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GCSE Science/Static Electricity. GCSE Science/Electricity Have you ever noticed a crackle when you pull off a sweater? Have you ever had your hair stick to your face after combing? What about seeing a balloon stick to the wall after it has been rubbed? All these effects are caused by static electricity. Static electricity is the imbalanced charges of matter. It was the Greeks who first noticed that when they rubbed a piece of amber, it attracted small pieces of paper. The Greek word for amber is elektron, and it is from this that we get our words electron and electricity. What causes static electricity? Usually materials are electrically neutral. This means that they are "not" electrically charged. However this doesn't mean that materials have no charges "inside" them. All materials are made of atoms. Atoms are made of particles called electrons, protons, and neutrons. Electrons have a negative charge, protons have a positive charge, and neutrons (as you can probably guess by the name) have no charge. Materials are partly made of charged particles. Materials have no overall charge whenever they have the same number of electrons and protons. The negative charge of the electrons exactly cancels out the positive charge of the protons. Test YourSelf: Q1) The element lithium has three protons. How many electrons must a neutral lithium atom have? Inside an atom the protons and neutrons are held firmly at the very centre in a structure called the nucleus. The electrons however are held much more loosely. Some can be found at the surface, and if the surface is rubbed, they can be rubbed away. This removal of electrons will leave the atom with more protons than electrons. It will have a positive charge because the protons are positively charged. Atoms that are charged are called ions. When you rub a balloon on your sweater some of the electrons are transferred from the sweater to the balloon. The sweater becomes positively charged. Test YourSelf: Q2) What charge will the balloon have? How do the two types of charge behave? The sweater is positively charged, the balloon negative. The balloon sticks to the sweater. This is because unlike charges attract. If you were to take two balloons, both of which had been negatively charged and brought them together you would find that they tried to push apart. This is because like charges repel. Test Yourself Q3) Look at the balloons above. The pair on the left are being repelled. The pair on the right are being attracted. Notice that one out of each pair of balloons is negatively charged. What is the sign (positive or negative) of the charges on the other two balloons? Sparks can fly! When a large enough charge is built up sparks can fly. A spark is just a flow of electrons through the air. This can sometimes be very dangerous. For example, petrol flowing through a pipeline can pick up a charge by friction. If a spark flies it could ignite the petrol. For this reason, pipes are earthed. Earthing means connecting the pipe to the ground by means of a copper wire. Copper, unlike air, is a very good conductor of electricity. The electrons can flow easily and safely to the ground without sparking. Some devices make use of sparks. A Van de Graaf generator consists of a large metal dome that is in contact with a rubber or plastic looped belt. As the belt moves, friction causes it to become charged; the charge is spread out over the metal dome where it builds up until it is large enough to cause a spark. In the diagram above a girl is standing on a washing up bowl and touching a Van de Graaf machine. Test Yourself Q4) What do you think is the purpose of the washing up bowl? Test Yourself Q5) Explain why the girl's hair is standing on end (no it's not her style, it's to do with the charge) Answers to questions | « Electricity | Uses of static electricity »

GCSE Science/Answers-Static Electricity. Back to GCSE Science/Static Electricity Q1) 3 --- all atoms have the same number of protons as electrons Q2) Negative --- electrons have been added to the balloon. Q3 left hand pair) Negative--- The balloons are repelled Q3 right hand pair)Positive --- The balloons are attracted. Remember '"like charges repel, unlike charges attract Q4) The purpose of the washing up bowl is to insulate the girl from the ground. People are reasonable conductors of electricity. If the girl just stood on the floor electricity would run through her body and leak away. She would act as an earth wire for the Van de Graaf. Q5) The girl's hairs all pick up static electricity from the Van de Graaf machine. Remember like charges repel, so each hair tries to get as far away from the other hairs as possible. That is why her hair stands on end.

GCSE Science/Uses of static electricity. GCSE Science/Electricity There are several practical uses of static electricity in our daily life. We will look at three of them on this page. There are many, many more, but these are the easiest to understand. Let’s take a look at them. Number One: The Photocopier. One example of the practical use of static electricity is a photocopier. A photocopier is a complicated piece of equipment, but the basic principle of how it works is fairly simple. The best way to understand what is going on is to consider it as a stage by stage process. Relates to xerography Stage one. Positive charge is applied onto a plate from a high voltage power supply which is called charging by friction. The plate is connected to the earth but the charge does not have quite enough energy to flow away from it. (The plate is not a good conductor of electricity.) Stage two. Paper is placed over the plate and a light shines onto the paper. Where the paper is white the light is reflected onto the plate. Where the paper is dark a shadow falls onto the plate. The light falling on the plate gives it just the extra energy needed to allow the charge to escape to earth. The plate becomes neutral where the paper is white but keeps its charge where the paper is black. The plate is now a copy of the paper with charges taking the place of ink. You could call this a template. Stage three. Toner particles are sprayed through a negatively charged nozzle onto the plate. As the toner passes through the nozzle it picks up the charge so that each particle of toner becomes negatively charged. The now charged toner is attracted to the areas of positive charge because opposite charges attract. More light then allows the positive charge to escape (However the negative charge on the toner remains.) Stage four. A sheet of paper is given a very strong positive charge, and then placed in contact with the plate. The paper attracts the toner. The paper is then removed from the plate and passed through a heating unit. The heat melts the toner and bonds it to the paper. In a real photocopier, there is no plate, just a large drum. As the drum rotates its surface goes through stages one through four. At the end of the sequence a scraper removes any toner left on the drum and the whole process is repeated with a new image. A good photocopier is capable of producing 20 duplicate pages per minute (20ppm), which is approximately one page every three seconds. Questions on Photocopiers. Q1) If the black areas of the image leave a positive charge in the plate what charge do the white areas of the image leave? ("Be very careful, the answer may not be what you think!") Q2) How does the light shining onto the charged plate allow it to lose its charge? Q3) Why is the toner given a negative charge? Q4) Why does the paper attract the toner? Other uses of static electricity. Number Two: Spray painting car parts. When paint is sprayed from a paint gun, the painter normally needs to use a fair amount of skill to ensure the paint goes on evenly. By connecting the spray nozzle to a negative electrode, it is possible to charge each droplet of paint. If the car part is then given the opposite charge, the paint droplets will be attracted to the car body part. This has several advantages: Questions. Q1) If the paint droplets are given a positive charge, what charge should the car part be given? A1) A negative charge as the positive will always be looking for a negative to balance it out. Q2) Why does less paint fall on the floor? Give reasons for your answer A2) This is because the oppositely charged particles are naturally attracted to each other and depending on the strength of the charge the range of attraction will increase/decrease respectively. Q3) In the application of painting cars, wouldn't negatively charging the spray source and positively charging the object being sprayed also attract dust, dirt, and trash too? Number Three: Pollution Control. Static electricity is used in pollution control by applying a static charge to dirt particles in the air and then collecting those charged particles on a plate or collector of the opposite electrical charge. Such devices are often called electrostatic precipitators. Out of the three this is the one people will know it most for. Factories use static electricity to reduce pollution coming from their smoke stacks. They give the smoke an electric charge. When it passes by electrodes of the opposite charge, most of the smoke particles cling to the electrodes. This keeps the pollution from going out into the atmosphere. Answers | «Static Electricity | Advanced topics»

Discrete Mathematics/Graph theory. Introduction. A "graph" is a mathematical way of representing the concept of a "network". A network has points, connected by lines. In a graph, we have special names for these. We call these points "vertices" (sometimes also called nodes), and the lines, "edges". Here is an example graph. The edges are red, the vertices, black. In the graph, formula_1 are vertices, and formula_2 are edges. Definitions of graph. There are several roughly equivalent definitions of a graph. Set theory is frequently used to define graphs. Most commonly, a graph formula_3 is defined as an ordered pair formula_4, where formula_5 is called the graph's vertex-set and formula_6 is called the graph's edge-set. Given a graph formula_3, we often denote the vertex—set by formula_8 and the edge—set by formula_9. To visualize a graph as described above, we draw formula_10 dots corresponding to vertices formula_11. Then, for all formula_12 we draw a line between the dots corresponding to vertices formula_13 if and only if there exists an edge formula_14. Note that the placement of the dots is generally unimportant; many different pictures can represent the same graph. Alternately, using the graph above as a guide, we can define a graph as an ordered triple formula_15: In the above example, If formula_20 is not injective — that is, if formula_21 such that formula_22 — then we say that formula_3 is a multigraph and we call any such edges formula_24 "multiple edges". Further, we call edges formula_25 such that formula_26 loops. Graphs without multiple edges or loops are known as simple graphs. Graphs can, conceivably, be infinite as well, and thus we place no bounds on the sets V and E. We will not look at infinite graphs here. Directions, Weights, and Flows. We define a directed graph as a graph such that formula_20 maps into the set of ordered pairs formula_28 rather than into the family of two-element sets formula_29. We can think of an edge formula_17 such that formula_31 as 'pointing' from formula_32 to formula_33. As such we would say that formula_32 is the "tail" of edge formula_35 and that formula_33 is the "head". This is one of the vagaries of graph theory notation, though. We could just as easily think of formula_32 as the head and formula_33 as the tail. To represent a directed graph, we can draw a picture as described and shown above, but place arrows on every edge corresponding to its direction. In general, a weight on a graph formula_3 is some function formula_40. A flow formula_41 is a directed graph formula_15 paired with a weight function such that the weight "going into" any vertex is the same amount as the weight "going out" of that vertex. To make this more formal, define sets Then, formally stated, our requirement on the weight function is formula_45 Algebraic Graph Theory. While set theory is frequently used when discussing graphs, other approaches can simplify certain operations. A set can be defined using an adjacency matrix formula_46 where element formula_47 is a 1, if there is an edge between vertex i and vertex j and 0 otherwise. Special Graphs. Some graphs occur frequently enough in graph theory that they deserve special mention. One such graphs is the "complete graph" on n vertices, often denoted by Kn. This graph consists of n vertices, with each vertex connected to every other vertex, and every pair of vertices joined by exactly one edge. Another such graph is the "cycle graph" on "n" vertices, for "n" at least 3. This graph is denoted C"n" and defined by V := {1,2..,n} and E := . Even easier is the "null graph" on "n" vertices, denoted N"n"; it has "n" vertices and no edges! Note that N1 = K1 and C3 = K3. Some Terms. Two vertices are said to be "adjacent" if there is an edge joining them. The word "incident" has two meanings: Two graphs "G" and "H" are said to be "isomorphic" if there is a one-to-one function from (or, if you prefer, one-to-one correspondence between) the vertex set of "G" to the vertex set of "H" such that two vertices in "G" are adjacent if and only if their images in "H" are adjacent. (Technically, the multiplicity of the edges must also be preserved, but our definition suffices for simple graphs.) Subgraphs. A "subgraph" is a concept akin to the subset. A subgraph has a subset of the vertex set V, a subset of the edge set E, and each edge's endpoints in the larger graph has the same edges in the subgraph. A A subgraph formula_48 of formula_3 is "generated" by the vertices {formula_50}formula_51 if the edge set of formula_48 consists of all edges in the edge set of formula_3 that joins the vertices in formula_54{formula_55}. A "path" is a sequence of edges formula_56 such that ei is adjacent to ei+1 for all i from 1 to N-1. Two vertices are said to be connected if there is a path connecting them. Trees and Bipartite Graphs. A "tree" is a graph that is (i) connected, and (ii) has no cycles. Equivalently, a tree is a connected graph with exactly formula_57 edges, where there are formula_10 nodes in the tree. A "Bipartite graph" is a graph whose nodes can be partitioned into two disjoint sets U and W such that every edge in the graph is incident to one node in U and one node in W. A tree is a bipartite graph. A "complete bipartite graph" is a bipartite graph in which each node in U is connected to every node in W; a complete bipartite graph in which U has formula_10 vertices and V has formula_60 vertices is denoted formula_61. Adjacent,Incident,End Vertices Self loops,Parallel edges,Degree of Vertex Pendant Vertex : Vertex Degree one "Pendant Vertex" Isolated Vertex : Vertex Degree zero "Isolated Vertex" Hamiltonian and Eulerian Paths. Hamiltonian Cycles: A Hamiltonian Cycle received its name from Sir William Hamilton who first studied the travelling salesman problem. A Hamiltonian cycle is a path that visits every vertex once and only once i.e. it is a walk, in which no edge is repeated (a trail) and therefore a trail in which no vertex is repeated (a path). Note also it is a cycle, the last vertex is joined to the first. A graph is said to be Eulerian if it is possible to traverse each edge once and only once, i.e. it has no odd vertices or it has an even number of odd vertices (semi-Eulerian). This has implications for the Königsberg problem. It may be easier to imagine this as if it is possible to trace the edges of a graph with a pencil without lifting the pencil off the paper or going over any lines. Planar Graphs. A "planar graph" is an undirected graph that can be drawn on the plane or on a sphere in such a way that no two edges cross, where an edge formula_62 is drawn as a continuous curve (it need not be a straight line) from u to v. Kuratowski proved a remarkable fact about planar graphs: A graph is planar if and only if it does not contain a subgraph homeomorphic to formula_63 or to formula_64. (Two graphs are said to be homeomorphic if we can shrink some components of each into single nodes and end up with identical graphs. Informally, this means that non-planar-ness is caused by only two things—namely, having the structure of formula_63 or formula_64 within the graph). Coloring Graphs. A graph is said to be planar if it can be drawn on a plane in such way that no edges cross one another except of course for meeting at vertices Each term, the Schedules Office in some university must assign a time slot for each final exam. This is not easy, because some students are taking several classes with finals, and a student can take only one test during a particular time slot. The Schedules Office wants to avoid all conflicts, but to make the exam period as short as possible. We can recast this scheduling problem as a question about coloring the vertices of a graph. Create a vertex for each course with a final exam. Put an edge between two vertices if some student is taking both courses. For example, the scheduling graph might look like this: Next, identify each time slot with a color. For example, Monday morning is red, Monday afternoon is blue, Tuesday morning is green, etc. Assigning an exam to a time slot is now equivalent to coloring the corresponding vertex. The main constraint is that adjacent vertices must get different colors; otherwise, some student has two exams at the same time. Furthermore, in order to keep the exam period short, we should try to color all the vertices using as few different colors as possible. For our example graph, three colors suffice: red, green, blue. The coloring corresponds to giving one final on Monday morning (red), two Monday afternoon (blue), and two Tuesday morning (green)... K Coloring. Many other resource allocation problems boil down to coloring some graph. In general, a graph G is kcolorable if each vertex can be assigned one of k colors so that adjacent vertices get different colors. The smallest sufficient number of colors is called the chromatic number of G. The chromatic number of a graph is generally difficult to compute, but the following theorem provides an upper bound: Theorem 1. A graph with maximum degree at most k is (k + 1)colorable. Proof. We use induction on the number of vertices in the graph, which we denote by n. Let P(n) be the proposition that an nvertex graph with maximum degree at most k is (k + 1)colorable. A 1 vertex graph has maximum degree 0 and is 1colorable, so P(1) is true. Now assume that P(n) is true, and let G be an (n + 1)vertex graph with maximum degree at most k. Remove a vertex v, leaving an nvertex graph G . The maximum degree of G is at most k, and so G is (k + 1)colorable by our assumption P(n). Now add back vertex v. We can assign v a color different from all adjacent vertices, since v has degree at most k and k + 1 colors are available. Therefore, G is (k + 1)colorable. The theorem follows by induction. Weighted Graphs. A weighted graph associates a label (weight) with every edge in the graph. Weights are usually real numbers, and often represent a "cost" associated with the edge, either in terms of the entity that is being modeled, or an optimization problem that is being solved.

Computer Programming/Linux Programming. About the platform. The GNU operating system was started by Richard Stallman as a free replacement for the UNIX operating system. At the same time Linus Torvalds was working on a kernel, which he adapted to fit the GNU operating system. As time progressed, many applications from UNIX and DOS were ported to GNU/Linux as well as the thousands of new applications written for it. GNU/Linux has become a completely self-sufficient operating system with applications ranging from the many console applications to the numerous highly advanced GUI applications (many of which are based on lower level console applications) and everything else in between. The most popular languages for use on the GNU/Linux platform include C/C++ and , however the range of programming languages supported by the GNU/Linux platform cover the entire spectrum of the software development world. Other popular languages are Perl, Python and Ruby. Shell scripting is often used for administrative tasks but cannot be called a complete high level language. Basic information. Most UNIX code is instantly portable to GNU/Linux systems - it can be compiled as on a UNIX system. GNU/Linux programming tools are mostly from the GNU project at http://www.gnu.org, including gcc (free C/C++ compiler), and equivalents of make, ld, as, etc. Numerous others are available for various languages, including java.

