing the advantages of this design include: Outside-mounted seals can be used when the radial or axial space in the chamber is not adequate or access is not available for an inside seal installation. Installation may be easier than with an inside seal. However, most equipment designs still require à ¢Ã¢â€š ¬Ã‚ ¨some disassembly. Less expensive materials may be used since à ¢Ã¢â€š ¬Ã‚ ¨many components may not be exposed to the pumped product. The seal can be observed and monitored for seal à ¢Ã¢â€š ¬Ã‚ ¨face wear. Adjustments can be made without à ¢Ã¢â€š ¬Ã‚ ¨equipment disassembly. The seal can often be backed-off for cleaning. Assessor Feedback Question 11 (8 marks) Explain the difference between static and dynamic seals? 0-rings are used for effective sealing in applications. Mostly, they are used to help repair or correct any manufacturing or installation defects seen in glands. 0-rings can be used in static as well as dynamic applications. The make of both these 0-rings will be different owing to the difference in application requirements. The following are some major differences between static and dynamic 0-rings: The material used to manufacture dynamic 0-rings should be tougher than that used to manufacture static 0-rings.This is because the dynamic 0-ring will have to undergo movement while the application is functioning. In dynamic applications, the surface finish and material of the gland should be such that it doesnt abrade the 0-ring during movement otherwise, the 0-ring could tear this is irrelevant in static applications, where the 0-ring doesnt move. 0-rings used in dynamic applications are likely to wear at a faster rate as compared to static 0-rings. This is because dynamic 0-rings are constantly moving. Hence, the interval of maintenance procedures for dynamic 0-rings should be shorter than that of static 0-rings. à ¢Ã¢â€š ¬Ã‚ ¢All 0-rings should be properly lubricated at all times. à ¢Ã¢â€š ¬Ã‚ ¢Dyna mic 0-rings require more lubrication than static ones. Depending on the application, static or dynamic seals will be used. O-rings are useful in a varied number of industries and applications. They are effective across a wide range of temperatures and pressures. However, using the right 0-ring for each application will help you increase the reliability and service life of the 0-ring. You can consult with your 0-ring manufacturer on the best fit for your application Assessor Feedback Question 12 (4 marks) Why are mechanical seals preloaded? Name four of the most common types of preloading for pump seals. Depending on the application it may be necessary to have either a positive or a negative operational clearance in the bearing arrangement. In the majority of applications, the operational clearance should be positive, i.e. when in operation, the bearing should have a residual clearance, however slight. However, in many cases, machine tool spindle bearings, pinion bearings in automotive axle drives, bearing arrangements of small electric motors, or bearing arrangements for oscillating movement, where a negative operational clearance, i.e. a preload, is needed to enhance the stiffness of the bearing arrangement or to increase running accuracy. The application of a preload, e.g. by springs, is also recommended where bearings are to operate without load or under very light load and at high speeds. In these cases, the preload serves to provide a minimum load on the bearing and prevent bearing damage as a result of sliding movements of the rolling elements, Helical Compression Spring, Wave Washer Springs, Single Belleville Washer Springs, Elastomeric Preloading Assessor Feedback Question 13 (4 marks) The table below contains a list of commonly used seal materials. For the given set of temperatures in degree centigrade, indicate the suitability of these materials by marking S for suitable and LS for limited suitability of short period durations. Type of Material Temperature in  ° C 50 100 200 300 350 Natural Rubber S S LS Nitrile S S S LS Neoprene S S S LS Viton S S S S S Silicone S S S S S Fluoro-elastomer S S S S S Question 14 (4 marks) What are the characteristics that make pure carbon-graphite the most favoured material in the chemical industry? Strongly anisotropic, Greasy feel, Readily marks, High thermal conductivity, High tensile strength, Low thermal expansion coefficient, Good resistance to thermal shock. Assessor Feedback Question 15 (4 marks) Ignoring temperature limitations, what type of elastomeric material would you suggest for the following applications? Sealing for Vacuum systems Buna-N, silicone, Fluorocarbon, and Perfluorocarbon Applications Vacuum systems Polyurethane Rotary shaft seals Fluorocarbon, Polyacrylate Applications that require high tear and abrasion resistance Natural Rubber Question 16 (4 marks) Why is it difficult to achieve a perfectly uniform load distribution across the shaft circumference, when using a single coil spring? What does this condition further lead to? What are the main advantages associated with the use of multi-coil springs? Typically, a single-coil spring used for a seal head has a relatively large wire cross section and therefore provides more substance to combat corrosion from the system fluid. But it is rigid in construction because of which there is difficulty in achieving a perfectly uniform load distribution across the shaft circumference. This may in turn lead to distortion of the primary seal ring face and this is particularly critical at high rotational shaft speeds. This arrangement consists of a series of small coil springs uniformly distributed along the circumference of the seal cartridge. The chief advantage with this design is that the possibility of distortion of the primary seal ring face is minimized and this is particularly true at higher rotational speeds of the shaft. The use of multiple-coil springs makes seal design independent of seal diameter sizes. Deterioration arising from chemical corrosion can be greatly minimized by the use of stainless steel for spring manufacture. Assessor Feedback Question 17 (4 marks) What is the three-point contact method? Explain in brief, the procedure involved. Three-point contact method where three setscrews positioned at 120 ° from each other ensure squareness of the rotating face, by deforming the sleeve to the shaft OD. Another set of three setscrews also located 120 ° apart and positioned between the earlier set of screws, enable locking of the sleeve to the shaft. Assessor Feedback Question 18 (4 marks) Metal impregnations are sometimes added to graphite seal rings in order to improve their properties. Give three areas of concern when selecting these metal additions. Both the metal filler and the carbon have to be compatible to the sealed liquid. The metal will heat up and expand more rapidly than the carbon. The coefficient of friction of the metal will be higher than the parent carbon and the seal face will run hotter than if it were made just from pure carbon. Assessor Feedback Question 19 (4 marks) Outline the nature of seal malfunction that may be caused by the following: Incorrect pressure differential between inside and outside seal face sets Cavitation or vaporization of liquid between sealing faces Thermal distress of material Large bearing clearances A change in temperature. Many products solidify at temperature extremes, the product is taking a pressure drop across the seal faces and solidifying. The inner face of a back to back double seal application is not positively locked in position. A snap ring must be installed to prevent the inboard stationary face from moving towards the rotating face when the high pressure barrier fluid pressure is lost or overcome by system pressure. Erosion / Corrosion. An accelerated attack caused by a combination of corrosion and mechanical wear. Vaporization, liquid turbulence, vane passing syndrome, and suction recirculation are special cases often called cavitation. Solids in the liquid and high velocity increase the problem Heat checking is caused by thermal distress of the material resulting in small radial cracks. Scoring may be present or uneven wear with the heat checking on the high spots. Occurs typically with tungsten carbides and silicon carbides Seal drips when stationary and when the shaft is rotating. Seal may pop from flashing during