Spanish/Exercises/Stem Changing Verbs. ^Lesson 4^ Fill in the blank. Please fill in the blank with the correct form of the verb: 1. Yo ____________________ (cerrar) la puerta. "I close the door." 2. Tú _______________________ (perder) tus llaves. "You lost your keys." 3. ¿_________________________(preferir) usted la langosta? "Do you prefer lobster?" 4. Nosotros _______________________ (entender) los ejercicios. "We understand the exercises." 5. Felipe y Juan ______________________(empezar) las prácticas de gramática. "Felipe and Juan begin the grammar practices." 6. Ellos ____________________ (querer) almorzar. "They want to eat lunch." 7. La chica _____________________ (perder) su pañuelo. "The girl loses her handkerchief." 8. ¿Qué ______________________ (pensar)? "What do you -singular- think?" 9. Sofía _______________________ (entender) a Julio. "Sofía understands Julio." 10. Yo no ______________________ (querer) la ensalada. "I don't want the salad" Bonus: Argentinian voseo 2. Vos _____________________ (perder) tus llaves. "You lose your keys." 8. ¿Qué ______________________ (pensar)? "What do you -singular- think?" Soluciones a los ejercicios "Solutions to the exercises" ^Lesson 4^

Biochemistry/Metabolism and energy. « Catalysis | pKa values » Metabolism. Anabolism and catabolism. Metabolism (Fig. 1) is, broadly speaking, the conversion of food into energy, cell components, and waste products. <br> Figure 1: Overview of metabolism The above diagram shows the different parts of metabolism: Catabolic reactions release energy and are therefore exergonic, while anabolic reactions use up energy and are therefore endergonic. High-energy phosphates. Due to the large variety of food compounds, and the large number of biochemical reactions which need energy in anabolism, it would be quite inefficient to couple a specific anabolic reaction to a specific energy source in catabolism. Instead, the cell uses an intermediate compound, a kind of universal energy currency. This intermediate is called "high-energy phosphate". But when is a phosphate group called "high-energy", and how does it differ from a "low-energy" phosphate? A giveaway is the ΔG0' of hydrolysis. Hydrolysis separates a phosphate from a compound by adding water:    O                      O R-OP-OH + H2O ⇌ R-OH + HO-P-OH    O                      O The ΔG0' of a low-energy (or "inorganic") phosphate group (called Pi) is 9-20 kJ mol-1, while the ΔG0' of a high-energy phosphate (denoted Ⓟ) is ~30 kJ mol-1. pKa value. Now what makes this Ⓟ so special? To explain this, we must take a little excourse into pH and pKa values. A phosphate group has between zero and three OH groups. This allows Ⓟ to exist in up to four different forms (0, 1, 2, and 3 OH groups, Fig. 2), depending on the pH value of the surrounding solution. A pKa value gives us the pH value at which 50% of the molecules are in one form (e.g., 1 OH group) and another (e.g., 2 OH groups). This is expressed by the "Henderson-Hasselbalch equation" : <br> Figure 2: The four possible forms of a phosphate group. pKa2 represents the conditions in the cell. Now to the promised difference between Ⓟ and PPi. The breaking of the ester bond of an ROⓅ releases more energy than the breaking of a PPi bond (Fig. 3), because of <br> Figure 3: Hydrolysis of Ⓟ and PPi. <br> Figure 4: Resonance stabilization of Pi. Resonance stabilization means that both OH and =O can "travel" around the phosphate. Of course, this is a crude analogy; they do not really move, the electrons are just "smeared" around the phosphate atom. This is also indicated by the use of the ↔ arrow, instead of ⇌; the three forms do not exist, they are just a way of writing down the chemical reality. As you can see in Fig. 3, the ΔG0' value for PPi⇌2Pi is ≪0, shifting the reaction strongly in favor of the 2Pi. Molecules using high-energy phosphates. Anhydride between phosphoric acid and carboxyl group. Hydrolysis : ΔG0' = -49.3 kJ mol-1<br> Guanidine phosphate. Hydrolysis : ΔG0' = -43.0 kJ mol-1<br> Enol phosphate. In the below picture, the final product should not have a carbon-carbon double bond, but a single bond with CH3 on the top. It is an error. Hydrolysis : ΔG0' = -61.9 kJ mol-1<br> ATP. Adenosine triphosphate contains one low-energy and two high-energy phosphate bonds:<br> <br> Low energy : ΔG0' = -14,2 kJ mol-1<br> High energy : ΔG0' = -30.5 kJ mol-1<br> Basically, any ATP-driven reaction is reversible, building ATP from ADP and Pi in the process. However, some ATP-driven reactions should never be reversed; these include nucleotide and protein synthesis. If these were reversed, the organism would disassemble its own DNA and proteins for energy, a rather unfortunate strategy. For reactions that should never be reversed, ATP can be broken down into AMP (adenosine monophosphate) and PPi, which in turn becomes 2×Pi. This reaction has a ΔG0' of -65,7 kJ mol-1, which is totally irreversible under "in vivo" conditions. It should be noted that AMP can not directly be converted to ATP again. Instead, the enzyme "AMP kinase" forms two ADP molecules from one ATP and one AMP. The resulting ADPs are then treated as described above. Non-covalent bonds. The destruction of covalent bonds takes up huge amounts of energy. The breakdown of an O2 molecule into two oxygen atoms needs ~460 kJ mol-1. Thus, nowhere in "living" biochemistry are covalent bonds actually destroyed; if one is broken, another one is created. This is where non-covalent bonds come in, they are weak enough to be broken down easily, and to form "bonds" again. For this reason, many biochemical functions are using so-called weak/secondary/non-covalent bonds. Weak bonds are created and destroyed much more easily than covalent ones. The typical range of energy needed to destroy such a weak bond is 4-30 kJ mol-1. Thus, the formation of weak bonds is energetically favorable, but these bonds are also easily broken by kinetic (thermal) energy (the normal movement of molecules). Biochemical interactions are often temporary (e.g., a substrate has to leave an enzyme quickly after being processed), for which the weakness of these bonds is essential. Also, biochemical specificity (e.g., enzyme-substrate-recognition) is achieved through weak bonds, utilizing two of their major properties: The link that follows demonstrates the type of non-covalent forces: There are three basic types of weak bonds, and a fourth "pseudo-bond": Ionic bonds. Ionic bonds are electrostatic attractions between permanently charged groups. Ionic bonds are not directed. Example: Hydrogen bonds. Hydrogen bonds are also established by electrostatic attraction. These attractions do not occur between permanently charged groups, but rather between atoms temporarily charged by a "dipole moment", resulting from the different electronegativity of atoms within a group. Hydrogen bonds are even weaker than ionic bonds, and they are highly directional, usually along a straight line. Besides being weaker than ionic bonds, hydrogen bonds are also weaker, and longer than similar covalent bonds. Hydrogen bonds are unique because they only exist when the Hydrogen is bonded to an oxygen (O), Nitrogen (N), or Fluorine (F), but the most common hydrogen bonds in biochemistry are: Hydrogen bonds equal an energy between 12-29 kJ mol, whereas covalent bonds are much higher. For example, the covalent bond between oxygen and hydrogen is about 492 KJ mol-1. Hydrogen Bonds and Water. Water has unique properties; after all, it is chosen to be the universal solvent. The unique properties of water are due to hydrogen bonding between all the oxygen and hydrogen atoms of the content. The hydrogen bonds occurring in water are about 2 angstroms apart from each other. Although hydrogen bonding is only about 5% as strong as covalent bond, they still cause water to have a high boiling point, and a high surface tension. The following link will take you to the structure of water and its Hydrogen Bonding. Van der Waals attractions. Van der Waals attractions are established between electron density-induced dipoles. They form when the outer electron shells of two atoms "almost" (but not quite) touch. The distance of the atoms is very important for these weak interactions. If the atoms are too far apart, the interactions are too weak to establish; if the atoms are too close to each other, their electron shells will repel each other. Van der Waals attractions are highly unspecific; they can occur between virtually any two atoms. Their energy is between 4-8 kJ mol-1. Hydrophobic interactions. Hydrophobic forces are not actually bonds, so this list has four items, but still just three bond types. In a way hydrophobic forces are the negation of the hydrogen bonds of a polar solute, usually water, enclosing a nonpolar molecule. For a polar solute like water, it is energetically unfavorable to "waste" a possible hydrogen bond by exposing it towards a nonpolar molecule. Thus, water will arrange itself around any nonpolar molecule in such a way that no hydrogen bonds point towards that molecule. This results in a higher order, compared to "freely" moving water, which leads to a lower entropy level and is thus energetically unfavorable. If there is more than one nonpolar molecule in the solute, it is favorable for the nonpolar molecules to aggregate in one place, reducing their surrounding, ordered "shell" of water to a minimal surface. Also, in large molecules, such as proteins, the hydrophobic (nonpolar) parts of the molecule will tend to turn towards the inside, while the polar parts will tend to turn towards the surface of the molecule. References. Cooke, Rosa-lee. "Properties of Water". Lecture 10. Mountain Empire Community College. n.d. Web. http://water.me.vccs.edu/courses/env211/lesson10_print.htm Kimball, John W.. "Hydrogen Bonds". Kimball’s Biology Pages. Feb. 12, 2011. Web. http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/H/Hbonds_water.gif Lower, Stephen. "States of matter: Water and hydrogen bonding". General Chemistry Virtual Textbooks. 2009. Aug. 26, 2010. Web. http://www.chem1.com/acad/webtext/states/water.html n.p. "Covalent vs. Non-Covalent Bonds". n.d. http://www.pearsonhighered.com/mathews/ch02/c02cv.htm W. W. Norton & Company. "Hydrogen Bonding in Water". Web. 2012. http://www.wwnorton.com/college/chemistry/gilbert2/tutorials/chapter_10/water_h_bond/ WyzAnt Tutoring. "WyzAnt Tutoring". Bonds. 2012. Web. http://www.wyzant.com/Help/Science/Chemistry/Bonds/ « Catalysis | pKa values »

Cell Biology/Lysosomes. Cell Biology | Parts of the cell | Organelles « Golgi apparatus | Lysosomes | Peroxisomes » Lysosomes. Membrane-bound sacs called lysosomes contain digestive enzymes that can break down such macromolecules as proteins, nucleic acids, and polysaccharides (Figure 6-23). Lysosomes have several functions. They fuse with incoming food vacuoles and expose the nutrients to enzymes that digest them, thereby nourishing the cell. Lysosomes also function like safety officers when they help destroy harmful bacteria. In certain cells—for example, your white blood cells—lysosomes release enzymes into vacuoles that contain trapped bacteria and break down the bacterial cell walls. Similarly, lysosomes serve as recycling centers for damaged organelles. Without harming the cell, a lysosome can engulf and digest another organelle. This makes molecules available for the construction of new organelles.The structures vary in size from 0.2 to 2 micrometers in diameter. The staining reveals a crystal like matrix in spherical vesicles. The crystalloid matrix is urate oxidase. These are small organelles containing around 40 enzymes for intercellular digestion. The lysosome membrane helps to protect the enzymes as much as it helps protect the cell. This is because the optimal pH for these enzymes is around a pH of 5. The membrane of the lysosome is again a lipid bilayer and is thought to have a ATP hydrolysis to pump H+ into the lysosome to maintain the pH. This also has another affect, that is free protons. Other small molecules can pass through the lysosome membrane, but will then become charged by picking up a free proton, then they are less likely to be able to leave the lysososome. A good reference on Lysosomes is at « Golgi apparatus | Lysosomes | Peroxisomes » Cell Biology | Parts of the cell Organelles

Cell Biology/Peroxisomes. Cell Biology | ../Parts of the cell/ | ../Organelles/ « Lysosomes | Peroxisomes | Cytosol » It used to be thought that peroxisomes are formed by the budding of smooth Endoplasmic Reticulum (ER). However, now it is thought that they form through self-assembly. (I will get more information references as I do some more thorough literature searches). The peroxisome is another major source of Oxygen utilization (along with the mitochondrion). There are specific proteins associated with the peroxisomes membrane, also there are 3 oxidation enzymes associated with peroxisomes: The enzyme contents vary with various types of cells. One of the main functions of peroxisomes in liver cells is detoxification. This is done by the oxidation of substances like: Why peroxisomes are not like lysosomes. Peroxisomes are organelles that contain oxidative enzymes, such as D-amino acid oxidase, urate oxidase, and catalase. They may resemble a lysosome, however, they are not formed in the Golgi complex. Peroxisomes are distinguished by a crystalline structure inside a sac which also contains amorphous gray material. They are self replicating, like the mitochondria. Components accumulate at a given site and they can be assembled into a peroxisome. They may look like storage granules, however, they are not formed in the same way as storage granules. Peroxisomes function to rid the body of toxic substances like hydrogen peroxide, or other metabolites. They are a major site of oxygen utilization and are numerous in the liver where toxic byproducts are going to accumulate. The peroxisome is made as a phospholipid bilayer, encapsulating oxidative materials. They would be 'sphere-ish' in shape, not necessarily a perfect sphere, and sometimes, they may take other shapes. But most electron micrographs I have seen (2 dimensions) show them as circles. (As you may be aware, the Cell membrane is also a phospholipid bilayer.) Peroxisomes have membrane proteins that are critical for peroxisomal function, to import proteins into their interiors, proliferate or segregate to daughter cells (This update, thanks to Babich Temps). The main differences would be: « Lysosomes | Peroxisomes | Cytosol » Cell Biology | ../Parts of the cell/ ../Organelles/

Cell Biology/Cytosol. Cell Biology | ../Parts of the cell/ | ../Organelles/ « Peroxisomes | Cytosol | Cytoskeleton and Microtubules » The cytosol (as opposed to cytoplasm, which also includes the organelles) is the internal fluid of the cell, and a large part of cell metabolism occurs here. Proteins within the cytosol play an important role in signal transduction pathways, glycolysis, and act as intracellular receptors and ribosomes. In prokaryotes, all chemical reactions take place in the cytosol. In eukaryotes, the cytosol contains the cell organelles. In plants, the amount of cytosol can be reduced due to the large tonoplast (central vacuole) that takes up most of the room of the cell. The cytosol is not a "soup" with free-floating particles, but highly organized on the molecular level. The cytosol also contains the cytoskeleton. It is made of fibrous proteins and (in many organisms) maintains the shape of the cell, anchors organelles, and controls internal movement of structures, e.g., transport vesicles. As the concentration of soluble molecules increases within the cytosol, an osmotic gradient builds up toward the outside of the cell. Water is flowing into the cell, making it larger. To prevent the cell from bursting apart, molecular pumps in the plasma membrane, the cytoskeleton, the tonoplast or a cell wall (if present) are used to counteract the osmotic pressure. « Peroxisomes | Cytosol | Cytoskeleton and Microtubules » Cell Biology | ../Parts of the cell/ | ../Organelles/

GCSE Science/Advanced static electricity topics. GCSE Science/Electricity Before reading this module check to see if you need to. If you intend to take the foundation paper, you may find that you do not need to do the work on this page. If in doubt check with your teacher. Where charge concentrates. When an object is charged up with electrons, the electrons try to spread out over the object to be as far apart as possible. This means they go to the surface rather than spread throughout. On a metal object the material of which the object is made shields the electrons from one another. They do not ‘’see’’ the electrons round the back. This means that highly curved objects can hold more electrons than flat objects. For a complicated shape, the electrons tend to congregate on the more highly curved areas, and to desert the flatter areas. Inducing charge separation on neutral objects. Consider a crystal of gold for example. {This argument works for all materials}. Normally the atoms are perfectly spherical, and completely neutral. Q1) Why are the atoms neutral? Remember that neutral atoms contain positive charges in the nucleus and negative electrons orbiting in their shell. Normally the center of the positive charges and the center of the negative electrons is in the same place: the exact center of the atom. If we bring up a charged object to them however, something important happens. Look at the diagram on the right. A charged rod is brought near the surface of the crystal. {Note: the rod is not shown, just the charges on it}. The electrons in the atoms try to get away from the negative charge because they are repelled. The positive charges in the nucleus try to get nearer to the negative rod because they are attracted to it. The result is the atom slightly changes shape. The center of the negative charges goes to the right of the center of the atom and the center of the positive charges goes to the left. We say there is a separation of charges Q2) What would happen if we brought up a positively charged rod? There is always an attractive force between the rod and the crystal no matter what the charge on the rod. To see why this is so, we need to know one more thing about electrostatics. The force of repulsion or attraction falls off with distance. In fact, rather like gravity it falls off as the "square" of the distance. This means if you go to twice the distance the force becomes only a quarter as much. If you go three times the distance it becomes only one ninth as great and so on. Now look at the diagram again. The negative charges in the atoms are repelled by the rod, the positive ones are attracted, but the positive charges are closer, so overall there is a force of attraction. Q3) Repeat the above argument with a positively charged rod to convince yourself that there is still an attractive force. Lightning. Lightning is basically a great big spark. In a thunderstorm, separation of charge occurs in big rain clouds. No one is really sure of "how" this occurs, although it appears to be caused by ice crystals rubbing together and becoming charged. but what "is" known is that storm clouds have a negative bottom and a positive top. The bottom of the cloud is nearer to the ground so it induces a positive charge on the ground. When the voltage becomes high enough a spark flies between the cloud and the earth; this is lightning. The spark is so hot, it causes the air to rapidly expand then collapse; this causes thunder. Q4) Why does the voltage need to be very high before lightning can occur? Lightning rods. Lightning rods are used to protect buildings from lightning strikes. They are usually made from a length of copper rod with a pointed end. They are attached to tall buildings and the lightning strikes them rather than the building itself. Q5) Why do you think the rods are made of copper rather than iron which is cheaper? Q6) Why do the rods have a pointed end? Q7) It is standard advice that if caught out in a storm you should "never" stand under a lone tree. Why is this advice good? Answers | «Uses of static electricity | Electrolysis»

Geometry. Welcome to the Wikibook of <br> GEOMETRY Preface. The word geometry originates from the Greek words ("geo" meaning world, "metri" meaning measure) and means, literally, to measure the earth. It is an ancient branch of mathematics, but its modern meaning depends largely on context. Geometry largely encompasses forms of non-numeric mathematics, such as those involving measurement, area and perimeter calculation, and work involving angles and position. It was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. This Wikibook is dedicated to high school geometry and geometry in general. High School Geometry. The outline of topics reflects the California curriculum content standards.