operation. The tendency for a seal to wedge is enhanced by a rough surface, lack of lubrication and high reciprocating speeds. Wedging is unlikely to occur with small clearance gaps in the range of 0.0550.127mm (0.002-0.005 inch). For clearances greater than 0.25 mm (0.010 inch) the possibility of wedging always exists as the radial clearance increases, the axial clearance increases as well the more room (radial clearance), the more the elements can shift in relation to each other. With a higher clearance there is more tolerance of thermal expansion effects, differential temperature between the inner and outer faces. Assessor Feedback Question 20 (4 marks) The leakage rate in a seal while running is found to be constant. Can the reason be attributed to a damaged seal face? State three important causes for each of the below: Intermittent leakage There is a leak between the face and the holder that becomes visible only when the unit comes up to operating temperature. A bending or bent shaft is causing the seal outside diameter to contact the inside diameter of the stuffing box, or some other stationary object. The shaft/ sleeve is too large in diameter and it is restricting movement of the seal. Spring loaded dynamic elastomers such as Teflon ® wedges, U- cups, chevrons and spring loaded O-ring designs are very sensitive to this problem Constant dripping in a seal. There is damage in the O-ring groove. Maybe the O-ring was removed with a sharp metal instrument and this has caused a scratch in the O-ring groove. Leaking between the gland and the stuffing box. This leak path is very visible in most applications Leaking between the cartridge sleeve and the shaft Question 21 (6 marks) It is a requirement to identify and select a suitable mechanical seal for a given application and process. What is the nature and type of questions that you would raise, in order to help arrive at the right selection? General Selection Considerations The process of mechanical seal selection involves a thorough evaluation of many important factors that include: Shaft diameter Rotational rubbing speed in the contact faces Service temperature Process fluid pressure Physical and chemical properties of the various liquid constituents Mechanical/structural properties of the primary seal components Environmental control systems Properties and resistance characteristics of the secondary sealing components. Pressure. Assessor Feedback Question 22 (4 marks) Which of the following conditions satisfy the requirements for sealing high-speed applications? Explain in brief: Lower spring load at seal faces Increased hydraulic balance ratio Face combinations such as carbon vs. tungsten carbide Stationary seal designs Number 4. Stationary seal designs: The Internal seal configuration, with the seal heads mounted stationary and the seal seats rotating with the shaft is advantageous, especially in high-speed applications where dynamic balancing considerations demand minimum mass of the rotating parts Assessor Feedback Question 23 (6 marks) A change in pumping fluid temperature adversely affect the seals in the stuffing boxes. What are the effects and How do you control the temperature in the stuffing box and the seal? a)Many fluids are adversely affected by a change in their temperature, and when this change takes place, seal failure is almost sure to follow. The failure can take several forms: Coated hard faces can heat check (crack). Elastomers can take a compression set and crack at elevated temperature Cold temperatures can cause elastomers to harden. The liquid can crystallize, restricting seal movement and open the faces. The liquid can vaporize between the faces forcing them open. The viscosity of the fluid can change either restricting seal movement, or making the fluid less of a lubricant. The liquids corrosion rate will double with an 18 ° Fahrenheit (10 ° C) rise in temperature. The liquid can convert to a film between the sliding seal components, restricting their movements. The magnetite that forms in hot water is a good example of this. A film can form on the seal faces causing them to separate. Lapped seal faces can distort and go out of flat at elevated or cryogenic temperatures. b) A balanced mechanical seal and installed at the proper compression, is your best insurance against a significant rise in stuffing box temperature: Proper face balance. 70/ 30 is the most common to 5000 fpm. (25 Meters per sec.) Low friction face materials. Carbon/graphite vs. a silicon carbide hard face is the best. The correct spring compression to control face loading. Faces with good heat conductivity. Tungsten carbide and silicon carbide have excellent thermal conductivity compared to most other hard face materials. A small cross section carbon/ graphite face press fitted into a metal holder is better than solid carbon/ graphite for removing heat from between the lapped faces. Sometimes, that is not good enough, so occasionally youll have to come up with some additional method of controlling the temperature in the stuffing box area and between the lapped seal faces. A heating /cooling jacket, quench flush or drain connection, dual seal, heat exchanger Assessor Feedback Question 24 (4 marks) The mechanical shaft seal should be selected according to the operating conditions at the shaft seal location. What important factors must be considered when selecting a mechanical shaft seal? For a specific ap

Ecology :: essays research papers

In the original Greek "oikos" means, "house". So ecology is "the study of the house" the place where you live, or the environment which technically includes all those factors, both nonliving and living, that affect an organism. Ecology then is the study of the interactions of organisms in their environment includes both the living (biotic) and physical (abiotic) factors of the environment. It's also the science, which formulates and tests hypotheses about environment. Ecology is the relationships, identification and analysis of problems common to all areas. Ecology studies the population and the community, evaluates cause and effects of the responses of populations and communities to environmental change. POPULATIONS The population is defined as an assemblage of individuals of a single species that live in the same place at the same time. Also, biologists add an additional condition: the individuals in a population must interact with each other to the point of being able to interbreed. Population is important to understanding many important ecological and evolutionary phenomena. Ecologists can use information from population ecology to predict the success of a given species or assemblage of species. One attribute of populations that is observed in nature is their dispersion, or the way in which individuals are distributed in a given area. Typically, biologists refer to three types of dispersion: - Clustered (aggregated), Regular (evenly spaced), Random (irregularly spaced) Populations showing a clustered pattern are common in nature and are found among many different types of organisms. Clustered dispersion patterns are often due to environment heterogeneity. Regular dispersion patterns are relatively rare in nature and occur when a resource is scarce. A good example of regular spacing occurs in animals that exhibit territoriality, a phenomenon in which animals establish an area for themselves and fight off all other individual seeking to invade that area. Regular dispersion patterns can also be observed in plants. Random patterns can be found in a variety of organisms (trout in lake or maple trees in a forest). Regardless of which organisms, the number of births almost always has the potential to be greater than the number of deaths. In other words populations of all species have the capacity to grow. That property is crucial importance to the success of all species. However, all species will not increase under all circumstance, but instead they can, given appropriate conditions. There are two models of population growth: the exponential model and the logistic model. One of the most basic models of population biology is the exponential growth equation, which is: )N/)t = rmaxN This equation states that, in a growing population, the rate of change in population size is determined by the maximal intrinsic rate of increase (rmax) multiplied by the number of individuals in that population (N). Ecology :: essays research papers In the original Greek "oikos" means, "house". So ecology is "the study of the house" the place where you live, or the environment which technically includes all those factors, both nonliving and living, that affect an organism. Ecology then is the study of the interactions of organisms in their environment includes both the living (biotic) and physical (abiotic) factors of the environment. It's also the science, which formulates and tests hypotheses about environment. Ecology is the relationships, identification and analysis of problems common to all areas. Ecology studies the population and the community, evaluates cause and effects of the responses of populations and communities to environmental change. POPULATIONS The population is defined as an assemblage of individuals of a single species that live in the same place at the same time. Also, biologists add an additional condition: the individuals in a population must interact with each other to the point of being able to interbreed. Population is important to understanding many important ecological and evolutionary phenomena. Ecologists can use information from population ecology to predict the success of a given species or assemblage of species. One attribute of populations that is observed in nature is their dispersion, or the way in which individuals are distributed in a given area. Typically, biologists refer to three types of dispersion: - Clustered (aggregated), Regular (evenly spaced), Random (irregularly spaced) Populations showing a clustered pattern are common in nature and are found among many different types of organisms. Clustered dispersion patterns are often due to environment heterogeneity. Regular dispersion patterns are relatively rare in nature and occur when a resource is scarce. A good example of regular spacing occurs in animals that exhibit territoriality, a phenomenon in which animals establish an area for themselves and fight off all other individual seeking to invade that area. Regular dispersion patterns can also be observed in plants. Random patterns can be found in a variety of organisms (trout in lake or maple trees in a forest). Regardless of which organisms, the number of births almost always has the potential to be greater than the number of deaths. In other words populations of all species have the capacity to grow. That property is crucial importance to the success of all species. However, all species will not increase under all circumstance, but instead they can, given appropriate conditions. There are two models of population growth: the exponential model and the logistic model. One of the most basic models of population biology is the exponential growth equation, which is: )N/)t = rmaxN This equation states that, in a growing population, the rate of change in population size is determined by the maximal intrinsic rate of increase (rmax) multiplied by the number of individuals in that population (N).

T.S. Eliots The Wasteland Essay -- Eliot Wasteland Survival Essays

T.S. Eliot's The Wasteland Cooperation is the key to human survival, and over time humans have been known to group together to survive. This strategy has allowed humans to develop massive cities and countries of immense power. Without the natural instinct to cling to one another, humans would not be as advanced as they are today, and may not have even made it out of the caves. Many authors display our natural instinct to cooperate in their works, allowing the characters to become more real to the readers. T.S Eliot’s The Wasteland displays our natural instinct to cooperate with each other as a key to our survival. As we struggle to survive when our world begins to fall apart, our basic instinct to cooperate with each other kicks in and we cling to each other for comfort. This concept is brought up in Chinua Achebe’s novel Things Fall Apart. And again W.B. Yeats’s says in one of his poems, "Things fall apart; the center cannot hold." In either case the concept of clinging to one another and cooperating when things fall apart is displayed as a basic instinct that is the key to our success as humans. The Wasteland describes how humans cling together as the world falls apart by depicting a world from a much different point of view then we are used to. Instead of seeing the world in a positive view, Eliot depicts the world in despair. As this world falls apart, humans cling together and cooperate to get through the bad times. Lines 139-172 depict a scene in a pub that illustrates how we cling to one another even though we may not be supportive of each other. In this scene, Albert tells his wife how he thinks she is ugly and can’t fulfill what he desires of her. As he goes on, she makes excuses about why she is ugly and can’t... ...Org: Public Affairs on the Web. 13 Dec. 2000: 24 Jan. 2001. http://www.c-span.org/campaign2000/bushspeech.asp. Brooks, David. Bobos in Paradise : The New Upper Class and How They Got There. New York: Simon, 2000. Eliot, T.S. The Waste Land, Prufrock and Other Poems. New York: Dover, 1998. Gore, Albert Jr., Concession Speech. C-Span.Org: Public Affairs on the Web. 13 Dec. 2000: 24 Jan. 2001. http://www.c-span.org/campaign2000/gorespeech.asp. Jin, Ha. Waiting. New York: Vintage, 2000. Maddy, Yulisa Amadu. No Past No Present No Future. Portsmouth, NH: Heinemann- Reed, 1996. Tanksley, Charlie. Speech on the Proposed New Flag. Ajc.com. 30 Jan. 2001. < http://www.accessatlanta.com/partners/ajc/flag/tankspeech.html>. Taylor, Mark. Remarks on the New Flag. Ajc.com. 30 Jan. 2001. http://www.accessatlanta.com/partners/ajc/flag/taylor0130.html.

Martha Graham Essay examples -- Dance Dancing Choreography Essays

Martha Graham Martha Graham was one of the most influential figures in American modern dance, and her techniques and styles are still practiced today. She became widely known throughout all ages and decades. Her first debut was in the 1920's. As time went on, she became more experienced and wiser in the modern dance field. Martha Graham, whose style was considered controversial, became one of the finest choreographers and dancers in the dance world. In 1894 Martha was born in Allegheny, Pennsylvania (Pratt 8). She was the daughter of Jane Beers and George Graham. Her father was a well-known physician who treated mental disorders. After living in Pennsylvania for 12 years, she and her family moved to Santa Barbara, California in 1908 (Harmon et al. 182). This was where she started studying modern dance in her earlier years. Martha's father played a big role in her life. Dr. Graham inspired his daughter to search for the meaning behind people's actions. As she sat in her father's office, she would look at the patients in bewilderment. The patients would blurt out words and move their arms and legs in a wild manner, making her even more curious about people's actions (Pratt 13). Dr. Graham then took his daughter to a performance of Ruth St. Denis in 1911 where she was mesmerized by the dancers (Harmon et al. 182). Martha entered Cumnock School of Expression after graduating from high school. There she trained in dance, drama, and self-expressions. Martha's love to study people's actions was incredibly strong. After Graham graduated from the junior college in 1916, she then enrolled in Denishawn School of Dance (182). She was recognized at the school for her talent and determination, not her potential a... ...d a bad case of pneumonia. Graham died on April 1, 1991 (100). Graham led an exciting and fulfilling life. Although her audiences may have had to get used to her innovative style of modern dance, she accomplished her dreams throughout the years and became a big success. Martha Graham became one of the finest dancers and choreographers in the world. Works Cited Harmon, Justin, et al. American Cultural Leaders. Santa Barbara: ABC-CLIO 1993. McLanathan, Richard and Gene Brown ed. The Arts. New York: New York Times Company, 1978. Mille, Agnes de and Helene Oblensky. American Dances. New York: Macmillan Publishing Co., Inc., 1980. "Modern Dance." Microsoft Encarta. 1997 ed. Pratt, Paula Bryant. The Importance of Martha Graham. San Diego: Lucent Books, Inc., 1995. Switzer, Ellen. Dancers! Horizons in American Dance. New York: Atheneum, 1982.