C Programming/Memory management. In C, you have already considered creating variables for use in the program. You have created some arrays for use, but you may have already noticed some limitations: "Dynamic memory allocation" in C is a way of circumventing these problems. The codice_1 function. void *calloc(size_t nmemb, size_t size); void free(void *ptr); void *malloc(size_t size); void *realloc(void *ptr, size_t size); The standard C function codice_1 is the means of implementing dynamic memory allocation. It is defined in stdlib.h or malloc.h, depending on what operating system you may be using. Malloc.h contains only the definitions for the memory allocation functions and not the rest of the other functions defined in stdlib.h. Usually you will not need to be so specific in your program, and if both are supported, you should use <stdlib.h>, since that is ANSI C, and what we will use here. The corresponding call to release allocated memory back to the operating system is codice_3. When dynamically allocated memory is no longer needed, codice_3 should be called to release it back to the memory pool. Overwriting a pointer that points to dynamically allocated memory can result in that data becoming inaccessible. If this happens frequently, eventually the operating system will no longer be able to allocate more memory for the process. Once the process exits, the operating system is able to free all dynamically allocated memory associated with the process. Let's look at how dynamic memory allocation can be used for arrays. Normally when we wish to create an array we use a declaration such as int array[10]; Recall codice_5 can be considered a pointer which we use as an array. We specify the length of this array is 10 codice_6s. After codice_7, nine other integers have space to be stored consecutively. Sometimes it is not known at the time the program is written how much memory will be needed for some data; for example, when it depends upon user input. In this case we would want to dynamically allocate required memory after the program has started executing. To do this we only need to declare a pointer, and invoke codice_1 when we wish to make space for the elements in our array, "or", we can tell codice_1 to make space when we first initialize the array. Either way is acceptable and useful. We also need to know how much an int takes up in memory in order to make room for it; fortunately this is not difficult, we can use C's builtin codice_10 operator. For example, if codice_11 yields 4, then one codice_6 takes up 4 bytes. Naturally, codice_13 is how much memory we need for 2 codice_6s, and so on. So how do we codice_1 an array of ten codice_6s like before? If we wish to declare and make room in one hit, we can simply say int *array = malloc(10*sizeof(int)); We only need to declare the pointer; codice_1 gives us some space to store the 10 codice_6s, and returns the pointer to the first element, which is assigned to that pointer. Important note! codice_1 does "not" initialize the array; this means that the array may contain random or unexpected values! Like creating arrays without dynamic allocation, the programmer must initialize the array with sensible values before using it. Make sure you do so, too. ("See later the function codice_20 for a simple method.") It is not necessary to immediately call codice_1 after declaring a pointer for the allocated memory. Often a number of statements exist between the declaration and the call to codice_1, as follows: int *array = NULL; printf("Hello World!!!"); /* more statements */ array = malloc(10*sizeof(int)); /* delayed allocation */ /* use the array */ A more practical example of dynamic memory allocation would be the following:Given an array of 10 integers, remove all duplicate elements from the array, and create a new array without duplicate elements (a ).A simple algorithm to remove duplicate elements: int arrl = 10; // Length of the initial array int arr[10] = {1, 2, 2, 3, 4, 4, 5, 6, 5, 7}; // A sample array, containing several duplicate elements for (int x = 0; x < arrl; x++) for (int y = x + 1; y < arrl; y++) if (arr[x] == arr[y]) for (int s = y; s < arrl; s++) if (!(s + 1 == arrl)) arr[s] = arr[s + 1]; arrl--; y--; Because the length of our new array depends on the input, it must be dynamically allocated: int *newArray = malloc(arrl*sizeof(int)); The above array will currently contain unexpected values, so we must use codice_23 to set our dynamically allocated memory block to the new values: memcpy(newArray, arr, arrl*sizeof(int)); Some security researchers recommend always using calloc(x,y) rather than malloc(x*y), for 2 reasons: Error checking. When we want to use codice_1, we have to be mindful that the pool of memory available to the programmer is "finite". Even if a modern PC will have at least an entire gigabyte of memory, it is still possible and conceivable to run out of it! In this case, codice_1 will return codice_26. In order to stop the program crashing from having no more memory to use, one should always check that malloc has not returned codice_26 before attempting to use the memory; we can do this by int *pt = malloc(3 * sizeof(int)); if(pt == NULL) fprintf(stderr, "Out of memory, exiting\n"); exit(1); Of course, suddenly quitting as in the above example is not always appropriate, and depends on the problem you are trying to solve and the architecture you are programming for. For example, if the program is a small, non critical application that's running on a desktop quitting may be appropriate. However if the program is some type of editor running on a desktop, you may want to give the operator the option of saving their tediously entered information instead of just exiting the program. A memory allocation failure in an embedded processor, such as might be in a washing machine, could cause an automatic reset of the machine. For this reason, many embedded systems designers avoid dynamic memory allocation altogether. The codice_28 function. The codice_28 function allocates space for an array of items and initializes the memory to zeros. The call codice_30 allocates codice_31 objects, each of whose size is sufficient to contain an instance of the structure codice_32. The space is initialized to all bits zero. The function returns either a pointer to the allocated memory or, if the allocation fails, codice_26. The codice_34 function. void * realloc ( void * ptr, size_t size ); The codice_34 function changes the size of the object pointed to by codice_36 to the size specified by codice_37. The contents of the object shall be unchanged up to the lesser of the new and old sizes. If the new size is larger, the value of the newly allocated portion of the object is indeterminate. If codice_36 is a null pointer, the codice_34 function behaves like the codice_1 function for the specified size. Otherwise, if codice_36 does not match a pointer earlier returned by the codice_28, codice_1, or codice_34 function, or if the space has been deallocated by a call to the codice_3 or codice_34 function, the behavior is undefined. If the space cannot be allocated, the object pointed to by codice_36 is unchanged. If codice_37 is zero and codice_36 is not a null pointer, the object pointed to is freed. The codice_34 function returns either a null pointer or a pointer to the possibly moved allocated object. The codice_3 function. Memory that has been allocated using codice_1, codice_34, or codice_28 must be released back to the system memory pool once it is no longer needed. This is done to avoid perpetually allocating more and more memory, which could result in an eventual memory allocation failure. Memory that is not released with codice_3 is however released when the current program terminates on most operating systems. Calls to codice_3 are as in the following example. int *myStuff = malloc( 20 * sizeof(int)); if (myStuff != NULL) /* more statements here */ /* time to release myStuff */ free( myStuff ); free with recursive data structures. It should be noted that codice_3 is neither intelligent nor recursive. The following code that depends on the recursive application of free to the internal variables of a struct does not work. typedef struct BSTNode int value; struct BSTNode* left; struct BSTNode* right; } BSTNode; // Later: ... BSTNode* temp = calloc(1, sizeof(BSTNode)); temp->left = calloc(1, sizeof(BSTNode)); // Later: ... free(temp); // WRONG! don't do this! The statement "codice_58" will not free codice_59, causing a memory leak. The correct way is to define a function that frees "every" node in the data structure: void BSTFree(BSTNode* node){ if (node != NULL) { BSTFree(node->left); BSTFree(node->right); free(node); Because C does not have a garbage collector, C programmers are responsible for making sure there is a codice_60 exactly once for each time there is a codice_61. If a tree has been allocated one node at a time, then it needs to be freed one node at a time. Don't free undefined pointers. Furthermore, using codice_3 when the pointer in question was never allocated in the first place often crashes or leads to mysterious bugs further along. To avoid this problem, always initialize pointers when they are declared. Either use codice_1 at the point they are declared (as in most examples in this chapter), or set them to codice_26 when they are declared (as in the "delayed allocation" example in this chapter). Write constructor/destructor functions. One way to get memory initialization and destruction right is to imitate object-oriented programming. In this paradigm, objects are constructed after raw memory is allocated for them, live their lives, and when it is time for them to be destructed, a special function called a destructor destroys the object's innards before the object itself is destroyed. For example: /* this is the type of object we have, with a single int member */ typedef struct WIDGET_T { int member; } WIDGET_T; /* functions that deal with WIDGET_T */ /* constructor function */ void WIDGETctor (WIDGET_T *this, int x) this->member = x; /* destructor function */ void WIDGETdtor (WIDGET_T *this) /* In this case, I really don't have to do anything, but if WIDGET_T had internal pointers, the objects they point to would be destroyed here. */ this->member = 0; /* create function - this function returns a new WIDGET_T */ WIDGET_T * WIDGETcreate (int m) WIDGET_T *x = 0; x = malloc (sizeof (WIDGET_T)); if (x == 0) abort (); /* no memory */ WIDGETctor (x, m); return x; /* destroy function - calls the destructor, then frees the object */ void WIDGETdestroy (WIDGET_T *this) WIDGETdtor (this); free (this); /* END OF CODE */

Abstract Algebra/Lattice theory. A "lattice" is a "poset" such that each pair of elements has a unique "least upper bound" and a unique "greatest lower bound".

GCSE Science/Electrolysis. [[GCSE Science/Electricity]] Electrolysis is the decomposition of certain types of substance using electricity. The types of substance that can be split are ionic substances. This just means that they are made of charged ions rather than neutral atoms. {Remember that an ion is just an atom that has either a positive or negative charge}. An example of an ionic substance is common table salt sodium chloride. The sodium atom has a positive charge, the chlorine atom has a negative charge. It is usually written as Na+Cl-. Q1) Check in a periodic table, what is the symbol for sodium: Na or Cl? As you may already know if you've studied the Metals module, a salt is any substance made by combining an acid with an alkali. Acids, alkalis, and therefore all salts are ionic. Q2) Which of the following substances can be broken up by electricity: sodium chloride, iron sulphate, copper nitrate? Basic experimental setup. Most ionic compounds are not liquid at room temperature. This is a problem because the ions need to be able to move for the electric current to be able to flow. This can be achieved by melting. Look at the electrical setup shown on the right. The electrodes are just two carbon rods connected to a battery. The one connected to the positive electrode is called the anode. The one connected to the negative electrode is called the cathode. this is due to a collision Consider for example the compound lead bromide. This compound is a solid at room temperature but can be molten over a Bunsen flame. So what you would do is put some lead bromide into a beaker. Put the beaker on a tripod over a bunsen flame. Melt the lead bromide, then put in the electrodes and turn the power supply on at a setting of, say, 2V. What you would see happening is the cathode, is a silvery coating of pure lead forming, and bromine forming at the anode. The current would continue to flow until all the lead bromide was turned into lead and bromine. Q3) It takes energy to split up a compound like lead bromide. Where does this energy come from? Q4) Predict what products you would get at the anode and cathode if copper chloride was the electrolyte. What happens at the anode. The anode is the positive electrode; it attracts negatively charged ions, because unlike charges attract. The bromine ions move through the melt until they reach the anode. Once they get there, they give up their two extra electrons to become bromine atoms. 2Br- → Br2 + 2e- The electrons flow up the anode to the positive terminal of the battery. What happens at the cathode. The cathode is the negative electrode; it attracts the positively charged ions. Metal ions are always positive and so the lead ions flow through the metal uhe negatively charged terminal of the battery and onto the lead ions. Some trick to remember cations and anions, cathodes and anodes. I have a cat...I call her by saying come here plussy! - cathodes attract positive ions ca+ions has a plus in it, cations are positive ions red cat: reduction occurs at the cathode Pb2+ + 2e- → Pb Q5) Solid ionic substances do not conduct electricity and are not split up by it. Why do you think that is? Quantity calculations (higher tier only). In the experiment with lead bromide, you saw that lead was deposited at the cathode. If you actually do the experiment you will see that the lead coats the cathode. In this section we will look at how much metal will coat a cathode in a given time. A scientist performed the following experiment. His results were: You can see from the results that the total amount of copper deposited depends on both the current and the time it flows. This is because the number of copper atoms that can be made from ions depends on the total amount of charge that flows. The unit of charge is the coulomb. One coulomb is the amount of charge when one Ampere flows for one second. Q6) Look at the results table above. How much copper is deposited when 1A flows for 3000 seconds? Q7) How much copper do you predict would be deposited if 1A were to flow for 6000 seconds. Q8) What about if 2A were to flow for 12000 seconds ? Electrolysis of Aqueous solutions (Advanced). "Before studying this section check with your teacher to see if you need to". Earlier on in this module you've learned that ions must be able to move in order for electrolysis to work. If the ions are held rigid {such as in a solid}, they can't move and no electricity will flow. We've looked at how the freeing up of ions can occur by melting the electrolyte. Another way to achieve this is by dissolving the electrolyte in water. The trouble with this method is, there will be more than one type of ion present. Water partially splits up into ions {this is why it's such a good solvent for ionic compounds}. It splits into hydrogen ions and hydroxide ions. H2O → H+ +OH- So at the cathode there will be two ions present: the metal ion and the hydrogen ion from the water. Which element is actually produced at the cathode depends on how reactive the metal is. If the metal is very reactive, such as potassium or sodium, then it is unlikely to be discharged. Hence hydrogen will be produced. If the metal is unreactive such as silver, the metal will be produced. To work out which ion "wins", the metal or the hydrogen, compare their reactivities in a the reactivity series. The one that is most reactive, will not be produced at the cathode. A similar situation occurs at the anode. Hydroxide ions {from the water} are usually discharged at the anode ultimately producing oxygen. However, if the concentration of the ions of Halites (group 7) are much higher than that of the hydroxide ions, then the halite ions are discharged. Sulphates are never discharged. OH- → OH + e- 4OH → 2H2O + O2. Q9) Sodium chloride is dissolved in water and subjected to electrolysis. Explain what you see at each of the electrodes. Answers | «Advanced static electricity | Circuits»

Hindi. नमस्ते! Hindi is an Indo-European language spoken as a first language in majority states in northern India and second language in many countries where these people have emigrated. It is written with the Devanagari, script which fairly closely follows the phonetics of the language. Spoken Hindi is very similar to spoken Urdu — as such they are both often classified as part of the Hindustani language. Feel free to use Wiktionary's Hindi Category to study words. Basic Hindi in 1,2,3 Steps. "To be reorganized"

Discrete Mathematics/Axiom of choice. Axiom of choice: If formula_1 is a surjective map, then there exists a map formula_2 such that formula_3 is the identity (trivial) map. Lemma: Every set can be well-ordered.

CACS/Glossary/ASProvider. An Application Service Provider (ASP) is a business model for delivery of business or IT services across a network. It may also be a service enterprise whose primary business is delivery of application services using the ASP model. ASP usually implies a central (vendor) data center that runs the application. For further discussion, see the Wikipedia article.

Algebra/Equalities and Inequalities. Solving linear inequalities involves finding solutions to expressions where the quantities are "not" equal. A number on the number line is always greater than any number on its left and smaller than any number on its right. The symbol "<" is used to represent "is less than", and ">" to represent "is greater than". For example: -5 -4 -3 -2 -1 0 1 2 3 4 5 From the number line, we can easily tell that 3 is greater than -2, because 3 is on the right side of -2 (or -2 is on the left of 3). We write it as formula_1 (or as formula_2). We can also derive that any positive number is always greater than negative number. Consider any two numbers, "a" and "b". One and only one of the following statements can be true: Now we can go on to solve any linear inequalities. Solving Inequalities. Solving inequalities is almost the same as solving linear equations. Let's consider an example: formula_29. All we have to do is to subtract 4 on both sides. We will then get formula_30, and that is the answer! Note, however, what you get is not a single answer, but a "set" of solutions, i.e., any number that satisfies the condition formula_30 (any number that is less than 9) can be a solution to the inequality. It is very convenient to represent the solution using the number line: <-------------------o 6 7 8 9 10 11 Let us try another more complicated question: formula_32. First, you may want to expand the right hand side: formula_33. Then we can simply rearrange the terms so that all the unknown variables are on one side of the equation, usually the left hand side: formula_34. Hence we can easily get the answer: formula_35. This solution is represented on the number line below. Note that the solution requires a closed circle ("●"), because the formula_11 is greater than "or equal to" 4. <-+-----+-----+-----+-----+-----+--> -6 -5 -4 -3 -2 -1 Inequalities with a variable in the denominator. For example consider the inequality In this case one cannot multiply the right hand side by formula_38 because the value of x is unknown. Since x may be either positive or negative, you can't know whether to leave the inequality sign as formula_39 (ie less than), or reverse it to > (ie greater than). The method for solving this kind of inequality involves four steps: Compound Inequalities. A compound inequality is a pair of inequalities related by the words "and" or "or". In an "and" inequality, both inequalities must be satisfied. All possible solution values will be located between two defined numbers, and if this is impossible, the compound inequality simply has no solutions. Consider this example: formula_56 and formula_57. First, solve the first inequality for x to get formula_35. All "and" inequalities can be rewritten as one inequality, like this: formula_59formula_57 (write x between two ≤'s or <'s or both with the smaller number on the left and the larger number on the right). Now, we can graph this inequality on a number line as a line segment. Remember, all solutions to ≤ or ≥ must be graphed with closed circles. Interpret this graphic as "all numbers between -4 and 2, including -4 and 2." <-+-----+-----+-----+-----+-----+--> -6 -4 -2 0 2 4 Now, let us consider "or" inequalities. "Or" inequalities usually do not have a set of solutions that satisfies both. Instead, they usually have two sets of infinite numbers that are solutions to each one. Because of this, "or" graphs define which numbers satisfy either equation. For example: formula_61 or formula_62. First, solve for x in the second inequality to get formula_63. Now, graph the two inequalities on the same number line. Remember to use open and closed circles accordingly. <-------------o ●--------> -1 0 1 2 3 4 Solving Inequalities with Absolute Value. Since formula_64 A inequality involving absolute value will have to solved in two parts. Solving formula_65 The first part would be formula_66 which gives formula_67. The second part would be formula_68 which solved yields formula_69. So the answer to formula_65 is formula_71 <-+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+--> 0 1 2 3 4 5 6 7 8 9 10 11 12 Graphing Linear Inequalities. The graphing of linear inequalities is very similar to the graphing of linear functions. A linear inequality is written in Previous: Solving equations <br> Next: Quadratic functions

JLPT Guide/JLPT N5 Kanji. JLPT Level N5. The following is a list of 81 kanji, which is most of the kanji necessary to pass the N5 level of the Japanese Language Proficiency Test (JLPT), prior to the updating of the list several years ago. There are now 103 kanji in the level N5 exam (24 more than the kanji listed below). Kanji used in the N5 test are used in more difficult levels, too. As of 2010, the JLPT no longer publishes an official vocabulary list. Unofficial lists for all JLPT levels are however published on .

CACS/Glossary/ASP. Active Server Pages (ASP) is a technology that creates dynamic Web Pages by executing Java Script or VB Script statements on a server, generating "HTML", and sending the resulting Webpage to a browser. ASP is packaged as a part of the "Personal Web Server (PWS)" and "Internet Information Server (IIS)" suites.

Computer Programming/MacOS Programming. About the platform. macOS is the primary operating system for the Macintosh computer. It was originally a system designed privately by Apple Inc, however with Mac OS X, it has been based on Unix. Specifically, a modified FreeBSD operating system called "Darwin". There are many different kinds of software that can be developed for Mac OS X. People generally think of applications, but we'll briefly cover some of the other kinds. Types of Software for Mac OS X. Applications. Applications are what people generally think of when they think about software for Mac OS X. Cocoa applications include: Finder, Mail, Address Book, Safari, Microsoft Word, and Microsoft Excel. mai hu doreamon ions using Apple's free development tools which includes XCode. Mac OS X applications are developed using Objective-C though there are other possible programming languages that could be used. The most popular languages for use on the macOS platform is Objective-C which could be thought of as Mac OS X's "native language" since the Mac OS X libraries, or "frameworks", all have an Objective-C interface. Objective-C includes everything that plain C can do, and adds object-oriented programming. See: . C++ can be used in developing for the Mac, but generally, it is used in addition to Objective-C rather than being in place of Objective-C. Using both Objective-C and C++ is called "Objective-C++" and is considered to be optional when developing software for Mac OS X: See for a lesson on the basics of Objective-C may also be of assistance. Some preliminary thoughts: Objective-C is the language most commonly used in Mac OS Programming. Objective-C entered Mac OS X and has ancestry in NeXT. . Before you learn Mac programming you "must " know the basics of C since it is the basis for Objective-C. There used to be three separate APIs for developing a Mac application with a GUI: 1. Classic (Mac OS 9 and lower). Developing for the Classic API is no longer done. When Mac OS X first came out, users and developers had a huge investment in software written for Mac Classic OS and Mac OS X used to have an emulation mode so that users could run their old software. Apple has long since stopped support of the Classic API and Classic emulation in Mac OS X. 2. Carbon (Mac OS 8.5 up to and including Mac OS X 10.6 Snow Leopard). Carbon was an API for developers to update their applications that used the Classic API to be run without the Classic emulator. Carbon was a great way that Apple provided developers to upgrade their software to run on Mac OS X without having to totally rewrite their software, but Carbon, like Classic, is no longer supported by Apple. 3. Cocoa (All versions of Mac OS X). Cocoa is the most native API that can be used to develop applications for Mac OS X that are truly "Mac-like". Generally, Objective-C will be used along with Cocoa, though there are other options such as Cocoa-AppleScript and Cocoa-Python, but Cocoa-Objective-C is really the "mainstream" way to develop Cocoa applications. Resource Forks Files in Mac OS X have a feature that is unique to Mac OS and that is that each file on disk can have two "forks". This feature used to be used for Classic and Carbon applications to separate code from resources (such as menus, windows, etc.), and the Mac OS X file system still supports two forks, but you should only use the "data fork". The resource fork is non-standard and can be lost when transferring Mac files to other file systems. AppleScripts. Another "native language" for developing Mac OS X applications is AppleScript. AppleScript is a language that Apple invented to automate repetitive tasks. The AppleScript application is located on your Mac at /Applications/Utilities/AppleScript Editor. AppleScript can be used to record AppleEvents, the events that applications send to themselves or to other applications. Why don't you try it out. Open AppleScript Editor, press the record button, do some things with your other applications and watch the script write itself. AppleScript can be used alone or it can be used along with XCode to develop Cocoa Applications using mostly AppleScript instead of Objective-C. This option is mostly for experienced AppleScript programmers who don't know Objective-C. Automator Workflows. Apple also provides an application called "Automator" that can be used to easily automate repetitive tasks. It is located at /Applications/Automator.app Shell Scripts. Mac OS X has an application called Terminal that provides a command-line interface to Mac OS X. It is possible to develop scripts for the command line. Terminal.app is located at /Applications/Utilities/Terminal.app To create a shell script, you need a text editor. There is a text editor that comes with Mac OS X called "TextEdit.app". It is located in /Applications/TextEdit.app. But actually, what is better than TextEdit is a program such as TextWrangler.app which is available for free from the following link: http://www.barebones.com/products/textwrangler/ The shell that Terminal.app uses by default is called "bash". Here is a simple tutorial on developing bash scripts http://www.maclife.com/article/columns/terminal_101_automate_terminal_bash_scripts We won't go any more deeply into shell scripts here in this wikibook, but it's just good to know what they are. You can always google for more information now that you know what to google for. Command Line Tools. When you open Terminal and you learn how to type in commands. The commands are usually command-line tools or scripts. Above, we just talked about developing your own scripts with a text editor. It's also possible to develop your own command-line tools, using XCode. This is an advanced thing to do. Usually, power-users will write a shell-script (or some other kind of thing such as an AppleScript or an Automator Workflow) but it's good to know what a command-line tool is. Command-line tools have a textual user-interface rather than a graphical user interface (GUI). Java. Java used to be treated by Apple as a "first class language" to develop for Mac OS, however in recent years, Apple has less support for Java. Now with Mac OS X 10.7 "Lion" and 10.8 "Mountain Lion", Java doesn't even come pre-installed in Mac OS X. Java is still available, but users have to download Java from Oracle's website and install it themselves. Apple's Mac App Store doesn't even allow Java apps to be sold at their store calling Java "deprecated". However, there still are Mac developers who use Java because it has the advantage of being cross-platform compatible. For example, the same source-code can be used to generate software that runs on Mac, Windows, and Linux. Apple has said that Java reduces the Mac to the "least common denominator". That's why they support it less. Python. Python is somewhat supported by Apple. In fact, Python is shipped with Mac OS X and is part of the System Folder. There are third-party libraries that allow developers to develop applications using Python and Cocoa together, but these are not very well maintained, and Python on the Mac is most suitable for developing command-line utilities, or cross-platform scripts that aren't really very Mac-like. Ruby. Similar to Python. Websites. Most Mac users use Safari for their web browser. Safari uses the standards set by w3c.org You can develop websites that work with Safari by following the standards of the w3c.org. Remember to validate your HMTL, CSS, and JavaScript. HTML Validator: http://validator.w3.org/ CSS Validator: http://jigsaw.w3.org/css-validator/ JavaScript Lint: http://www.javascriptlint.com/online_lint.php If you're developing websites using your Mac and using Safari, remember to test your webpages on other platforms and with other web browsers. Mac OS X Specific Languages. Objective-C is really the "native" language for Mac OS X development You could call AppleScript a "native" language too, but it isn't really used to make commercial applications. It was designed to be used by real power-users to automate their tasks. Although it is possible to use AppleScript to build Cocoa applications in XCode, this would be more for users who already know AppleScript and don't want to learn Objective-C.

CACS/Hardware Introduction. This part contains a survey of the world of computer hardware. This chapter introduces computer hardware and provides a very short history of computing. This section introduces the computing environment thrugh a brief history of computers and an overview of the subjects within hardware. Outline of computer history. There is some disagreement about when the digital age began. After all, the Babylonians used a kind of abacus about 500 BC. If we call it the computer age, we can get a much cleaner mark. 1951 was a watershed year, and two events identify it as the beginning. The UNIVAC became the first commercially available digital computer. That same year a research team at MIT completed the first user-interactive computer (named Whirlwind) that used a keyboard and a television screen or CRT. Considering developments by decades gives a pretty clear picture of the evolution of computers. Vacuum tubes. computer hardware notes Computer Hardware. All notes of Computer hardware

Sanskrit. Sanskrit is an old Indo-Aryan language once spoken throughout India. Many poems, epics, and prayers are written in it. Although not widely spoken anymore, it gave rise to many of the modern languages of India and influenced several more languages that are not related to it; Sanskrit is also still used as a language of culture and religion in India. In the past, Sanskrit was written in a variety of scripts by people from various places. Today, a modified version of the Devanagari script has been agreed upon as a standard. Sanskrit script. Harvard-Kyoto coding. a A i I u U e ai o au aM aH (or a:) ka kha ga gha Ga (nasal "ng") ca cha ja jha Ja (nasal "ny") ta tha da dha na Ta Tha Da Dha Na (retroflex) pa pha (not "fa") ba bha ma ya ra la va ha A bb ah See also. Wikner's introduction to Sanskrit is a good start. "Sanskrit: An Easy Introduction to an Enchanting Language" by Professor Ashok Aklujkar is also recommended.

Latin. This is an elementary Latin course accompanied with a detailed grammar based upon Kennedy's Public School Latin Grammar designed to introduce one to the world of . A basic understanding of would be helpful; however, it is not required. Basic definitions of terms will be explained in Lessons 1 and 2, and later elaborated as needed. For detailed explanations and examples of English grammatical terms, please consult the English Grammar textbook. However, Latin grammar is quite different from that of English, and thus it requires different grammatical terms to explain the concepts. These will be taught as needed. Preface. This book will attempt to teach the reader about Latin from the ground up. Please read the Introduction to the origins and structure of Latin carefully, as it introduces the concept of a stem. As is typical in many other languages, the infinitive stem (present tense, active voice) is used for conjugating verbs. [The introduction of additional information in parentheses is done simply to avoid confusing a student who has already had exposure to Latin.] Advice. Parts of this book may have been edited by people who do not speak English as their first language. All Wikibooks are written in the particular English dialect of the writer, which may not be standard usage. If you see something particularly unclear, please feel free to correct it, but please alter this article in a constructive manner. If something doesn't make sense to you, delete or preferably fix it if you are skilled enough; otherwise, try to emphasize that text marking it with some keyword, e.g., "grade 12 [grade] American [system] revert?" reporting that thing in the of the book. The "revert" keyword allows your editors to know that you are not a skilled editor but that you are just trying to learn, and you are confused. Your changes are not permanent. In any case, please, edit this book responsibly. Spoken Latin. This is a test chapter to teach those who wish to learn Latin which they can use in their daily lives. About the Book. Please leave ideas for additional chapters on the page. See also. Cultural insights in other wiki books / wiki articles.

Latin/Lesson 1. =What is Latin?= Latin was the language originally spoken in the region around the city of Rome called Latium. It gained great importance as the formal language of the Roman Empire. All — including Italian, French, Spanish, Portuguese, Romanian, and others — descend from a Latin parent, and many words in English and other languages today are based on Latin roots. Moreover, Latin was a "lingua franca", the learned language for scientific and political affairs in Europe, for more than one and a half thousand years, being eventually replaced by French in the 18th century and English by the middle of the 20th. Latin remains the formal language of the Roman Catholic Church to this day and is the official language of the Vatican. Romance languages are not derived from Classical Latin, a literary language for writing and oration, but rather from Vulgar Latin, the language spoken by the common people, or " vulgus, " of Rome. Classical Latin and Vulgar Latin (Romance) differ (for example) in that Romance had distinctive stress whereas Classical had distinctive length of vowels. In Italian and Sardo logudorese, there is distinctive length of consonants and stress, in Spanish only distinctive stress, and in French even stress is no longer distinctive. Stress refers to the emphasis of pronunciation on syllabic units. Most English nouns not derived from other parts of speech have an emphasis on the first syllable. Foreign loan words in English sometimes retain their original stress, which may be on the second or third syllable, though assimilation into English will usually result in a vowel shift towards emphasis on the first syllable. Another major distinction between Classical and Romance is that modern Romance languages, excluding Romanian, have lost their case endings (suffixes at the end of the word used in place of prepositions) in most words (some pronouns being exceptions). Romanian is still equipped with several cases though some, notably the ablative, are no longer represented. Here are some current English words which are Latin derivativesː =Introduction to the Latin Language= Simple and Compound Words. In Latin, words are either: Word Parts. Inflected words (i.e., words having ending- or spelling-changes according to their grammatical functions in the sentence) have a stem and a root. The Stem The stem is the part of the word to which various suffixes are added. The final suffix determines either the role of the word in the sentence (for example, when a Roman slave wished to address his "dominus" (master), he used the vocative form "domine" -- equivalent to "O master" in English) or the person/subject involved in the action (for example, "I dominate" may be expressed as "domin-or", and "they dominate" as "domin-antur"). In these cases, "domin-" is the stem and "-us", "-e", "-or" and "-antur" are suffixes. The addition of such suffixes is called "inflection". This is discussed further in the Summary. The Root The root is the part of the word that carries the essential meaning. For example the stem of "agitō" (I drive onward) is "agit-", whose root is "ag" (do, drive), which is in common to words of similar meaning: "agō" (I do, drive), "agmen" (that which is driven, such as a flock), etc. Notice the essential difference between a root and a stem. To the root "ag" has been added a suffix "(i)tō-" which denotes frequency of action (so "agit-" means to do or drive more than once, hence "agit-ō", I agitate, I keep (something) moving, I urge, I impel). In contrast, English uses word order more than inflection to determine the function of a word within a sentence. English also uses words like pronouns (I, she, etc.) and prepositions (to, at, etc.) where Latin generally prefers inflexions. Thus "dom-ī" (noun -- "at home"), "ag-unt" (verb -- "they do/drive"). Primitives Primitives occur when both the stem and the root are the same. For example, in the word "agere" (to do, drive) both the stem and the root are the same: "ag-". Derivatives Derivatives occur when the root or stem is modified. For example, the stem "flamm-" from the noun "flamma" has the root "flag" ("blaze"), "nōscō" (I know) from the verb "nōscere" has the root "gnō-" ("know"). Suffixes Latin attaches suffixes ("endings") to stems to turn them into words (most stems and roots cannot be used in sentences without an ending). This inflection is essential to forming Latin sentences. The various suffixes and their translations will be learned in the later lessons. =Types of Words used in Latin= Nouns. A noun (Latin: "nōmen") is "something perceived or conceived by the mind." There are two kinds of nouns: Substantives and Pronouns. 1. Substantive ("nōmen substantīvum") is a name simply denoting something perceived or conceived: "psittacus" - the parrot, "nix" - the snow, "virtus" - virtue. 2. Pronoun ("prōnōmen") is a word used in place of a "substantivum", usually when the "substantivum" is already known: "ea" - she, "ille" - that man Nouns have changing endings on the stem (known as declension) and three incidents: number, gender and case. Number concerns whether the thing referred to is singular or plural (and the ending shows this); gender classifies a substantive as masculine, feminine or neuter (this determines how the endings of adjectives and pronouns behave) and case (where the ending must show how the noun fits in to the sentence). Adjectives and Pronouns must agree in all incidents when they refer to a substantive. Verbs. Verbs ("verba") express an action or a state of being, e.g., "agō" (I do), "dīxit" (he said), "venīs" (you come). Conjugation is the term for adding inflections to verb stems to indicate person (first, second or third), number (singular or plural), tense (present, future, imperfect, perfect, pluperfect or future perfect), voice (active or passive), and mood (indicative, subjunctive or imperative). A verb can be either "finite" or "infinite": 1. Finite verbs ("verba finīta") are inflected and have a subject, e.g., I run, you run, he runs, they drive, the computer is turned on. 2. The infinite verbs ("verba infinīta") are not inflected and have no subject, e.g. to run, to drive, to turn on, to have drawn. "Participles", which are inflected as substantives rather than as verbs, may also be considered infinite, e.g., the "running" boy. Modifiers. 1. Adjectives ("adiectīva") are used to describe nouns. They indicate a quality perceived or conceived as inherent in, or attributed to, something denoted. E.g., "vir magnus" (the great man), "puella pulchra" (the fair girl) 2. Adverbs ("adverbia") are similar to adjectives, except that they are used to qualify verbs, adjectives or other adverbs, rather than nouns. In practice, they restrict the meaning of the verb or adjective by specifying how or how much. E.g., "currō celeriter" (I run quickly), "pugnat fortiter" (he fights bravely), "vērē iūcundus est" (he's really nice), "incrēdibile callida est" (she's incredibly clever). Other. Particles are uninflected words that provide extra meaning. 1. Prepositions ("praepositiōnēs") are little words which tell you how one word is behaving in relation to another word ("the duck was near the pond", "she went towards the wood"). In Latin, the noun that follows a preposition takes a particular ending (called a "case"), depending on the nature of the relationship, or on the nature of the preposition itself. E.g., "ad" (by), "in" (in), "sub" (under). What all this means is that a preposition is a sort of adverb, telling you how something is done. For example, "you go" is a simple statement, but "you go in" suggests that you don't just "go", you go so as to enter something, and so you need a noun for the "something". In English, we might say "you go into the house". In Latin, this would be: "in domum inīs". Notice the form "in domum", which means "into" the house -- you're going into it, you're not yet exactly inside it (the ending -um of "domum" is called "accusative"). When you are inside the house, what you do is "in" the house, which is "in domō" (the ending -ō of "domō" is called "ablative"). 2. Conjunctions ("coniunctiōnēs") join together clauses and sentences. E.g., "et" (and), "atque" (as well as), "sed" (but). 3. Interjections ("interiectiōnēs") are exclamations used to express feeling or to gain attention. E.g., "ō!" (oh!), "ēheu!" (alas!), "ecce!" (behold!). Articles. Latin has no definite article or indefinite article, respectively "the" and "a/an". When translating Latin into English the appropriate article must be added. =Summary= =Exercises=

Latin/Lesson 2. Spelling and Pronunciation. The Latin alphabet, on which the English alphabet is based, has mostly the same letters as the English alphabet, except that it has no <k> or <w>, and that in its original form, it lacked <j>, which only some modern texts use, and <u>. Many European languages use the Latin alphabet as the basis for their own alphabet. Latin pronunciation has varied somewhat over the course of its long history, and there are some differences between Old Latin, spoken in the Roman Republic, Classical Latin, spoken in the Roman Empire, Medieval Latin, spoken in the Middle Ages, and Ecclesiastical Latin, spoken in the Catholic Church. This text focuses on the pronunciation of Classical Latin. Note that Latin, as written by the Romans, did not have <j>, <k>, <u>, <w>, or macrons over vowels (the lines indicating that vowels are long), although they did sometimes mark long vowels with apices (e.g. <ó> for /oː/); macrons are used today as pronunciation guides and do not necessarily need to be written. /w/, /ʊ/, and /uː/ were all represented with <v>. Modern texts often use <v> for /w/, <u> for /ʊ/, and <ū> for /uː/. In some modern texts (this Wikibook not included), <j> is used for /j/. Declension Tables. The following tables will be both referenced and explained in all of the following sections, and hence are placed here. Note that nouns in the 3rd declension nominative can have any ending, hence why none is given in bold. Grammar Part 1: Nouns and Their Role in Sentences. Nouns in Latin are inflected, which means that endings (also known as suffixes or "suffices") are appended to the end of the stem to denote these things: Most nouns in English can be modified to indicate number (cat versus cats), and many pronouns can be modified to indicate case (who versus whose) or gender (he versus she, his versus hers). Case is especially important in Latin as meaning cannot be determined by word order as it can be in English, but purely by word endings, or "inflection". Indeed, the words in a Latin sentence can appear in almost any order with little change in meaning. Two sentences with the word orders "Sam ate the orange" and "The orange ate Sam" could potentially mean the same thing in Latin, though the spellings of "orange" and "Sam" would have to change slightly to denote which was the subject (the one eating) and which was the object (the one being eaten). It is important to note here that although the genders of many words make sense (for example, "puella", meaning a girl, is feminine) many are simply assigned and hold no real meaning. Luckily, as you will find, the gender can often be determined by the spelling of the word (words ending in "us" are almost always masculine, and words ending in "a" are almost always feminine). For many words, however, you will simply have to memorize their gender. Adjectives themselves must match the number, case, and gender of the noun (be it a substantive or a pronoun) they modify. If a noun is nominative singular feminine (see case table below), then the adjective describing it must also be nominative singular feminine. If the noun is accusative plural masculine, then the adjective must be accusative plural masculine. This will be expanded on in the Adjectives section below. The advantage of this system is that adjectives do not need to be adjacent to their respective nouns, as one would be able to tell which noun they modify by which noun they appear to agree with. Declension. All substantives are part of one of 5 categories, called declensions. A substantive is a stem, modified by adding a declension suffix. Each declension has a set of standard suffixes that indicate case and number. Usually gender is indicated by the suffix, although there are many exceptions. Therefore, you must memorize the gender of every substantive you learn. By familiarizing yourself with the above tables, you could deduce that originally the suffix indicating number, case, and gender was the same for every noun. However, as the language developed, nouns with a common stem formed declensions and sounds changed. Similar processes happen continually over time, even today. The above tables allow you to familiarize yourself with the existence of each declension, though by no means are you expected to memorize it now. Nonetheless, you will have to memorize it as you are formally introduced to individual cases and declensions in future lessons. Because of its introductory purpose, it is considerably simplified and incomplete, and therefore should not be used as a reference in the future. Adjectives are also classed into declensions which must match the declension of the noun they describe: Pronouns are not part of any declension, as they are all irregular, and simply have to be memorized. Case. Cases (Latin: "casus") determine the role of the noun in the sentence in relation to other parts of the sentence. There are six cases, Nominative, Genitive, Dative, Accusative, Ablative, and Vocative. Vocative case (Lesson 3), can be considered a sort of miniature case, generally not being accepted as a true one. Additionally, some nouns have a vocative case, which will be covered later. As nominative and accusative are the most basic, these will be taught first (the rest will be covered in later lessons). Gender. All substantives, including inanimate objects, have a particular gender (genera), which is either masculine, feminine, or neuter. For example, Vir, "a man," is masculine. Marītus, "a husband," is also masculine. Puella, "a girl," is feminine. Māter, "a mother," is feminine. Even inanimate objects are assigned gender, including all the moons, stars, trees, tools, and so forth. Logic will give you little help in determining what the genders of inanimate objects are, and with many nouns memorization is required. Luckily, for many nouns, the spelling of the word indicates the gender. Certain rules may be utilized to determine the gender of an inanimate substantive. Declension is a good indication of gender, especially for 1st and 2nd declension substantives. 1st declension substantives (substantives with an -a suffix) are usually feminine and second declension nouns (substantives with an -us suffix) are usually masculine or neuter. There are a few exceptions, and they will have to be learned. 3rd declension nouns can be either masculine, feminine or neuter (thus the gender will often have to be memorized). 4th declension nouns are usually masculine, sometimes neuter while 5th declension nouns are usually feminine. Nouns undeclined, words which are not substantives but used as such, sentences used as substantives and the products of trees are generally neuter. 1st/2nd declension adjectives alternate the set of endings depending on the gender of the noun it describes (see the next section below). If the adjective describes a feminine noun, the adjective must use 1st declension endings, if the adjective describes a masculine noun, the adjective must use 2nd declension masculine endings, if the adjective describes a neuter noun, the adjective must use 2nd declension neuter endings. 3rd declension adjectives use the same set of endings for masculine and feminine nouns. However, a slightly different set of endings are used when describing neuter nouns. Adjectives. As stated above, adjectives must match the gender, number, and case of the noun (be the noun a substantive, or a pronoun) they modify. Similar to the "Sam ate the orange" example above, if the adjective uses the wrong declension it could change the meaning of the sentence. For example, "The girl loves big trees," versus "the big girl loves trees" have different meanings. There are many occasions where logic cannot be used to determine the gender of inanimate objects, as genders are generally arbitrary when the noun has no literal gender. Furthermore, the declension of the noun, often determined by the spelling, can in turn be used to determine the gender, especially for the 1st and 2nd. However, this is never the case for the third declension, as the declension itself is not primarily assigned to any gender and the spelling of the nominative ("default") stem is random, leaving you with no hints. A noun and its adjective must also be in the same case. Otherwise, it is impossible to tell which nouns pair up to their respective adjectives in a sentence, as the words in a Latin sentence can appear in any order. See the examples below. Recapitulation. Therefore: Before you proceed to the next lesson, complete the exercises below so you will be able to apply this knowledge to Latin.