Sonnys Blues

tells of seeing his brother play piano in a jazz club, and of sending up to his brother a drink—a mixture of Scotch whiskey and milk. As the story closes this unusual mixture sets atop Sonny’s piano â€Å"like the very cup of trembling. † Discuss how this drink serves as a symbolic conclusion to Baldwin’s story. How does it symbolize for the reader the resolution, or synthesis, of various tensions in the story? Indeed what are the main lines of tension, opposition, and division in â€Å"Sonny’s Blues†? At the end of the story, the narrator describes a glass sitting over Sonny’s piano as shaking â€Å"like the very cup of trembling† to highlight what a difficult and complicated position Sonny is in. This image is borrowed from the Bible, where the cup of trembling is used as a symbol to describe the suffering and fear that have plagued the people. The biblical passage promises a relief from that suffering, but Baldwin’s us e of the cup of trembling as a symbol is less overt. * Sonny’s drinking from the cup of trembling serves as a reminder of all the suffering he has endured, while also offering the chance for redemption and peace.As a musician, Sonny takes all his suffering and that of those around him and transforms it into something beautiful. * Like the figures from the Bible, Sonny is moving toward salvation, but his fate remains uncertain. Perhaps he will continue to suffer, suffering being the cost he has to pay for being a musician. There is something Christ like about Sonny’s pain, and suffering for Sonny is at once inevitable and redemptive * At the end of the story, it remains unclear whether he will continue to suffer in order to play his music or whether a greater peace and redemption awaits everyone involved.The fact that the glass is filled with scotch and milk only further highlights the tension and duality Sonny faces. SUFFERING QUOTE A great block of ice got settled in my belly and kept melting there slowly all day long, while I taught my classes algebra. It was a special kind of ice. . . . Sometimes it hardened and seemed to expand until I felt my guts were going to come spilling out or that I was going to choke or scream. (12)| People don't always outwardly express their anguish. The narrator's suffering is immense (it threatens to overpower him here), but he can't just fall apart.Perhaps his suffering is made even greater because this great, big block of ice just stays where it is. He can't get it out of his system. SUFFERING QUOTE â€Å"Tell me,† I said at last, â€Å"why does he want to die? He must want to die, he's killing himself, why does he want to die? † (38)| The narrator is making a desperate plea with this unanswerable question. He can't imagine anyone doing what Sonny has done to himself unless he no longer has the will to live. He just wants to know â€Å"why? †Ã‚   His suffering is as great as Sonny's here. SU FFERING QUOTEYou don't know how much I needed to hear from you. I wanted to write you many a time but I dug how much I must have hurt you and so I didn't write. But now I feel like a man who's been trying to climb out of some deep, real deep and funky hole and just saw the sun up there, outside. I got to get outside. (127)| Sonny suffers on multiple levels. He suffers from his drug addiction and from being stuck in jail. But he also suffers from the knowledge that he's hurt his family and that, because of this, he didn't dare reach out to them even when he needed to the most. Sonnys Blues tells of seeing his brother play piano in a jazz club, and of sending up to his brother a drink—a mixture of Scotch whiskey and milk. As the story closes this unusual mixture sets atop Sonny’s piano â€Å"like the very cup of trembling. † Discuss how this drink serves as a symbolic conclusion to Baldwin’s story. How does it symbolize for the reader the resolution, or synthesis, of various tensions in the story? Indeed what are the main lines of tension, opposition, and division in â€Å"Sonny’s Blues†? At the end of the story, the narrator describes a glass sitting over Sonny’s piano as shaking â€Å"like the very cup of trembling† to highlight what a difficult and complicated position Sonny is in. This image is borrowed from the Bible, where the cup of trembling is used as a symbol to describe the suffering and fear that have plagued the people. The biblical passage promises a relief from that suffering, but Baldwin’s us e of the cup of trembling as a symbol is less overt. * Sonny’s drinking from the cup of trembling serves as a reminder of all the suffering he has endured, while also offering the chance for redemption and peace.As a musician, Sonny takes all his suffering and that of those around him and transforms it into something beautiful. * Like the figures from the Bible, Sonny is moving toward salvation, but his fate remains uncertain. Perhaps he will continue to suffer, suffering being the cost he has to pay for being a musician. There is something Christ like about Sonny’s pain, and suffering for Sonny is at once inevitable and redemptive * At the end of the story, it remains unclear whether he will continue to suffer in order to play his music or whether a greater peace and redemption awaits everyone involved.The fact that the glass is filled with scotch and milk only further highlights the tension and duality Sonny faces. SUFFERING QUOTE A great block of ice got settled in my belly and kept melting there slowly all day long, while I taught my classes algebra. It was a special kind of ice. . . . Sometimes it hardened and seemed to expand until I felt my guts were going to come spilling out or that I was going to choke or scream. (12)| People don't always outwardly express their anguish. The narrator's suffering is immense (it threatens to overpower him here), but he can't just fall apart.Perhaps his suffering is made even greater because this great, big block of ice just stays where it is. He can't get it out of his system. SUFFERING QUOTE â€Å"Tell me,† I said at last, â€Å"why does he want to die? He must want to die, he's killing himself, why does he want to die? † (38)| The narrator is making a desperate plea with this unanswerable question. He can't imagine anyone doing what Sonny has done to himself unless he no longer has the will to live. He just wants to know â€Å"why? †Ã‚   His suffering is as great as Sonny's here. SU FFERING QUOTEYou don't know how much I needed to hear from you. I wanted to write you many a time but I dug how much I must have hurt you and so I didn't write. But now I feel like a man who's been trying to climb out of some deep, real deep and funky hole and just saw the sun up there, outside. I got to get outside. (127)| Sonny suffers on multiple levels. He suffers from his drug addiction and from being stuck in jail. But he also suffers from the knowledge that he's hurt his family and that, because of this, he didn't dare reach out to them even when he needed to the most.