Latin/Lesson 1-Nominative. The Nominative Case. The Nominative case refers to the subject of a sentence. For example: The girl is pretty "The girl" is the subject of this sentence. In its simplest form a sentence will have a subject stated as a noun and will give some further information about the subject. The second part of this sentence tells the reader that the girl is pretty. This is called predicating the noun. This sentence consists of a subject and a predicate. As you know from English, an adjective is a word that denotes some quality, which in this sentence is attractiveness. The noun and adjective are joined together by the word "is", which is called the copula. Note that the copula simply connects the words and gives almost no information about the subject. The sentence in Latin has the same grammatical elementsː puella est pulchra The noun is followed by the predicate. The only difference is the absence of an article which has to be supplied by the translator. Puella can be translated as "girl", "the girl", or "a girl". Can you tell which word is the copula? Translate the followingː Which region of Europe was the Roman historian Tacitus referring to as Caledonia in his book "Agricola", which records the military campaigns of his father-in-law? Translate the followingː Note the conjunction given in the Vocabulary, and translate the followingː Give the meaning of the complete word on this inscription fragment from Roman Britainː Vocabulary. Key to Vocabulary: Overview of Adjectives. An adjective is any word that qualifies a noun. For example: Adjectives in Latin. Adjectives must agree with the nouns they describe in gender, number, and case. These words will look like the adjective antiquus (old, ancient): Third declension adjectives typically look more like ferox, ferocis (wild, bold). This is because the third declension has no stem assigned to the nominative singular. Adjectives often come after the word they describe. Since word order is not central to the meaning of a Latin sentence the adjective may appear anywhere in the sentence. In the following examples the "-us" is masculine (m.), "-a" is feminine (f.) and "-um" is neuter (n.). So magnus is masculine, magna is feminine, and magnum is neuter. Basic verbs. Verbs in Latin work quite differently than those in English. Study the following table then view the examples below. Personal Endings. Archaic Latin was spoken and written in Europe for over two thousand years and since all languages change gradually this sometimes makes it difficult for beginners to see patterns of change. English has also had a long development that is now divided into three periods called Old English, Middle English and Modern English. Compare the following English verbsː The contraction of the archaic "laborao" to "laboro" would have undergone the same gradual process. The archaic "amao" (I love) eventually became "amo". If you look at the Vocabulary you will see that "amat" and "amant" retain the original letter "a" of the stem. Further Examples. Example 2. Notes: In the same way, the adjective "pulcher -ra -rum" must agree with "puella" in gender, number, and case, so the correct form is "pulchra" (agreement with the feminine nominative singular noun of the first declension). Example 4. Notes: The adjective "magnus -a -um" in this case must agree with "lūdī" in gender, number, and case, so the correct form is "magnī" (masculine nominative plural). Third Declension Nouns and Adjectives. Third declension nouns and adjectives follow a different pattern. The nominative singular stem is not defined, and as such, any letter (or letters) can serve as a third declension stem. For example, "Māter" (mother) is a third declension noun in the nominative case. When pluralized, it becomes "Mātrēs". "-ēs" is attached to the end of a third declension noun to pluralize it, as opposed to changing the ending completely, because there is no uniform way to do so. You may have also noticed that the "e" in "Māter" was dropped when pluralized. This often happens when a stem is attached to a third declension noun of similar spelling (example, "Pater" (father) becomes "Patrēs") Examples: Third declension nouns are listed with the nominative case and the genitive case to provide the main stem. For example: All other types of nouns are also generally listed with the genitive Adjectives with a nominative ending in -is and the same stem in the nominative and in the other cases (eg. fortis) end in -e in the neuter and -ia in the neuter plural. For example:

Latin/Appendix F. English abbreviations derived from Latin. Common English abbreviations from Latin. Latin External Links. ^ Latin ^

Latin/Authors. Authors of the Latin Wikibook include the following contributors: and many anonymous Wikibooks contributors.

Latin/Appendix E. Latin This page provides a list of Latin phrases and their English translations. This page is copied from the article . Check that page to see the latest changes to this page. V. from , the Free encyclopedia. ^ Latin ^

Latin/Lesson 5-Accusative. Grammar: The Accusative. As you learned in the last lesson, the verb 'esse' (to be) usually takes the nominative case, because then the word after it is a complement. Most other verbs take the 'accusative' case. In a sentence, the accusative is the "what" - in English grammar, this is known as the direct object. For example: The girl sells the box. What did the girl sell? The box. Thus, box is the direct object, and when we translate it into Latin: Cistam, then, is in the accusative, because it is the direct object. Again, when an adjective describes a noun in the accusative case, the adjective must agree in number, case, and gender. Because Latin uses cases to mark the subject and the object of a sentence, word order does not matter. Consider: Examples of Adjectives Agreeing with the Nominative and Accusative Case. "Bonus", a first and second declension adjective, is masculine, nominative, and singular to agree with "puer", the word it is describing. "Ferocem", a third declension adjective, is masculine, accusative, and singular to agree with "canem". "Canem" is accusative because it is the object of "amat". Here is an example of plural adjectives: The words "bonus" and "ferocem" become "boni" and "feroces" to agree with the plurals "pueri" and "canes". However, if a girl (puella) happened to love that boy: "Bonus" must become "bona" in order to modify "puella", which is feminine. Finally, if the girl isn't good, but rather wild: Even though "puella" is first declension, "ferox" remains third declension. In the same way, a good lion would be "bonus leo". Exercise 2. Determine whether the adjective agrees with the substantive in all three categories: case, gender, number. Grammar: The Use of the Accusative. The newly introduced verbs, ama-t, curri-t, and porta-t take the accusative as the 'object'. Unless specified, any verb you look up in the dictionary will take the accusative, not the nominative. This means that they are transitive verbs, verbs that happen to someone or something, e.g.: I heal you. ("acc.") You make my day. ("acc.") She hit your arm. ("acc.") In the examples above, the bold words are the subject of the sentence clause. Because something happens "to" them, they can't be in nominative.

English in Use/Nouns. A noun, or noun substantive, is a part of speech (a word or phrase) which functions as the head of a noun phrase. The word "noun" derives from the Latin "nomen" meaning "name", and a traditional definition of nouns is that they are only those expressions that refer to a person, place, thing, event, substance, quality, or idea. They serve as the subject or object of a verb and as the governed term of a preposition, and can co-occur with articles and attributive adjectives. There are different groups of nouns: Each of these different groups of nouns have different properties, each making them different in how we use them. Thus, nouns are names of objects, places, people and things. They are used with adjectives to describe something, and with verbs to show an action. Concrete nouns. Concrete nouns are proper nouns and common nouns. Proper nouns. Proper nouns are the names of people, places, groups or dates: as, "Adam", "Boston", "the Hudson", "the Romans", "the Azores", "the Alps". They almost always have a capital letter as their first letter. Example: Common nouns. Common nouns are the names of a sort, kind, or class, of beings or things: as, "beast", "bird", "fish", "insect", "creatures", "persons", "children". They often refer to objects or things which we can see, touch and feel, like the word "chair". Example: Individual nouns. Their refer to only one thing of the same kind, for eg: man, player, cow, chicken, minister. Collective nouns. Collective nouns are the names of a groups of objects or many individuals together: as, "council", "meeting", "committee", "flock". Example: Abstract nouns. Abstract nouns are the names of some particular qualities considered apart from its substance: as, "goodness", "hardness", "pride", "frailty". They are often names of the things that we cannot touch or see, but are there all the same. Example: Verbal nouns. Verbal nouns or participial nouns are the names of some actions, or states of being; and are formed from a verb, like a participle, but employed as a noun: as, Sui generis. A thing sui generis, (i.e., of its own peculiar kind,) is something which is distinguished, not as an individual of a species, but as a sort by itself, without plurality in either the noun or the sort of thing: as, "galvanism", "music", "geometry". Inflections of Nouns. Nouns have modifications of genders, numbers, and cases. Genders. Genders, in grammar, are modifications that distinguish objects in regard to sex. There are three genders; the masculine, the feminine, and the neuter: Hence, names of males are masculine; names of females, feminine; and names of things inanimate, literally, neuter. Numbers. Numbers, in grammar, are modifications that distinguish unity and plurality. There are two numbers; the singular and the plural. The singular number is that which denotes but one: as, The plural number is that which denotes more than one: as, Regular plurals. The plural form is usually represented orthographically by adding "s" to the singular form. The phonetic form of the plural morpheme is by default. When the preceding sound is a voiceless consonant, it is pronounced . Examples: "boy" makes "boys"; "girl", "girls"; "chair", "chairs"; "cat", "cats". Where a noun ends in a sibilant sound, the plural is formed by adding "es" (pronounced ), which is spelled "es" if the word does not already end with "e": "glass" makes "glasses"; "dish, dishes; witch, witches; phase, phases; judge, judges". Most nouns ending in "o" preceded by a consonant also form their plurals by adding "es" (pronounced ): "hero" makes "heroes"; "potato, potatoes; volcano, volcanoes". Nouns ending in a "y" preceded by a consonant drop the "y" and add "ies" (pronounced ): "cherry" makes "cherries"; "lady, ladies". Proper nouns (particularly those for people or places) ending in a "y" preceded by a consonant form their plurals regularly: "Harry" makes "Harrys"; "Germany, Germanys". This does not apply to words that are merely capitalised common nouns: as, "P&O Ferries". A few common nouns ending in a "y" preceded by a consonant form their plurals regularly: "henry" makes "henrys"; "zloty, zlotys". Words ending in "ey" form their plurals regularly, in order to avoid the unpleasant-appearing vowel sequence "eie": "monkey, monkeys". Almost-regular plurals. Many nouns of Italian or Spanish origin are exceptions to the oes rule: "canto" makes "cantos"; "piano, pianos; portico, porticos; quarto, quartos; solo, solos". Many nouns ending in a voiceless fricative mutate that sound to a voiced fricative before adding the plural ending. In the case of changing to the mutation is indicated in the orthography as well: "calf" makes "calves"; "bath, baths; mouth, mouths; house, houses". Some retain the voiceless consonant: "proof" makes "proofs"; "moth, moths; place, places; dwarf, dwarfs or dwarves; hoof, hoofs or hooves; staff, staffs or staves; turf, turfs or turves; roof, roofs or rooves". Irregular plurals. There are many other less regular ways of forming plurals. While they may seem quirky, they usually stem from older forms of English or from foreign borrowings. Irregular Germanic plurals. The plural of a few Germanic nouns can also be formed from the singular by adding "n" or "en", stemming from the obsolete weak declension: "ox" makes "oxen"; "child, children". The plural is sometimes formed by simply changing the vowel sound of the singular, in a process called umlaut (these are sometimes called "mutated plurals"): "foot" makes "feet"; "goose, geese; louse, lice; man, men; mouse, mice; tooth, teeth; woman, women". Some nouns have singular and plural alike, although they are sometimes seen as regular plurals: as, "aircraft, sheep, deer, fish, cod, trout, head, cannon". Generally, plurals refer to several species or kinds of animal, while the unmarked plural is used to describe multiple individual animals; one would say "the classification of fishes", but "five fish in an aquarium". Irregular plurals of foreign origin. Such nouns often retain their original plurals. In some cases both forms are still vying: for a librarian, the plural of "appendix" is "appendices"; for physicians, the plural of "appendix" is "appendixes". A radio engineer works with "antennas" and an entomologist deals with "antennae". The "correct" form is the one that sounds better in context. Correctly formed Latin plurals are the most acceptable, in academic and scientific contexts. In common usage, plurals with "s" are sometimes preferred. Cases. Cases, in grammar, are modifications that distinguish the relations of nouns or pronouns to other words. There are three cases; the nominative, the possessive, and the objective. The nominative case. The nominative case is that form or state of a noun or pronoun, which usually denotes the subject of a finite verb: as, The subject of a finite verb is that which answers to who or what before it: as, Boy is therefore here a noun in the nominative case, or nominative. For example: The possessive case. The possessive case is that form or state of a noun or pronoun, which usually denotes the relation of property: as, Boy is here a noun in the possessive case, or possessive. The possessive case of nouns is formed, in the singular number, by adding to the nominative "s" preceded by an apostrophe; and, in the plural, when the nominative ends in "s", by adding an apostrophe only: as, singular, boy's; plural, boys'; sounded alike, but written differently. The objective case. The objective case is that form or state of a noun or pronoun which usually tells the object of a verb, participle, or preposition: as, The object of a verb, participle, or preposition, is that which answers to whom or what after it: as, Boy is therefore here a noun in the objective case, or objective. The nominative and the objective of nouns, are always alike in form, being distinguishable from each other only by their place in a sentence, or by their simple dependence according to the sense. For example: The declension of nouns. The declension of a noun is a regular arrangement of its numbers and cases. Thus: A short syntax. The subject must be in the nominative case, as "You say it." The subject is placed before the attribute, as "Peace dawned on his mind," except the following cases: a question, as "How many loaves have you?" imperative mood, as "Go you," strong feeling, as "May she be happy!" a supposition, as "Were it true," "neither" or "nor", as "Neither shall you touch it," emphasis, as "Here am I," no regimen, as "Echo the mountains round," dialogue, as "My name is Hassan," and the adverb "there", as "There lived a man." A noun in apposition is put in the same case as the noun it explains, as "But he, our gracious master, knows us." A possessive is governed by the name of the thing possessed, as "Man's life." A possessive comes immediately before the governing noun, as "Nature's peace," except the following cases: an intervening adjective, as "Flora's earliest smells," affirmation or denial, as "The book is not John's," a possessive without sign, as "Brother Absalom's house," or "David and Jonathan's friendship." The predicate is governed by attribute in objective case, as "I found her." A noun or a pronoun put after a non-transitive verb or participle, agrees in case with a preceding noun or pronoun referring to the same thing, as "The child was named John." The case of absolute noun or pronoun depends on no other word, as "Your fathers, where are they?"

Organic Chemistry/Analytical techniques/Elemental analysis. Elemental analysis is the process for determining the partial or complete chemical formula for a substance. Most commonly, it involves the complete combustion in air or oxygen of the substance and then quantifying the amount of elemental oxides produced. In the case of organic compounds, the carbon is converted to carbon dioxide and the hydrogen to water. From these, the percent carbon and percent hydrogen in the substance can be found and compared with a proposed chemical formula for the substance at hand. Element test: Put a small amount of the solid into a small piece of Na metal then roll it around the solid, followed by introduction into a fusion tube. The tube is heated with a gentle flame at a slow rate (in order not to evaporate N2 present in solid) then strong heating till the bottom of the tube become red hot. The tube is then put in a beaker containing a minimal amount of water then heated, cooled, filtered and the filtrate divided into three parts. 1. Test for nitrogen: The filtrate and ferrous sulfate are boiled and cooled and dilute sulfuric acid is added. If green or blue color occurs the solid contain nitrogen. The chemistry behind what happened:<br> Na+C+N --> NaCN<br> FeSO4+NaCN gives Fe[CN]2<br> Fe[CN]2+4NaCN give the complex Na4[Fe(CN)6]<br> ferrous oxidizes to ferric by the acid so 3Na4[Fe(CN)6]+4Fe3+ --> Fe4[Fe(CN)6]3 2. Test for sulfur: The filtrate is exposed to dilute acetic acid and lead acetate, yielding a brown or black precipitate. The chemistry behind what happened:<br> Na+S --> Na2S<br> Na2S +Pb(CH3CO2H)2 yields lead sulfide, a black precipitate. or: The filtrate and sodium nitro prusside yield a violet color Na2S+Na2[Fe(CN)5NO] --> Na4[Fe(CN)5NOS] = violet color 3. Test for chlorine: a) In the absence of N or S: The filtrate is exposed to dilute nitric acid and silver nitrate. Formation of a white precipitate suggests the presence of chlorine. b) In the presence of N and/or S : The filtrate is exposed to dilute sulfuric acid then boiled to 1/3 initial volume and cooled. Formation of a white precipitate after the addition of dilute nitric acid and silver nitrate suggests the presence of chlorine. Equations: NaCN+AgNO3 --> AgCN white ppt<br> Na2S+AgNO3 gives Ag2S black ppt<br> In the presence of N or S these two precipitates may interfere with the white colour of the result of the chlorine test. Therefore dilute sulfuric acid is added because in the presence of N or S: Na2S+ dilute H2SO4 gives H2S gas NaCN+ dilulte H2SO4 gives HCN gas There is no interference with the white colour expected from the chlorine test in solid.

Organic Chemistry/Analytical techniques/Chromatography. Chromatography involves the physical separation of a mixture of compounds. Chromatography can be used as a purification method but also sees wide use for the identification of compounds based on their chromatographic behavior. =Theory= There are many variations of chromatography, but all involve the dissolution of an analyte into a fluid known as the mobile phase and the passage of this fluid solution across a stationary phase, often a solid or liquid-coated solid. As the mobile phase comes into contact with the stationary phase, some of the analyte molecules dissolve or adsorb onto the mobile phase. The more the molecules of that substance are retained, the slower their progress through the chromatographic apparatus. Different substances will then move through at different rates, ideally resulting in distinctly identifiable retention times for each substance. Commonly used chromatographic techniques are identified through the nature of the stationary and mobile phases used, the method for passing the mobile phase through the apparatus, and how separated components are identified. =Paper chromatography= In paper chromatography the stationary phase is a specialized paper made to absorb water to a high level. The mobile phase is usually water or a concentrated salt solution. Paper chromatography has many uses in forensic chemistry due to it's simplicity and availability. However, paper chromatography is limited by the characteristics that only water soluble components can be separated and inaccuracy in RF values. This makes paper chromatography mostly useful to distinguish the differences between two residues rather than their similarities. =Thin layer chromatography= In thin layer chromatography (TLC) a plastic or glass plate is coated with the stationary phase, often alumina, silica, or alkylated silica. The analyte is dissolved in a quick-drying solvent and spotted near the bottom of the plate. The edge of the plate beneath the spot or spots is then dipped and left in a solution of the mobile phase, either an organic solvent or aqueous solution (depending on the nature of the analyte and stationary phase). Capillary action is then allowed to draw the solvent front through the spotted analyte, carrying with it and in the process separating out the analyte's components. =Gas chromatography= In gas chromatography (GC) the analyte and mobile phase must both be gases or be readily introduced into the gas phase by heating. The mobile phase gas must be inert and not reacting with the sample to be analysed. Examples of inert gases are helium and nitrogen gas; while not as inert as helium and nitrogen, hydrogen may also be used. The gases are passed through a long, narrow (and most often, coiled) tube either packed with a porous stationary phase or whose inner walls are coated with a stationary phase, and the analyte components are detected as they emerge from the far end of the tube. The tube is commonly known as GC column. Often a time-varying temperature gradient, from lower temperature to higher temperature, is applied to the tube. This first allows the analyte components to partition into the stationary phase and then, as the temperature rises, to differentially force them back into the mobile phase. Common detectors for gas chromatography are flame ionization detector (FID), electron capture detector (ECD) and mass spectrometry (MS). Different types of sample analysis would require the use of a different type of detectors. =Column chromatography= Column chromatography, like gas chromatography, uses a tube packed with a stationary phase, but the mobile phase is a liquid instead of a gas (It is sometimes known as liquid chromatography or LC). Instead of temperature gradients, a gradient in the composition of the liquid phase can be used to separate components. Column chromatography can be performed on larger molecules which may not be readily introduced into the gas phase. On the other hand, because of the increased viscosity of liquids compared with gases, liquid chromatography can be a more ponderous process. HPLC (variously "high-pressure liquid chromatography" or "high-performance liquid chromatography") speeds the process and improves its selectivity and sensitivity to a significant degree by forcing the mobile phase through the chromatographic column with high-pressure pumps. =Detection methods= The root of the word chromatography, "chroma" (Greek khrōma, color) and grafein is "to write", indicates that the separated components in some forms of the technique can be identified by their color alone. But chromatography has now long been performed on colorless compounds that can be identified in other ways. Analyte components on thin-layer chromatography plates are often identified under ultraviolet light, or by chemical staining in, for example, an iodine chamber or potassium permanganate. Gas chromatographic analytes are detected by changes in the ionization levels of a flame at the output end of the column or by changes in the electrical conductivity of the gas mixture at the end of the column. Liquid chromatography fractions are often analyzed through spectrophotometric techniques, notably UV-visible spectroscopy. When separation with GC or LC is performed in tandem with mass spectrometry (the "hyphenated" techniques of GC-MS and LC-MS), masses of individual fractions are rapidly determined. These methods are frequently employed in analytical and forensic science.

Botany/Introduction Botany. Chapter 1 Botany as a Science. Botany is the branch of biology concerned with the scientific study of plants. Traditionally, botanists studied all organisms that were not generally regarded as animal. However, advances in our knowledge about the myriad forms of life, especially microbes (viruses and bacteria), have led to spinning off from Botany the specialized field called Microbiology. Still, the microbes are usually covered in introductory Botany courses, although their status as neither animal nor plant is firmly established. Plants are living entities, and material presented within "Biology" will have relevance here, most particularly at the cellular and subcellular levels of organization (Chapter 2). Both plants and animals deal with the same problems of maintaining life on planet Earth — their approaches seem quite different, but the end result is the same: continued existence in an organized state, as part of a universe whose tendency is towards greater disorganization. Back on Earth, however, it is a fact that microbes, plants, and animals comprise a very interdependent system. We divide them apart, because our minds work best that way. We categorize and learn common features or properties of the categories. This approach is neither right nor wrong, but is clearly efficient for our minds. Nonetheless, it is desirable to regularly step back and realize that the boundaries between categories are often just constructs, and exceptions to our categories usually abound. It was alluded to in the opening definition that Botany is a science. Just what makes Botany, or anything else a science? It is important to acquire a grasp of the fundamentals of science itself to fully appreciate both how botanical knowledge was gained as well as how it can be used. It usually becomes uninteresting to acquire facts simply for the sake of knowing. Humans do not just appreciate mountains "because they are there", they climb them because they are there! Living Systems. Biology is defined as the study of life, and Botany is that discipline within Biology concerned with the study of living organisms called plants and with certain other living things that have been traditionally studied with plants i.e. Fungi and Algae. Defining 'Plant'. Like many words in common usage that apply to biological entities or concepts, the term plant is more difficult to define than might be at first obvious. Although botanists describe a Kingdom Plantae, the boundaries defining members of Plantae are more inclusive than our common concept of a "plant". We are tempted to regard "plant" as meaning a multicellular, eukaryotic organism that generally does not have sensory organs or voluntary motion and has, when complete, a root, stem, and leaves. However, botanically only vascular plants have a root, stem, and leaves, and even some vascular plants, such as certain carnivorous plants and duckweed, fall afoul of that definition. But to be fair, the vascular plants are the plants we tend to encounter every day and that most people would readily regard as "plants". A more significant point of departure between Plantae and plants occurs among the seaweeds. Technically, only a relatively minor group of seaweeds (the chlorophytes or green algae) are members of the Kingdom Plantae. The majority of seaweeds, like the kelps (very large brown algae from the Order Laminariales), despite a superficial appearance of such, lack true stems, leaves, roots, and any kind of vascular systems as found in higher plants. Thus, the kelps are not Plantae; but are they plants? Certainly if we regard the green algae as plants, it is difficult to exclude the more prominent red and brown algae of our coastal waters. Another, much broader definition for "plant" is that it refers to any organism that is photoautotrophic—produces its own food from raw inorganic materials and sunlight. This is not an unreasonable definition, and is one that focuses on the role plants typically play in an ecosystem. However, there are photoautotrophs among the Prokaryotes, specifically photoautotrophic bacteria and cyanophytes. The latter are sometimes called (for good reasons) blue-green algae. Then there arises the problem that many people would consider that a mushroom is a plant; a mushroom is the fruiting body of a fungus (Kingdom Fungi) and not "photoautotrophic" at all, but "saprophytic". However, there are more than a few species of flowering plants, fungi, and bacteria that are not autotrophic, but "parasitic". We cannot hope to offer a firm answer. The list of characteristics that separate the Plantae from the other biological kingdoms provides at least a technical definition, but realize it is only a technical definition. The problem this lack of precision or agreement in the definition of "plant" presents is one of understanding statements, often encountered in "Wikipedia" (and other) articles, of the sort: "...xylem is one of the two transport tissues of plants". In general it cannot be assumed this means all plants, algae through flowering plants. It very probably does not include fungi or bacteria. Indeed, it is usually safest to assume the discussion is about vascular plants (essentially the ferns, conifers, flowering plants, and a few others; see discussion below on "General Terminology") unless stated differently (e.g., "...in vascular and non-vascular plants this is "such and such). Plants as Organisms. The distinction between life and non-life is not as easily made as you might think. There exist intracellular "parasites" that are progressively less alive in terms of being metabolically active. Plants and their Uses. There can be no disputing the fundamental significance of plants to the ecology of our planet. Photosynthetic plants utilize energy arriving from the sun to create complex organic molecules from inorganic substances, and by this process contribute oxygen to the atmosphere. Advanced animal life is very much dependent upon this source of oxygen, as well as the organic molecules that form the basis of nearly every food web on the planet. However, humans utilize plants in many ways, especially as sources of pleasure, food, and material for shelter, clothing, and more. Consider here the role plants play in our everyday lives and in our economy. Introduction to Plant Classification. At the beginning of this chapter it was suggested that each of us categorizes information we encounter on a daily basis. Our minds seem to want to find relationships between facts and observations, to erect mental bins in which to place new items with previous "facts". This natural human process is the basis for prejudice, in as much as "facts" categorized together can become strongly associated. But these are personal constructs. In order for scientists of many races, speaking many languages, and coming from all manner of backgrounds and experiences to work productively together to solve common problems, the objects with which they work must be classified within a universally accepted framework. The classification of living things is called systematics, or taxonomy, and ideally should reflect the evolutionary history (phylogeny) of the different organisms. Taxonomy arranges organisms in groups called taxa, while systematics seeks clues to their relationships. The dominant system of "Scientific Classification" is called Linnaean taxonomy, and includes classification ranks as well as an organism naming convention called binomial nomenclature. Traditionally, all living things were divided into five kingdoms: However, this five-kingdom system has been replaced by Carl Woese's three-domain system, which focuses on phylogenic roots and comparison of DNA structures. The older approach utilized visual observation as the basis of classification. The three domains reflect whether cells have nuclei (eukaryotic) or not (prokaryotic), as well as differences in cell membranes and cell walls. Recall (and review as necessary) how these groupings relate to the sequence of events in the evolutionary history of life as summarized in . You will return to the subject of Scientific Classification to consider in much more detail the groups of organisms studied in Botany, beginning with Chapter 7. First, however, we shall turn our attention to the structure and function of cells and eventually to gain an understanding of plant structure ("plant anatomy") and function ("plant physiology"). General Terminology. In Section II of this text we will delve much deeper into "plant" systematics. But you should be aware of some general terms related to classificatory schemes that are used regularly in discussing plants. You have probably encountered these terms many times, although may not be aware of their exact definitions. For example, much of the material in Section I of this textbook is biased towards flowering plants. That is, much of the descriptive material here as well as at Wikipedia refers specifically to these. Flowering plants are angiosperms; plants that have flowers and produce seeds, and comprise the majority of the plants we would normally encounter in say a nursery if not on the street, field, or empty lot. Seed-bearing plants include both the angiosperms and the gymnosperms, the latter now treated as a modern group called conifers. The conifers are also common plants, especially in higher latitudes, but bear cones instead of flowers. Both conifers and flowering plants develop vascular tissues internally that conduct fluids (especially water) throughout the plant. Included in the vascular plants are ferns. Ferns have vascular tissue, but reproduce by spores. They do not produce seeds and do not bear flowers.

Botany/Plant cells. Chapter 2 Chapter 2. Plant Cells Introduction. A cell is a very basic structure of all living systems, consisting of protoplasm within a containing cell membrane. Only entities such as viruses— on the boundary between non-living chemicals and living systems—lack cells or basic cell structure. All plants, including very simple plants called "algae", and all animals are made up of cells, and these are organized in various ways to create structure and function in an organism. Biologists recognize two basic types of cells: prokaryotic and eukaryotic. "Prokaryotic cells" are structurally more simple. They are found only in single-celled and some simple, multicellular organisms (all bacteria and some algae, which all belong to Bacteria and Archaea domains). "Eukaryotic cells" are found in most algae, all higher plants, fungi, and animals (Eukarya domain). Thus, differences between these two cell types are critical to how an organism is classified, and an important consideration in the evolutionary sequence of life on the planet Earth. Plant Cell Structure. Nearly all cells are too small to be seen with the unaided eye. As always there are some exceptions, but generally magnification is required to detect a cellular structure. In plants, a good hand-lens or loupe (see photo at right) will sometimes suffice, but in working with cells or observing how cells are organized to form tissues and structures, a high power is used. Questions: Basic Cell Function. You should, by now, have a general appreciation for the complexity of cellular structure. Improvements in microscopy, especially development of the , have revealed that cells are not merely membranous sacks containing fluid of gel-like consistency. The degree of organization of the cytoplasm into organelles and their membranes should have you convinced that much (perhaps most) of what is really going on around you on this planet is occurring at a scale that is simply inaccessible to your eyes. And while you cannot be expected to directly observe chemical reactions at a molecular scale, contemplate that you cannot, even with powerful optics, directly observe most of the structure where these reactions are somehow controlled to produce outcomes favorable to life—indeed, are life. Hopefully, as you acquire knowledge and become a biologist—a botanist—you will learn to recognize the relevant phenomena by their macroscopic expressions (that which you can readily observe with the unaided eye). To appreciate basic cell function, it is necessary to first list the processes or outcomes that cells must accomplish to further existence. More specialized functions will be discussed under plant cell structure, as our interest must eventually focus on plants. For now, recall that in your reading you have already encountered these several basic abilities of cells: Now explore each in turn. Think initially of a single-celled organism with no special abilities, only a "will" to stay alive and perpetuate itself. Remember, the environment will not be kind. The cell must grow and reproduce to counter the tendency of outside forces to breakdown molecular structure and destroy life. Then consider the situation where a cell is part of a multicellular organism, and may be performing more limited and specialized functions. Questions: Plant Cell Specializations. We will learn about the cells of algae and other organisms (e.g., bacteria and fungi) traditionally covered within Botany in later chapters on those organisms (Chapters 5 - 7). Here, we concentrate on the cells of plants. The simplest type of plant cell is called a parenchyma cell and most of the basic metabolic and reproductive processes of the plant occur in these cells. A term for "parenchyma" cells with chloroplasts, is chlorenchyma cells. Other plant cell types that we shall be considering are: Laboratory Exercises for Chapter 2 »<br> Discussion of questions for Chapter 2 »> Energy. How does plant cells get its energy? It gets its energy nutrients. With those nutrients, they gather the energy through sunlight. They use photosynthesis to convert materials into energy for the plants to power its cells.

Botany/Plant structure. Chapter 4 Chapter 4. Plant Vegetative Organs <br> Introduction. As was noted in the previous chapter, most plant cells are specialized to a greater or lesser degree, and arranged together in tissues. A tissue can be "simple" or "complex" depending upon whether it is composed of one or more than one type of cell. Tissues are further arranged or combined into organs that carry out life functions of the organism. Plant organs include the leaf, stem, root, and reproductive structures. The first three are sometimes called the "vegetative organs" and are the subject of exploration in this chapter. Reproductive organs will be covered in Chapter 5. The relationships of the organs within a plant body to each other remains an unsettled subject within plant morphology. The fundamental question is whether these are truly different structures, or just modifications of one basic structure (Eames, 1936; Esau, 1965). The plant body is an integrated, functional unit, so the division of a plant into organs is largely conceptual, providing a convenient way of approaching plant form and function. A boundary between stem and leaf is particularly difficult to make, so botanists sometimes use the word shoot to refer to the stem and its appendages (Esau, 1965). The Leaf. The plant leaf is an organ whose shape promotes efficient gathering of light for photosynthesis. The form of the leaf must also be balanced against the fact that most of the loss of water a plant might suffer is going to occur at its leaves (transpiration). Leaves are extremely variable in terms of their size, shape, and adornments (such as small hairs on the face of the leaf). Although the leaves of most plants carry out the same basic functions, there is nonetheless an amazing variety of leaf sizes, shapes, margin types, forms of attachment, ornamentation (hairs), and color. Examine the Leaves (forms) page to learn the extensive terminology used to describe this variation. Consider that there are functional reasons for the modifications from a "basic" type. The Stem. The stem arises during development of the embryo as part of the "hypocotyl-root axis", at the upper end of which are one or more cotyledons and the shoot primordium. The Root. The root is the (typically) underground part of the plant axis specialized for both anchoring the plant and absorbing water and minerals. Basically, there are two types of roots normally spotted for plants grown on ground namely : taproot and fibrous root Most of the material you have read discusses the root organ as found in the angiosperms (flowering plants). However, among the vascular plants, only Psilotales lack such an organ, having instead rhizomes that bear hair-like absorbing structures called rhizoids (Eames, 1936 in Esau, 1965). Questions: 4-1. At this point the conceptual differences between cell types, tissues, organs, and organisms may be somewhat confusing. Using the leaf as an example, describe this structure in a way that considers the cell types, tissues, and organs for that part of the leaf where photosynthesis is concentrated.