Bag of Bones CHAPTER THIRTEEN

I caught the measles when I was eight, and I was very ill. ‘I thought you were going to die,' my father told me once, and he was not a man given to exaggeration. He told me about how he and my mother had dunked me in a tub of cold water one night, both of them at least half-convinced the shock of it would stop my heart, but both of them completely convinced that I'd burn up before their eyes if they didn't do something. I had begun to speak in a loud, monotonously discursive voice about the bright figures I saw in the room angels come to bear me away, my terrified mother was sure and the last time my father took my temperature before the cold plunge, he said that the mercury on the old Johnson & Johnson rectal thermometer had stood at a hundred and six degrees. After that, he said, he didn't dare take it anymore. I don't remember any bright figures, but I remember a strange period of time that was like being in a funhouse corridor where several different movies were showing at once. The world grew elastic, bulging in places where it had never bulged before, wavering in places where it had always been solid. People most of them seeming impossibly talldarted in and out of my room on scissoring, cartoonish legs. Their words all came out booming, with instant echoes. Someone shook a pair of baby-shoes in my face. I seem to remember my brother, Siddy, sticking his hand into his shirt and making repeated arm-fart noises. Continuity broke down. Everything came in segments, weird wieners on a poison string. In the years between then and the summer I returned to Sara Laughs, I had the usual sicknesses, infections, and insults to the body, but never anything like that feverish interlude when I was eight. I never expected to believing, I suppose, that such experiences are unique to children, people with malaria, or maybe those suffering catastrophic mental breakdowns. But on the night of July seventh and the morning of July eighth, I lived through a period of time remarkably like that childhood delirium. Dreaming, waking, moving they were all one. I'll tell you as best I can, but nothing I say can convey the strangeness of that experience. It was as if I had found a secret passage hidden just beyond the wall of the world and went crawling along it. First there was music. Not Dixieland, because there were no horns, but like Dixieland. A primitive, reeling kind of bebop. Three or four acoustic guitars, a harmonica, a stand-up bass (or maybe a pair). Behind all of this was a hard, happy drumming that didn't sound as if it was coming from a real drum; it sounded as if someone with a lot of percussive talent was whopping on a bunch of boxes. Then a woman's voice joined in a contralto voice, not quite mannish, roughing over the high notes. It was laughing and urgent and ominous all at the same time, and I knew at once that I was hearing Sara Tidwell, who had never cut a record in her life. I was hearing Sara Laughs, and man, she was rocking. ‘You know we're going back to MANderley, We're gonna dance on the SANderley, I'm gonna sing with the BANderley, We gonna ball all we CANderley Ball me, baby, yeah!' The basses yes, there were two broke out in a barnyard shuffle like the break in Elvis's version of ‘Baby Let's Play House,' and then there was a guitar solo: Son Tidwell playing that chickenscratch thing. Lights gleamed in the dark, and I thought of a song from the fifties Claudine Clark singing ‘Party Lights.' And here they were, Japanese lanterns hung from the trees above the path of railroad-tie steps leading from the house to the water. Party lights casting mystic circles of radiance in the dark: red blue and green. Behind me, Sara was singing the bridge to her Manderley song mama likes it nasty, mama likes it strong, mama likes to party all night long but it was fading. Sara and the Red-Top Boys had set up their bandstand in the driveway by the sound, about where George Footman had parked when he came to serve me with Max Devore's subpoena. I was descending toward the lake through circles of radiance, past party lights surrounded by soft-winged moths. One had found its way inside a lamp and it cast a monstrous, batlike shadow against the ribbed paper. The flower-boxes Jo had put beside the steps were full of night-blooming roses. In the light of the Japanese lanterns they looked blue. Now the band was only a faint murmur; I could hear Sara shouting out the lyric, laughing her way through it as though it were the funniest thing she'd ever heard, all that Manderley-sanderley-canderley stuff, but I could no longer make out the individual words. Much clearer was the lap of the lake against the rocks at the foot of the steps, the hollow clunk of the cannisters under the swimming float, and the cry of a loon drifting out of the darkness. Someone was standing on The Street to my right, at the edge of the lake. I couldn't see his face, but I could see the brown sportcoat and the tee-shirt he was wearing beneath it. The lapels cut off some of the letters of the message, so it looked like this: ORMA ER OUN I knew what it said anyway in dreams you almost always know, don't you? NORMAL SPERM COUNT, a Village Cafe yuck-it-up special if ever there was one. I was in the north bedroom dreaming all this, and here I woke up enough to know I was dreaming . . . except it was like waking into another dream, because Bunter's bell was ringing madly and there was someone standing in the hall. Mr. Normal Sperm Count? No, not him. The shadow-shape falling on the door wasn't quite human. It was slumped, the arms indistinct. I sat up into the silver shaking of the bell, clutching a loose puddle of sheet against my naked waist, sure it was the shroud-thing out there the shroud-thing had come out of its grave to get me. ‘Please don't,' I said in a dry and trembling voice. ‘Please don't, please.' The shadow on the door raised its arms. ‘It ain't nuthin but a barn-dance sugar!' Sara Tidwell's laughing, furious voice sang. ‘It ain't nuthin but a round-and-round!' I lay back down and pulled the sheet over my face in a childish act of denial . . . and there I stood on our little lick of beach, wearing just my undershorts. My feet were ankle-deep in the water. It was warm the way the lake gets by midsummer. My dim shadow was cast two ways, in one direction by the scantling moon which rode low above the water, in another by the Japanese lantern with the moth caught inside it. The man who'd been standing on the path was gone but he had left a plastic owl to mark his place. It stared at me with frozen, gold-ringed eyes. ‘Hey Irish!' I looked out at the swimming float. Jo stood there. She must have just climbed out of the water, because she was still dripping and her hair was plastered against her cheeks. She was wearing the two-piece swimsuit from the photo I'd found, gray with red piping. ‘It's been a long time, Irish what do you say?' ‘Say about what?' I called back, although I knew. ‘About this!' She put her hands over her breasts and squeezed. Water ran out between her fingers and trickled across her knuckles. ‘Come on, Irish,' she said from beside and above me, ‘come on, you bastard, let's go.' I felt her strip down the sheet, pulling it easily out of my sleep-numbed fingers. I shut my eyes, but she took my hand and placed it between her legs. As I found that velvety seam and began to stroke it open, she began to rub the back of my neck with her fingers. ‘You're not Jo,' I said. ‘Who are