GCSE Science/Circuits. GCSE Science/Electricity You've probably done quite a lot of work in basic electrical circuits in lower school, but we will revise them here so don't worry if you've forgotten them. Before we start you need to know a whole host of circuit symbols. Q1)See how many of the following you can name: You should already know about half of them. For the others see here. You need to learn all these symbols by heart, but don't worry about that just yet. It's much easier to learn the symbols if you know what the components actually do, and we will be looking at that later on. What is a circuit? A circuit is a loop in which electricity can flow. Consider a simple circuit with a cell, a switch and a bulb. The current flows from the cell, via the closed switch to the bulb. The bulb lights because the electricity carries energy. But even after the bulb there current still needs to go around the rest of the loop back to the cell. If there is a break "anywhere" in the loop, the bulb will not light. This is a concept that is not all that difficult, yet most people do not understand it. Ask a selection of adults you know and many will say:<br> "Electricity flows from the cell to the bulb, where it gets used up" Q2) What is wrong with the above statement? Q3) Look at the selection of circuits below. What is wrong with each of them? What we have been looking at so far has been largely revision. You should already be familiar with what a circuit is and how it works. Let's now go on to some more advanced work. « Electrolysis | Current, voltage resistance and Ohm's law

Botany/Contributors. Contributors. While Wikibooks offers somewhat clearer opportunities for "authorship" than Wikipedia, there remains the fact that anything put here is really just a contribution, and everyone who furthers the effort is a contributor. In this respect there are no "authors". If you are interested in developing a particular subject within the field of botany as part of this textbook, please start the module and link it here. We will work out the chapter arrangement after you get started. Of course, you can also just expand on an existing chapter. «Return to Contents Page

GCSE Science/Circuits answers. Did you get many right? You should already know, cell, battery, bulb, switch and resistor. You will have to learn the others as well before the exam. «Back

Botany/Plant reproduction. Chapter 5 Chapter 5. Plant Reproduction Vegetative Reproduction. Vegetative reproduction is a type of asexual reproduction—other terms that apply are "vegetative propagation," "clonal growth", or "vegetative multiplication". Vegetative growth is enlargement of the individual plant; vegetative reproduction is any process that results in new plant "individuals" without production of seeds (see "The Seed" below) or spores. It is both a natural process in many, many species as well as one utilized or encouraged by horticulturists and farmers to obtain quantities of economically valuable plants. In this respect, it is a form of cloning that has been carried out by humankind for thousands of years and by "plants" for hundreds of millions of years. Sexual Reproduction. The Flower. The flower is the reproductive organ of plants classified as "angiosperms"—that is, the flowering plants comprising the Division Magnoliophyta. All plants have the means and corresponding structures for reproducing sexually, and these other cases will be explored in later chapters. However, because flowering plants are the most conspicuous plants in almost all terrestrial environments, we justifiably devote this chapter to the flowering plants alone. You will learn how other plant groups (and non-plant groups, such as fungi) reproduce sexually in Section II of "The Guide". The basic function of a flower is to produce seeds through sexual reproduction. Seeds are the next generation, and serve as the primary method in most plants by which individuals of the species are dispersed across the landscape. Actual dispersal is, in most species, a function of the fruit: structural parts that typically surround the seed. But the seed contains the germ of life of the next generation. The Seed and Germination. the primary purpose of the seed is one of preserving the continuity of life—starting a new generation in a new physical location. For large plants (shrubs and trees), this can be especially important because successful germination and growth close to the parent may be difficult or impossible; the established plant monopolizes light and water resources in its immediate vicinity. Seeds can also serve the function of overwintering or surviving harsh conditions. The entire generation—every individual—may die in the Fall or the dry season. In many annual species, only the seed exists during unfavorable dry or cold conditions. The Fruit. The fruit is the actual agent of dispersal in most flowering plants.

GCSE Science/Current, voltage resistance and Ohm's law. Electronics GCSE Science/Electricity What is electricity anyway? So far in this module we have been using words like electricity, current, voltage, and resistance without actually explaining in depth what these words mean. On this page you will learn what these words mean, and how they relate to one another. What is electricity on an atomic level. Let's think about a wire, made of copper. You should already know that it is made of particles called copper atoms, which have a positive nucleus surrounded by negative electrons. We need not concern ourself with the nucleus, because it does not move. They are stuck in a rigid crystal structure. Instead we need to look at the electrons. Copper, like all metals, has some loose electrons. These electrons are not held rigidly by the atoms but are free to roam about anywhere as long as they stay somewhere in the metal. We call them "conduction electrons" because they are the ones that conduct electricity. To see how electric current flows imagine a small petri dish, with an even smaller one glued inside. The channel between the two dishes is then filled with peas. The channel represents the wires in a circuit, the peas the electrons. Charge is the quantity of free charged particles (in this case electrons). The SI unit of charge is the coulomb. You "could" count the electrons, but there are an awful lot of electrons! Each electron carries a "tiny" charge, of −1.602×10-19 coulomb. We can turn this figure on its head and say that if we grouped together 6.2415×1018 electrons we would have −1 coulomb of charge. Electric field. An electric field is a region where an object experiences a force due to its charge. The strength of the electric field (electric field strength E) is described by considering how much force is experienced by a unit charge (a charge of 1 coulomb) when it's placed in the field. The electric field at any point is therefore expressed in newtons per coulomb. Some fields (such as the field between two parallel charged plates) have the same field strength throughout the field - uniform fields. Others (particularly radial fields due to isolated point charges) do not have constant field strength. In a battery there is a negative and positive terminal. The conventional current flows from positive to negative (the large line to the small line). Because opposites attract, these charges in the battery will be attracting each other, but they can not move directly to each other through the battery because of the chemical processes. If there is a complete external circuit, this attraction from the battery will give the free electrons in the metal (i.e. the wire) a force which will make them move. If you think about it these electrons are being forced to the other side of the battery because of this attraction. We call this driving force the Electro-motive Force (e.m.f). Emfs are measured in volts, and are sometimes referred to simply as voltage. The larger the emf (the voltage) the more quickly electrons flow round the circuit. What is the rate of flow of the electrons?...the current. so, a larger voltage means a larger current. Current. Now imagine that you were to put your finger on one pea and push it in a clockwise direction. All the peas would move because they are all touching one another. This is just what happens when an electric current flows. Current is the flow of charged particles (the particles are usually electrons). The SI unit of current is the ampere (symbol A). To understand how current is defined think of standing at a given point in the wire. Electrons are flowing past you. One Ampere is a flow of one coulomb going past every second. Definition of the ampere. BUT this flow of charge idea is NOT the definition of the ampere. The ampere is defined in terms of the force produced between two wires each carrying identical currents:- "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length." Voltage. Having looked at charge and current, we now need to look at what voltage means. As you know, electrons repel each other. If you hold one electron near another electron, you have to push against it to hold it in place. If you try to bring it even closer, you have to do work (force times distance) to get it to that new position. The voltage between one point and another is simply how much work per coulomb is required to move any small test charge from point A to point B. In most electronic components, it doesn't matter much which path the test charge takes in-between point A and point B. Voltage is related to the "energy" of the charges. Let's go back to the peas in the petri dish. They can be pushed slowly or they can be pushed quickly. The faster they go, the more energy they have. It's a similar situation for the electrons, except the push isn't provided by a finger! It's provided by the battery. The battery gives the charges energy. This energy is given up to the various components in the circuit, e.g. bulbs, resistors etc. The energy per unit charge is called the voltage (or the potential difference). Definition of the volt. One volt means one joule of energy per coulomb of charge. More accurately it has 2 definitions: Electromotive Force is the amount of energy converted from non-electrical to electrical form when driving 1 coulomb of charge around a completed and closed circuit. Potential Difference is the amount of energy converted from electrical to non-electrical form when driving 1 coulomb of charge around a completed and closed circuit. The potential difference between 2 points in a conductor is defined as 1 volt, if 1 Joule of energy is converted from electrical form to non-electrical form, when 1 coulomb of charge per second (1 amp) flows through it. Note: This will only occur between 2 points in a conductor, that has a resistance, defined as 1 ohm. See resistance below. Resistance and Ohm's law. Resistance is easy to understand. It's just how difficult it is for the charges to flow through an electrical component or from one point to another in an electrical circuit. Imagine a group of walkers travelling down a road. They approach a fork in the road. To the left is a flat straight road leading to a nearby town. To the right is a huge mountain, over which a steep and winding road traverses. This road also leads to the nearby town. Naturally all the walkers chose the left route. Let's now suppose that there are millions of walkers. They are jam packed on the road, and they are all in a hurry to get to the town as quickly as possible. Now when they come to the fork in the road which way should they go? Most will still go to the left, but a few might chose to go to the right, the road is more difficult but there is no traffic jam, so they might get there quicker. It's a similar thing with moving charges. Like charges repel, so they would rather not pack in very closely together. Some routes, like wires have very low resistance, while other routes like bulbs have much higher resistance. More charges will go down a low resistance route than a high resistance one. The unit of resistance is the ohm, represented by the Greek letter Omega (Ω). Ohm's Law. This law relates resistance, current, and voltage. It's very easy to remember because it's obvious when you think about it. Let's think of a wire carrying current from a battery, to a bulb then back to the battery. The voltage of the battery provides the energy of the flowing electrons. Let's assume we want to increase the rate of flow of charge. Remember that current is the rate of flow of charge so we want to increase the current. So formula_1 Rearranging gives : In symbols: This is Ohm's law. Learn it by heart. Q2) A wire has a resistance of two Ω and a voltage of 3 V is applied. What is the current? Q3) A wire has a 5 V potential difference applied. the current is 10 A, what is the resistance? Q4) A current of 2 A is flowing through a wire with a voltage of 20 V. What is the resistance of the wire? (Remember to give the units for all your answers). Answers | «Circuits | Circuits Part 2»

Botany/Introduction. « Contents Page Introduction to the Botany Study Guide. This "Study Guide to the Science of Botany" is a textbook at Wikibooks shelved at the and intended to establish a course of study in the subject of Botany, utilizing articles provided in Wikipedia, with links to other relevant web sites and other Wikibooks as appropriate. In some cases, portions of the text from "Wikipedia" articles have been used to materially develop introductory text within the Guide. For the new user, it need be pointed out that "Wikipedia" differs from a standard encyclopedia in two important respects: 1) it is a hypertext document, and 2) it is open and editable, and therefore constantly changing. For the student following this or any guide through "Wikipedia" to cover a specific subject, it is recommended that each article (page) be read first in its entirety, before any hyperlinks are followed to other topics or explanations. It is too easy, otherwise, to simply become lost in a maze of links, and miss the main thrust of an article presented as an assignment from the Guide. Because "Wikipedia" is constantly changing (and, it is believed, improving) the quality of each article encountered will be variable. Some articles are well written and go to adequate depth, whereas others, lacking a proponent, are shallow and incomplete. Short or sloppy looking articles may contain questionable facts. These short-comings should diminish with time, but can be a problem for the student. One clear advantage to using this Guide linked to a hypertext like "Wikipedia" is the "circular redundancy with serendipity" factor that arises when an article is read and its hyperlinks followed; this factor can be a powerful learning tool. The persistent reader is subjected to a fairly high degree of repetitive reading, often presenting slightly differing perspectives on the same general topic, with the result that learning comes from redundancy and seeing difficult concepts presented in more than one way. At the same time, some hyperlinks lead down less relevant paths, bringing new and unanticipated knowledge. If, as a student, you are truly interested in mastering the subject of botany, you must be prepared to read beyond the basic assignments; in some cases, beyond Wikipedia to explore other, "outside" web sites. It seems likely that the typical user of the "Study Guide to the Science of Botany" is not necessarily an active student taking a course in botany at the high school (AP) or college level, but a person with a strong interest in plants—an amateur naturalist or a gardener. Therefore the guide must incorporate both the basic biological and physiological aspects of plants as well as extensive taxonomy-based coverage of the diversity of plants and related organisms. The amount of material now available on the web covering the latter subject is becoming nothing short of phenomenal. In effect, one now has access to much of the world's plant diversity, with photographs and descriptions, in many cases from web sites maintained by specialists. One goal of the guide is to provide a systematics-based approach to capturing this kind of information, hopefully giving the student a strong background in plant systematics. The importance of this approach is not that everyone should become a taxonomist—or become more familiar with plant taxonomy, a specialized field of botanical science with a relatively narrow following—but that appreciation for (and understanding of) species diversity is most critical at this time in our earth's history marked by accelerated species extinctions and destruction of native ecosystems by both human population expansion and man-induced spread of non-native species. The "Study Guide to the Science of Botany" includes two other "parallel" documents intended to enhance the usefulness of the Guide. These could also be used separately or independently as source documents for a beginning course in Botany. They are the "Discussion" pages and the "Laboratory Exercise" pages. Both are explained in detail in the next Section titled "How to use this Guide".

Botany/How to use. « Contents Page How to Use the "Botany Study Guide" The purpose of the "Study Guide to the Science of Botany" is to weave - out of the information on Life Science and especially Botany contained in "Wikipedia" - a course of study for the student or layman. It is anticipated that this course will be either supplemental to instruction being received at a school or college, or will be self-directed. In either case, the Guide is not a novel and should not be approached as one. A smooth flow of dialogue is simply not possible and should not be anticipated. The Guide may be closer to the sometimes disjointed notes generated by a student from a lecture or careful reading of a detailed textbook. Within each subsection of a Chapter, introductory text is followed by one or more "reading assignments" of the form: Following (that is "clicking" on) the link (to "Wikipedia" "Botany" in this case) will open an article intended to provide the details of the Chapter subsection. Recommended articles should be read from top to bottom, and then re-read following some or all of the links embedded in the article to other articles for expanded elucidation or to clarify terms; that is, in most cases, completion of an "assignment" (recommended article) includes at least some or all articles linked to the first. Obviously, it cannot be the case that all links are followed to articles, whose links are then followed to articles, and so on until no new material is encountered. It is likely there would be no quick end to such a pursuit. The amount of time spent wandering beyond the original article is partly a personal matter of how much the reader is getting out of the foray than anything else. Realize it is certainly possible to wander well off the subject at hand. As in the example above, notes are provided with assignments giving some direction for pursuing links. An instruction NOT to follow links simply means the additional material will be encountered later in the course of instruction, and going beyond the assigned article may provide too much detail for a beginning student. The following example: specifies that two other links ARE part of the assignment. Other links encountered may be followed to expand your knowledge or, as always, to aid in understanding of technical terms encountered. Hyperlinks included with the text in the Guide are there simply for convenience, usually to topics somewhat peripheral to the main one. In all cases, finding your way back to the Guide may become tricky, but we have to leave this up to you to establish, beyond pointing out that your browser's "Back" button is intended for this purpose. Discussion Questions. At the end of each subsection are posted one to several questions. In general, you will get more out of these questions if you write out your answer on a piece of paper. You may wish to accomplish this on the re-read, allowing each question to guide your quest for an answer. A discussion page for each chapter provides answers to the questions posed. However, the questions are intended to be thought-provoking, and may not have a single straight-forward answer. Answers on the discussion pages are also necessarily much longer than would be expected of any one student; it is expected that each student answer will fit somewhere within the broad discussion presented. Laboratory Exercises. A natural sciences course laboratory unit is supposed to provide hands-on experience in exploring topics raised in the text and lecture units. The best that a website can give towards this goal is a manual that is liberally provided with pictures and diagrams. The student must provide the "hands on" from the neighboring natural world. Fortunately, in botany, this is much easier to accomplish than in almost any other field of science. Both the outdoors, the local market, and (if available) a botanical garden can be sources of materials for study. Indeed, we may teach the structure of a "pome" using an apple in the hope that the student will end up with a pear. In using any of the Laboratory Exercises, it is always best to read through the entire module before actually doing anything. Resist the temptation to view the material as an instruction manual to be followed in a specific order. For one thing it is difficult to write a module that covers, at each step, all that the student should know before proceeding on to the next step. The value of any exercise will be significantly enhanced if you have a pretty good idea where it is going in advance. General Navigation. The "Study Guide" is divided into Sections and Chapters which define the subject material of each module. At the bottom of each text page (main text of a module), is a short version of the Table of Contents, allowing the reader to jump between chapters within a Section. Here is an example of the "Wiki Contents Table" for Section I: Note that at the beginning of each module, links are provided to both the previous chapter and the succeeding chapter, as well as to the main Table of Contents. Links to units associated with a module, as for example to a Laboratory Exercise, appear near the end of the module Final Note. As a final note, read the next Section and consider how you might make a contribution to the Guide.

Botany/Plant structure discussion. Further Discussion. The questions posed in Chapter 3. Plant Structure are discussed further on this page. Remember, some questions are intended to be thought-provoking and more than one answer may be "correct". Question: Photosynthesis is concentrated in the mesophyll of the leaf. The "mesophyll" is a type of "tissue" composed of two layers or arrangements of chlorenchyma cells: an upper pallisade layer of tightly packed parenchyma (called pallisade chlorenchyma), and a lower spongy layer of loosely packed parenchyma (or spongy chlorenchyma). One could regard these layers as different tissue types ("simple tissues") and the mesophyll as a "complex tissue". The mesophyll is packed between two protective layers of epidermal cells (tissue: epidermis of epidermal cells and cuticle), which along with the vascular tissue and perhaps other structural tissues form an "organ" called the leaf whose primary function is food production for the "organsim": the plant. Leaves usually have a stem-like structural part called a petiole by which they attach to another plant organ termed the stem. « Chapter 3

Botany/A final note about the Guide. Botany Both this Guide and all articles in "Wikipedia" are that can be added to or edited by anyone. It is an opportunity for the user of these documents to contribute information, or even state given information more clearly, simply by editing a page. As a student with a textbook and a lecturer (teacher), you may find yourself in possession of useful facts, another point of view on existing facts, or a report you prepared of exceptional quality. Any of these can be added to an appropriate page in this Guide or the "Wikipedia". However, this caution is strongly advised: "Do not place into the Guide any text or pictures taken verbatim (or close to verbatim) from a text book, web site, or other copyrighted source without permission of the copyright holder". In general, this means, anything you submit should be your own work. To learn how to edit or contribute material to this textbook, first read the introduction at: "".

Organic Chemistry/Introduction to reactions/Gibbs free energy. Gibbs free energy is represented by the following equation: The basic principle is that "total" entropy increases. This increase can be because of an increase in the entropy of the chemicals, "ΔS", or because the reaction has produced heat, increasing the entropy of the environment. The Gibbs free energy lets us calculate the total increase in entropy, including the effects on the environment, without needing to know anything about the environment. At "low" temperatures, "ΔG" is approximately "ΔH", and nature favours the reaction with lowest energy products, which release the most heat. This may "reduce" the entropy of the "system", but the "increase" in the entropy of the "environment" more than compensates. At "high" temperatures, "ΔG" is approximately "-TΔS", and nature favours the reaction with high energy products, which may actually absorb heat. This may "reduce" the entropy of the "environment", but the "increase" in the entropy of the "system" more than compensates. Either way, the Gibbs free energy "always" decreases.