you?' But no one was there to answer. I was in the woods. It was dark, and on the lake the loons were crying. I was walking the path to Jo's studio. It wasn't a dream; I could feel the cool air against my skin and the occasional bite of a rock into my bare sole or heel. A mosquito buzzed around my ear and I waved it away. I was wearing Jockey shorts, and at every step they pulled against a huge and throbbing erection. ‘What the hell is this?' I asked as Jo's little barnboard studio loomed in the dark. I looked behind me and saw Sara on her hill, not the woman but the house, a long lodge jutting toward the nightbound lake. ‘What's happening to me?' ‘Everything's all right, Mike,' Jo said. She was standing on the float, watching as I swam toward her. She put her hands behind her neck like a calendar model, lifting her breasts more fully into the damp halter. As in the photo, I could see her nipples poking out the cloth. I was swimming in my underpants, and with the same huge erection. ‘Everything's all right, Mike,' Mattie said in the north bedroom, and I opened my eyes. She was sitting beside me on the bed, smooth and naked in the weak glow of the nightlight. Her hair was down, hanging to her shoulders. Her breasts were tiny, the size of teacups, but the nipples were large and distended. Between her legs, where my hand still lingered, was a powderpuff of blonde hair, smooth as down. Her body was wrapped in shadows like moth-wings, like rose-petals. There was something desperately attractive about her as she sat there she was like the prize you know you'll never win at the carny shooting gallery or the county fair ringtoss. The one they keep on the top shelf. She reached under the sheet and folded her fingers over the stretched material of my undershorts. Everything's all right, it ain't nuthin but a round-and-round, said the UFO voice as I climbed the steps to my wife's studio. I stooped, fished for the key from beneath the mat, and took it out. I climbed the ladder to the float, wet and dripping, preceded by my engorged sex is there anything, I wonder, so unintentionally comic as a sexually aroused man? Jo stood on the boards in her wet bathing suit. I pulled Mattie into bed with me. I opened the door to Jo's studio. All of these things happened at the same time, weaving in and out of each other like strands of some exotic rope or belt. The thing with Jo felt the most like a dream, the thing in the studio, me crossing the floor and looking down at my old green IBM, the least. Mattie in the north bedroom was somewhere in between. On the float Jo said, ‘Do what you want.' In the north bedroom Mattie said, ‘Do what you want.' In the studio, no one had to tell me anything. In there I knew exactly what I wanted. On the float I bent my head and put my mouth on one of Jo's breasts and sucked the cloth-covered nipple into my mouth. I tasted damp fabric and dank lake. She reached for me where I stuck out and I slapped her hand away. If she touched me I would come at once. I sucked, drinking back trickles of cotton-water, groping with my own hands, first caressing her ass and then yanking down the bottom half of her suit. I got it off her and she dropped to her knees. I did too, finally getting rid of my wet, clinging underpants and tossing them on top of her bikini panty. We faced each other that way, me naked, her almost. ‘Who was the guy at the game?' I panted. ‘Who was he, Jo?' ‘No one in particular, Irish. Just another bag of bones.' She laughed, then leaned back on her haunches and stared at me. Her navel was a tiny black cup. There was something queerly, attractively snakelike in her posture. ‘Everything down there is death,' she said, and pressed her cold palms and white, pruney fingers to my cheeks. She turned my head and then bent it so I was looking into the lake. Under the water I saw decomposing bodies slipping by, pulled by some deep current. Their wet eyes stared. Their fish-nibbled noses gaped. Their tongues lolled between white lips like tendrils of waterweed. Some of the dead trailed pallid balloons of jellyfish guts; some were little more than bone. Yet not even the sight of this floating charnel parade could divert me from what I wanted. I shrugged my head free of her hands, pushed her down on the boards, and finally cooled what was so hard and contentious, sinking it deep. Her moon-silvered eyes stared up at me, through me, and I saw that one pupil was larger than the other. That was how her eyes had looked on the TV monitor when I had identified her in the Derry County Morgue. She was dead. My wife was dead and I was fucking her corpse. Nor could even that realization stop me. ‘Who was he?' I cried at her, covering her cold flesh as it lay on the wet boards. ‘Who was he, Jo, for Christ's sake tell me who he was!' In the north bedroom I pulled Mattie on top of me, relishing the feel of those small breasts against my chest and the length of her entwining legs. Then I rolled her over on the far side of the bed. I felt her hand reaching for me, and slapped it away if she touched me where she meant to touch me, I would come in an instant. ‘Spread your legs, hurry,' I said, and she did. I closed my eyes, shutting out all other sensory input in favor of this. I pressed forward, then stopped. I made one little adjustment, pushing at my engorged penis with the side of my hand, then rolled my hips and slipped into her like a finger in a silk-lined glove. She looked up at me, wide-eyed, then put a hand on my cheek and turned my head. ‘Everything out there is death,' she said, as if only explaining the obvious. In the window I saw Fifth Avenue between Fiftieth and Sixtieth all those trendy shops, Bijan and Bally, Tiffany and Bergdorf's and Steuben Glass. And here came Harold Oblowski, north bound and swinging his pigskin briefcase (the one Jo and I had given him for Christmas the year before she died). Beside him, carrying a Barnes and Noble bag by the handles, was the bountiful, beauteous Nola, his secretary. Except her bounty was gone. This was a grinning, yellow-jawed skeleton in a Donna Karan suit and alligator pumps; scrawny, beringed bones instead of fingers gripped the bag-handles. Harold's teeth jutted in his usual agent's grin, now extended to the point of obscenity. His favorite suit, the doublebreasted charcoal-gray from Paul Stuart, flapped on him like a sail in a fresh breeze. All around them, on both sides of the street, walked the living dead mommy mummies leading baby corpses by the hands or wheeling them in expensive prams, zombie doormen, reanimated skateboarders. Here a tall black man with a last few strips of flesh hanging from his face like cured deer-hide walked his skeletal Alsatian. The cab-drivers were rotting to raga music. The faces looking down from the passing buses were skulls, each wearing its own version of Harold's grin Hey, how are ya, how's the wife, how's the kids, writing any good books lately? The peanut vendors were putrefying. Yet none of it could quench me. I was on fire. I slipped my hands under her buttocks, lifting her, biting at the sheet (the pattern, I saw with no surprise, was blue roses) until I pulled it free of the mattress to keep from biting her on the neck, the shoulder, the breasts, anywhere my teeth could reach. ‘Tell me who he was!' I shouted at her. ‘You know, I know you do!' My voice was so muffled by my mouthful of bed-linen that I doubted if anyone but me could have understood it. ‘Tell me, you bitch!' On the path between Jo's studio and the house I stood in the dark with the typewriter in my arms and that dream-spanning erection quivering below its metal bulk all that ready and nothing willing. Except maybe for the night breeze. Then I became aware I was no longer alone. The shroud-thing was behind me, called like the moths to the party lights. It laughed-a brazen, smoke-broken laugh that could belong to only one woman. I didn't see the hand that reached around my hip to grip me the typewriter was in the way but I didn't need to see it to know its color was brown. It squeezed, slowly tightening, the fingers wriggling. ‘What do you want to know, sugar?' she asked from behind me. Still laughing. Still teasing. ‘Do you really want to know at all? Do you want to know or do you want to feel?' ‘Oh, you're killing me!' I cried. The typewriter thirty or so pounds of IBM Selectric was shaking back and forth in my arms. I could feel my muscles twanging like guitar strings. ‘Do you want to know who he was, sugar? That nasty man?' ‘Just do me, you bitch!' I screamed. She laughed again that harsh laughter that was almost like a cough and squeezed me where the squeezing was best. ‘You hold still, now,' she said. ‘You hold still, pretty boy, ‘less you want me to take fright and yank this thing of yours right out by the . . . ‘ I lost the rest as the whole world exploded in an orgasm so deep and strong that I thought it would simply tear me apart. I snapped my head back like a man being hung and ejaculated looking up at the stars. I screamed I had to and on the lake, two loons screamed back. At the same time I was on the float. Jo was gone, but I could faintly hear the sound of the band -Sara and Sonny and the Red-Top Boys tearing through ‘Black Mountain Rag.' I sat up, dazed and spent, fucked hollow. I couldn't see the path leading up to the house, but I could discern its switchback course by the Japanese lanterns. My underpants lay beside me in a little wet heap. I picked them up and started to put them on, only because I didn't want to swim back to shore with them in my hand. I stopped with them stretched between my knees, looking at my fingers. They were slimed with decaying flesh. Puffing out from beneath several of the nails were clumps of torn-out hair. Corpsehair. ‘Oh Jesus,' I moaned. The strength went out of me. I flopped into wetness. I was in the north-wing bedroom. What I had landed in was hot, and at first I thought it was come. The dim glow of the nightlight showed darker stuff, however. Mattie was gone and the bed was full of blood. Lying in the middle of that soaking pool was something I at first glance took to be a clump of flesh or a piece of organ. I looked more closely and saw it was a stuffed animal, a black-furred object matted red with blood. I lay on my side looking at it, wanting to bolt out of the bed and flee from the room but unable to do it. My muscles were in a dead swoon. Who had I really been having sex with in this bed? And what had I done to her? In God's name, what? ‘I don't believe these lies,' I heard myself say, and as though it were an incantation, I was slapped back together. That isn't exactly what happened, bur it's the only way of saying that seems to come close to whatever did. There were three of me one on the float, one in the north bedroom, one on the path and each one felt that hard slap, as if the wind had grown a fist. There was rushing blackness, and in it the steady silver shaking of Bunter's bell. Then it faded, and I faded with it. For a little while I was nowhere at all. I came back to the casual chatter of birds on summer vacation and to that peculiar red darkness that means the sun is shining through your closed eyelids. My neck was stiff, my head was canted at a weird angle, my legs were folded awkwardly beneath me, and I was hot. I lifted my head with a wince, knowing even as I opened my eyes that I was no longer in bed, no longer on the swimming float, no longer on the path between the house and the studio. It was floorboards under me, hard and uncompromising. The light was dazzling. I squinched my eyes closed again and groaned like a man with a hangover. I eased them back open behind my cupped hands, gave them time to adjust, then cautiously uncovered them, sat all the way up, and looked around. I was in the upstairs hall, lying under the broken air conditioner. Mrs. Meserve's note still hung from it. Sitting outside my office door was the green IBM with a piece of paper rolled into it. I looked down at my feet and saw that they were dirty. Pine needles were stuck to my soles, and one toe was scratched. I got up, staggered a little (my right leg had gone to sleep), then braced a hand against the wall and stood steady. I looked down at myself. I was wearing the Jockeys I'd gone to bed in, and I didn't look as if I'd had an accident in them. I pulled out the waistband and peeked inside. My cock looked as it usually did; small and soft, curled up and asleep in its thatch of hair. If Noonan's Folly had been adventuring in the night, there was no sign of it now. ‘It sure felt like an adventure,' I croaked. I armed sweat off my forehead. It was stifling up here. ‘Not the kind I ever read about in The Hardy Boys, though.' Then I remembered the blood-soaked sheet in the north bedroom, and the stuffed animal lying on its side in the middle of it. There was no sense of relief attached to the memory, that thank-God-it-was-only-a-dream feeling you get after a particularly nasty nightmare. It felt as real as any of the things I'd experienced in my measles fever-delirium . . . and all those things had been real, just distorted by my overheated brain. I staggered to the stairs and limped down them, holding tight to the bannister in case my tingling leg should buckle. At the foot I looked dazedly around the living room, as if seeing it for the first time, and then limped down the north-wing corridor. The bedroom door was ajar and for a moment I couldn't bring myself to push it all the way open and go in. I was very badly scared, and my mind kept trying to replay an old episode of Alfred Hitchcock Presents, the one about the man who strangles his wife during an alcoholic blackout. He spends the whole half hour looking for her, and finally finds her in the pantry, bloated and open-eyed. Kyra Devore was the only kid of stuffed-animal age I'd met recently, but she had been sleeping peacefully under her cabbage-rose coverlet when I left her mother and headed home. It was stupid to think I had driven all the way back to Wasp Hill Road, probably wearing nothing but my Jockeys, that I had What? Raped the woman? Brought the child here? In my sleep? I got the typewriter, in my sleep, didn't I? It's sitting right upstairs in the goddam hallway. Big difference between going thirty yards through the woods and five miles down the road to I wasn't going to stand out here listening to those quarrelling voices in my head. If I wasn't crazy and I didn't think I was listening to those contentious assholes would probably send me there, and by the express. I reached out and pushed the bedroom door open. For a moment I actually saw a spreading octopus-pattern of blood soaking into the sheet, that's how real and focused my terror was. Then I closed my eyes tight, opened them, and looked again. The sheets were rumpled, the bottom one mostly pulled free. I could see the quilted satin hide of the mattress. One pillow lay on the far edge of the bed. The other was scrunched down at the foot. The throw rug a piece of Jo's work was askew, and my water-glass lay overturned on the nighttable. The bedroom looked as if it might have been the site of a brawl or an orgy, but not a murder. There was no blood and no little stuffed animal with black fur. I dropped to my knees and looked under the bed. Nothing there not even dust-kitties, thanks to Brenda Meserve. I looked at the ground-sheet again, first passing a hand over its rumpled topography, then pulling it back down and resecuring the elasticized corners. Great invention, those sheets; if women gave out the Medal of Freedom instead of a bunch of white politicians who never made a bed or washed a load of clothes in their lives, the guy who thought up fitted sheets would undoubtedly have gotten a piece of that tin by now. In a Rose Garden ceremony. With the sheet pulled taut, I looked again. No blood, not a single drop. There was no stiffening patch of semen, either. The former I hadn't really expected (or so I was already telling myself), but what about the latter? At the very least, I'd had the world's most creative wet-dream a triptych in which I had screwed two women and gotten a handjob from a third, all at the same time. I thought I had that morning-after feeling, too, the one you get when the previous night's sex has been of the headbusting variety. But if there had been fireworks, where was the burnt gunpowder? ‘In Jo's studio, most likely,' I told the empty, sunny room. ‘Or on the path between here and there. Just be glad you didn't leave it in Mattie Devore, bucko. An affair with a post-adolescent widow you don't need.' A part of me disagreed; a part of me thought Mattie Devore was exactly what I did need. But I hadn't had sex with her last night, any more than I had had sex with my dead wife out on the swimming float or gotten a handjob from Sara Tidwell. Now that I saw I hadn't killed a nice little kid either, my thoughts turned back to the typewriter. Why had I gotten it? Why bother? Oh man. What a silly question. My wife might have been keeping secrets from me, maybe even having an affair; there might be ghosts in the house; there might be a rich old man half a mile south who wanted to put a sharp stick into me and then break it off; there might be a few toys in my own humble attic, for that matter. But as I stood there in a bright shaft of sunlight, looking at my shadow on the far wall, only one thought seemed to matter: I had gone out to my wife's studio and gotten my old typewriter, and there was only one reason to do something like that. I went into the bathroom, wanting to get rid of the sweat on my body and the dirt on my feet before doing anything else. I reached for the shower-handle, then stopped. The tub was full of water. Either I had for some reason filled it during my sleepwalk . . . or something else had. I reached for the drain-lever, then stopped again, remembering that moment on the shoulder of Route 68 when my mouth had filled up with the taste of cold water. I realized I was waiting for it to happen again. When it didn't, I opened the bathtub drain to let out the standing water and started the shower. I could have brought the Selectric downstairs, perhaps even lugged it out onto the deck where there was a little breeze coming over the surface of the lake, but I didn't. I had brought it all the way to the door of my office, and my office was where I'd work . . . if I could work. I'd work in there even if the temperature beneath the roofpeak built to a hundred and twenty degrees . . . which, by three in the afternoon, it just might. The paper rolled into the machine was an old pink-carbon receipt from Click!, the photo shop in Castle Rock where Jo had bought her supplies when we were down here. I'd put it in so that the blank side faced the Courier type-ball. On it I had typed the names of my little harem, as if I had tried in some struggling way to report on my three-faceted dream even while it was going on: Jo Sara Mattie Jo Sara Mattie Mattie Mattie Sara Sara Jo Johanna Sara Jo MattieSaraJo. Below this, in lower case: normal sperm count sperm norm all's rosy I opened the office door, carried the typewriter in, and put it in its old place beneath the poster of Richard Nixon. I pulled the pink slip out of the roller, balled it up, and tossed it into the wastebasket. Then I picked up the Selectric's plug and stuck it in the baseboard socket. My heart was beating hard and fast, the way it had when I was thirteen and climbing the ladder to the high board at the Y-pool. I had climbed that ladder three times when I was twelve and then slunk back down it again; once I turned thirteen, there could be no chickening out I really had to do it. I thought I'd seen a fan hiding in the far corner of the closet, behind the box marked GADGETS. I started in that direction, then turned around again with a ragged little laugh. I'd had moments of confidence before, hadn't I? Yes. And then the iron bands had clamped around my chest. It would be stupid to get out the fan and then discover I had no business in this room after all. ‘Take it easy,' I said, ‘take it easy.' But I couldn't, no more than that narrow-chested boy in the ridiculous purple bathing suit had been able to take it easy when he walked to the end of the diving board, the pool so green below him, the upraised faces of the boys and girls in it so small, so small. I bent to one of the drawers on the right side of the desk and pulled so hard it came all the way out. I got my bare foot out of its landing zone just in time and barked a gust of loud, humorless laughter. There was half a ream of paper in the drawer. The edges had that faintly crispy look paper gets when it's been sitting for a long time. I no more than saw it before remembering I had brought my own supply stuff a good deal fresher than this. I left it where it was and put the drawer back in its hole. It took several tries to get it on its tracks; my hands were shaking. At last I sat down in my desk chair, hearing the same old creaks as it took my weight and the same old rumble of the casters as I rolled it forward, snugging my legs into the kneehole. Then I sat facing the keyboard, sweating hard, still remembering the high board at the Y, how springy it had been under my bare feet as I walked its length, remembering the echoing quality of the voices below me, remembering the smell of chlorine and the steady low throb of the air-exchangers: fwung-fwung-fwung-fwung, as if the water had its own secret heartbeat. I had stood at the end of the board wondering (and not for the first time!) if you could be paralyzed if you hit the water wrong. Probably not, but you could die of fear. There were documented cases of that in Ripley's Believe It or Not, which served me as science between the ages of eight and fourteen. Go on! Jo's voice cried. My version of her voice was usually calm and collected; this time it was shrill. Stop dithering and go on! I reached for the IBM's rocker-switch, now remembering the day I had dropped my Word Six program into the Powerbook's trash. Goodbye, old pal, I had thought. ‘Please let this work,' I said. ‘Please.' I lowered my hand and flicked the switch. The machine came on. The Courier ball did a preliminary twirl, like a ballet dancer standing in the wings, waiting to go on. I picked up a piece of paper, saw my sweaty fingers were leaving marks, and didn't care. I rolled it into the machine, centered it, then wrote Chapter One and waited for the storm to break.