Latin/Appendix G. Latin Mottos. Latin External Links. The internet is one of the best media to obtain Latin resources. A few sites to get you started are listed here. ^ Latin ^

Latin/Index II. This Page is incomplete For explanations of terms used in these grammar tables, check the Glossary. Declension of Nouns. 5th Declension Masculine/Feminine (each word has a set gender): res. NOTES 4/5th declensions are modified 3rd declensions, thus behave similarily. 3rd declension is either M/F/N, 4th declension is either M/F/N and 5th declension is either M/F. So for 3rd, 4th, and 5th declension is of most importance to memorise the gender because the adjective will still need to agree (ie have the same) with the noun in both case, gender, and number. The Vocative only changes for the 2nd declension masculine singular (however not for the nouns that leave the -us suffix when in nominative). There are a few exceptions in the 1st declension which are not feminine. Such nouns are poet-a (1st declension masculine, so to agree you need to use -us on the adjective) and naut-a. There are a few second declension nouns with irregularities. It is of most importance that you memorise them. When memorising a noun's meaning, make sure that you also memorise any irregularities the noun has, the gender, and the declension. Without doing this you may have trouble translating. For example, 2nd declension masculines have -us in the nominative singular; however, 4th declension masculines have -us in the nominative singular, nominative plural and accusative plural. This may get you confused if you do not memorise the declension of each noun. Single Declension Theory. If you look at the above list of declensions, you may feel that you are going to be overcome if you have to memorize all of it. Memorization is indeed the key, but it will be easier than you think. Each word in Latin has three parts: the root, the stem vowel, and the ending. There are five vowels in Latin, so there are five stem vowels: A,O,I,U,E. Any word not really having a stem vowel naturally was given to I. If you study the declension patterns enough you will see that there are many similarities in the declensions. All accusative singulars end in "m" except neuters that sometimes still do. All accusative plurals end in 's' except neuters that always end in "a". All genitive plurals end in "um", be it "ium, rum, uum" or whatever else. If you read enough Latin you will actually find that authors would switch a declension of a word at will if it made the sentence clearer. Thus many words that are of the 4th declension were sometimes written as if 2nd, and 5th declension as if 3rd and vice versa. Some ending patterns that we use for one declension may also be used in another, again to make the sentence clearer. Thus "filiabus" would be used in any sentence where we want to make it clear that we are talking about the Daughters and specifically not the Sons. We also see examples of this in "animabus". Some think that the "IS" used in the first and second declensions was actually an abbreviation of "bus". Some students find the ablative difficult since it sometimes looks like the nominative singular, dative plural or neither. All you really need to do to get the hang of this is to know that in the plural, the ablative always looks like the dative. If there is no preposition in front of it then it is probably a dative, unless it is being used in an ablative construction that would likely be apparent. If there is a preposition and it looks like a dative, just remember that no preposition takes a dative, only ever ablative and sometimes accusative. Dative plural plus preposition equals ablative. The ablative singular is really just the root plus the stem vowel with no ending to speak of, since the preposition tells you the grammar of the word. Some students also get confused by words that are the same in the nominative singular and plural. Don't worry about that; the verb will tell you which it is since the verb always agrees with the nominative. It is thought that originally there was only one declension, but during the task of applying it to every word in natural speech it was found that some words naturally changed the way the basic sounds of the original declension worked. Here is one idea of the original basic declension. When speaking in everyday conversation, Latin speakers would shorten the word in their pronunciation so long as it still made sense. If you go to New Orleans you will likely hear someone say 'prowly'. This is not a new dish at a restaurant or a new new code name for the police, it is actually the local pronunciation of the word "probably". It is ok to shorten this word because when it is shortened everyone can still understand it. The Latins did the same thing. It is known that "I" can change to "E" and vice versa, so we can see that pattern in the dative singular of all declensions. The "IS" of the genitive was kept in the 3rd declension, shortened in the 1st, 2nd, and 5th and slightly altered in the 4th. The 'add "M"' rule of the accusative singular is seen in the altering of the stem vowel in the 2nd and 3rd declensions. The "ES" of the nominative plural became "E" in 1st, "I" in 2nd, and "US" in 4th. The "RUM" of the genitive plural was shortened in the 3rd and 4th declensions. The accusative plural as a rule never changes, but keep in mind that neuter words followed a different pattern of using "A" for the accusative plural, and all neuters took the accusative singular or plural for the nominative of the same number. The "BUS" of the dative/ ablative plural was shortened to "IS" in the 1st and 2nd declensions but kept in the others. The 4th declension has a tendency to copy the "IBUS" of the 3rd in some authors but retain the "UBUS" in others. When studying Latin declensions you really should strive to memorize the patterns, but also look to see how they are similar to other patterns in the language as it will help you to remember. Also note that the "IS" of the genitive singular is what eventually gave us the word "HIS" and the 'add 's'" rule of English. Latin also gave us the 'add 's'" to make a plural by way of the accusative plural. If you study other inflexive languages related to Latin, such as Greek, you will notice even similarities across languages.

Latin/Lesson 2-Genitive and Dative. The Genitive. The genitive case is a descriptive case. The genitive case describes the following features of the described noun: Quite simply, a word in the genitive case is translated with the preposition "of". Note that Latin does not have a separate form for the possessive genitive ("Marcus's dog" vs "The dog of Marcus"), as English does. A word in the genitive case showing possession can be translated either way. Exercise 1. Indicate the word in the genitive: Agreeing with the Adjectives. When adjectives are used to describe nouns in the genitive case, they must have the same case, number, and gender as the noun to which it refers. Example. It's that simple. The Dative. The dative case, also known as the indirect object case indicates: Latin does not distinguish between "to" or "for", though this is sometimes the case in English: Example 1. 'For' is the preposition indicating a dative. 'For' can be used in some other constructs. To determine whether it is dative, analyse the meaning of the sentence (see Example 3). Practice will enable you to quickly spot the case of a noun in the sentence without much effort. Example 2. "He gave the book to John"; "He gave to John the book"; or "He gave John the book". This demonstrates how English can use prepositions to change word order and even 'presume' a certain preposition exists that has been left out, giving a dative construct. Also, the dative is used only for a noun Exercise 2: Translate into English. Note that "placeo" requires the dative case, as opposed to the accusative case. Verbs such as this are denoted with "(+dat.)" or similar abbreviations. Roman Numerals. The Romans did not use the Hindu-Arabic numerals we use today. They used their own symbols and own numeric system. We still use Roman Numerals today. Note the declensions of the first three numbers. "Nullus" is the Latin equivalent of zero, for example: "nullam puellam in agro video" means "I see no girl in the field".

Spanish/Exercises/Verbs ser And estar - Solutions. Soluciones a los ejercicios. "Solutions to the exercises" Llena los espacios en blanco con la forma verbal correcta del verbo "ser". "Fill the blank spaces with the correct form of the ver "ser" (to be)." Llena los espacios en blanco con la forma verbal correcta del verbo "estar"."Fill the blank spaces with the correct form of the ver "estar" (to be)." Llena los espacios en blanco con la forma verbal correcta del verbo "ser" o "estar". "Fill the blank spaces with the correct form of the ver "ser" or "estar" (to be)." Enlace a los Ejercicios "Link to exercices" Enlace a la lección 1 "Link to the lesson 1."

Organic Chemistry/Haloalkanes. Haloalkanes are otherwise simple alkanes that contain one or more members of the halogen family. In practice, the halogens found in organic molecules are chlorine (Cl), bromine (Br), fluorine (F), and iodine (I). Some texts refer to this class of compounds as halogenoalkanes or alkyl halides. This text (and the chemical literature) will frequently use the terms haloalkane and alkyl halide interchangeably. "Note:" The X in R-X represents a generic halogen atom. =Preparation= Methods for preparation are found elsewhere in this text: =Properties= Naming Haloalkanes. Haloalkanes are named by adding a prefix to the name of the alkane from which they are derived. The prefix denotes the particular halogen used. F = "Fluoro-"<br> Cl = "Chloro-"<br> Br = "Bromo-"<br> I = "Iodo-"<br> If other substituents need to be named, all prefixes are still put in alphabetical order. When necessary, numbers identify substituent locations. Physical properties. R-X bond polarity: C—F > C—Cl > C—Br > C—I The difference in electronegativity of the carbon-halogen bonds range from 1.5 in C-F to almost 0 in C-I. This means that the C-F bond is extremely polar, though not ionic, and the C-I bond is almost nonpolar. Physical appearance: Haloalkanes are colourless when pure. However bromo and iodo alkanes develop colour when exposed to light. Many volatile halogen compounds have sweet smell. Boiling point: Haloalkanes are generally liquids at room temperature. Haloalkanes generally have a boiling point that is higher than the alkane they are derived from. This is due to the increased molecular weight due to the large halogen atoms and the increased intermolecular forces due to the polar bonds, and the increasing polarizabilty of the halogen. For the same alkyl group, the boiling point of haloalkanes decreases in the order RI > RBr > RCl > RF.This is due to the increase in van der Waals forces when the size and mass of the halogen atom increases. For isomeric haloalkanes, the boiling point decrease with increase in branching. But boiling points of dihalobenzenes are nearly same; however the para-isomers have higher melting points as it fits into the crystal lattice better when compared to ortho- and meta-isomers. Density: Haloalkanes are generally more dense than the alkane they are derived from and usually more dense than water. Density increases with the number of carbon and halogen atom. It also increases with the increase in mass of halogen atom. Solubility: The haloalkanes are only very slightly soluble in water, but dissolves in organic solvents. This is because for dissolving haloalkanes in water the strong hydrogen bonds present in the latter has to be broken. When dissolved in organic (non polar) solvents, the intermolecular attractions are almost same as that being broken. Bond Length: C—F < C—Cl < C—Br < C—I Larger atoms means larger bond lengths, as the orbitals on the halogen is larger the heavier the halogen is. In F, the orbitals used to make the bonds is 2s and 2p, in Cl, it's 3s and 3p, in Br, 4s and 4p, and in I, 5s and 5p. The larger the principal quantum number, the bigger the orbital. This is somewhat offset by the larger effective nuclear charge, but not enough to reverse the order. Chemical properties. Bond strength: C—F > C—Cl > C—Br > C—I The orbitals C uses to make bonds are 2s and 2p. The overlap integral is larger the closer the principal quantum number of the orbitals is, so the overlap is larger in the bonds to lighter halogens, making the bond formation energetically favorable. Bond reactivity: C—F < C—Cl < C—Br < C—I Stronger bonds are more difficult to break, making them less reactive. In addition, the reactivity can also be determined by the stability of the corresponding anion formed in solution. One of the many trends on the periodic table states that the largest atoms are located on the bottom right corner, implying that iodine is the largest and fluorine being the smallest. When fluorine leaves as fluoride (if it does) in the reaction, it is not so stable compared to iodide. Because there are no resonance forms and inductive stabilizing effects on these individual atoms, the atoms must utilize their own inherent abilities to stabilize themselves. Iodide has the greatest surface area out of these four elements, which gives it the ability to better distribute its negative charge that it has obtained. Fluorine, having the least surface area, is much more difficult to stabilize. This is the reason why iodine is the best leaving group out of the four halogens discussed. =Reactions= Determination of Haloalkanes: A famous test used to determine if a compound is a haloalkane is the Beilstein test, in which the compound tested is burned in a loop of copper wire. The compound will burn green if it is a haloalkane. The numbers of fluorine, chlorine, bromine and iodine atoms present in each molecule can be determined using the sodium fusion reaction, in which the compound is subjected to the action of liquid sodium, an exceptionally strong reducing agent, which causes the formation of sodium halide salts. Qualitative analysis can be used to discover which halogens were present in the original compound; quantitative analysis is used to find the quantities. Substitution reactions of haloalkanes. R-X bonds are very commonly used throughout organic chemistry because their polar bonds make them reasonably reactive. In a substitution reaction, the halogen (X) is replaced by another substituent (Y). The alkyl group (R) is not changed. Substitutions involving haloalkanes involve a type of substition called Nucleophilic substitution, in which the substituent Y is a nucleophile. A nucleophile is an electron pair donor. The nucleophile replaces the halogen, an "electrophile", which becomes a leaving group. The leaving group is an electron pair acceptor. Nuclephilic substition reactions are abbreviated as SN reactions. Example: Suggest a reaction to produce the following molecule. Answer: OR "Any halogen could be used instead of Br" Reaction mechanisms. Nucleophilic substitution can occur in two different ways. SN2 involves a backside attack. SN1 involves a carbocation intermediate. SN2 mechanism SN1 mechanism Comparison of SN1 and SN2 mechanism. Stereochemistry: <br> SN2 - Configuration is inverted (i.e. R to S and vice-versa). <br> SN1 - Product is a mixture of inversion and retention of orientation because the carbocation can be attacked from either side. In theory the products formed are usually racemic due to the 50% chance of attack from the planar conformation. Interestingly, the amount of the inverted product is often up to 20% greater than the amount of product with the original orientation. Saul Winstein has proposed that this discrepancy occurs through the leaving group forming an ion pair with the substrate, which temporarily shields the carbocation from attack on the side with the leaving group. <br> Rate of reaction:<br> SN2 - Rate depends on concentrations of both the haloalkane and the nucleophile. SN2 reactions are fast.<br> SN1 - Rate depends only on the concentration of the haloalkane. The carbocation forms much slower than it reacts with other molecules. This makes SN1 reactions slow.<br> Role of solvent:<br> SN2 - Polar aprotic solvents favored. Examples: Acetone, THF (an ether), dimethyl sulfoxide, n,n-dimethylformamide, hexamethylphosphoramide (HMPA).<br> Nonpolar solvents will also work, such as carbon tetrachloride (CCl4)<br> Protic solvents are the worst type for SN2 reactions because they "cage," or solvate, the nucleophile, making it much less reactive.<br> SN1 - Polar protic solvents favored. Examples: H2O, Formic acid, methanol.<br> Aprotic solvents will work also, but protic solvents are better because they will stabilize the leaving group, which is usually negatively charged, by solvating it. Nonpolar solvents are the worst solvent for SN1 reactions because they do nothing to stabilize the carbocation intermediate.<br> Role of nucleophile:<br> SN2 - Good nucleophiles favored<br> SN1 - Any nucleophile will work (since it has no effect on reaction rate)<br> Carbocation stability:<br> 3° carbon - most stable = SN1 favored<br> 2° carbon - less stable = either could be favored<br> 1° carbon - seldom forms = SN2 favored<br> CH3+ - never forms = SN2 favored<br> The reason why the tertiary carbocation is most favored is due to the inductive effect. In the carbocation intermediate, there is a resulting formal charge of +1 on the carbon that possessed the haloalkane. The positive charge will attract the electrons available. Because this is tertiary, meaning that adjacent carbon atoms and substituents are available, it will provide the most electron-density to stabilize this charge. Example. Predict whether the following reactions will undergo SN2 or SN1 and tell why. 1: 2: 3: Answers:<br> 1) SN2. Good nucleophile, polar solvent.<br> 2) SN1. Tertiary carbon, polar solvent. Very slow reaction rate.<br> 3) SN2. Primary carbon, good nucleophile, nonpolar solvent.<br> Grignard reagents. Grignard reagents are created by reacting magnesium metal with a haloalkane. The magnesium atom gets between the alkyl group and the halogen atom with the general reaction as stated below: R-Br + Mg → R-Mg-Br Gringard reagents are very reactive and thus provide a means of organic synthesis from haloalkanes. For example, adding water gives the alcohol R-OH. Basic: R-X + Mg → R-Mg-X For example (X=Cl and R=CH3): CH3-Cl + Mg → CH3MgCl Elimination reactions. With alcoholic potassium hydroxide, haloalkanes lose H-X and form the corresponding alkene. Very strong bases such as KNH2/NH3 convert vic-dihalides (haloalkanes with two halogen atoms on adjacent carbons) into alkynes.

US History/Early Colonial Period. The Arrival of Columbus. Christopher Columbus and three ships - the "Niña", the "Pinta", and the "Santa Maria" - set sail on August 3, 1492. On October 12, a lookout cried out that he had sighted land. The crew set foot on an island that day, naming it San Salvador. It is unknown which exact island was discovered by Columbus. (Note that the island presently called San Salvador is so-called in honor of Columbus' discovery; it is not necessarily the one on which Columbus set foot.) The Native Americans inhabiting the islands were described as "Indians" by Columbus, who had believed that he had discovered the East Indies (modern Indonesia). In reality, he had found an island in the Caribbean. He continued to explore the area, returning to Spain. Columbus' misconception that he found Asia was corrected years later by the Italian explorer Amerigo Vespucci, after whom "America" may be named. The Protestant Reformation. In Europe, the power of the Pope and the influence of Catholicism was undoubted. The Catholic religion affected every aspect of politics on the continent. However, in the sixteenth century, the conditions were ripe for reform. Gutenberg's printing press made the spread of ideas much easier. The influence of nationalism grew, and rulers began to resent the power possessed by the Pope. The Protestant movement may have commenced earlier, but the publication of "Ninety-Five Theses" by Martin Luther in 1517 spurred on the revolution within the Church. Luther attacked the Church's theology, which, he believed, misrepresented The Bible and placed too much authority in the hands of the clergy, and wished to reform the Church. After being excommunicated, Luther published many books on Reform. Luther's works were most influential in Germany and Scandinavia. Persons other than Luther championed the cause of Reform. In Switzerland, Huldreich Zwingli advanced Protestant ideas, which mostly affected his home country. Similarly, Frenchman John Calvin helped the spread of Protestantism in France and the Netherlands. English Protestantism resulted from the direct influence of the British monarch. Henry VIII (1509-1547) sought to divorce his wife, Catherine of Aragon, because she had failed to produce a viable male heir to the throne. When his divorce led to excommunication by the Pope, Henry simply declared the entire country free of Catholic domination and a bastion of Protestantism. Henry reasoned that England could survive under its own religious regulation (Anglican) and he named himself head of the church. Elizabethan England. Elizabethan Succession<br> After Henry VIII died, he was succeeded by his son Edward VI (1547-1553) who reigned briefly before dying. Edward's death led to the ascension of Henry's daughter by Catherine, Mary I (1553-1558). A staunch Catholic, Mary sought to return England back to the Catholic church. Her religious zeal and persecution of Protestants earned her the nickname, "Bloody Mary." After a short reign, she was succeeded by her half-sister, Elizabeth. Elizabeth I (1558-1603) was the daughter of Henry's second wife, Anne Boleyn. Her ascendency to the throne resulted when neither of her half siblings, Edward and Mary, produced an heir to the throne. Religious Reform<br> Under her siblings' reign, the nation constantly battled religious fervor as it sought to identify itself as either Protestant or Catholic. Henry VIII had severed ties with the Roman Catholic Church upon his excommunication after divorcing Catherine of Aragon. He established the Church of England (the precursor to the Anglican Church) as the official state religion and named himself, not the Pope, as its head. Under Mary, the country returned to Catholic rule. The Elizabethan Age brought stability to English government. Elizabeth sought a compromise (the Elizabethan Settlement) which returned England to a nation governed by Protestant theology with a Catholic ritual. Elizabeth called Parliament in 1559 to consider the Reformation Bill that re-established an independent Church of England and redefined the sacrament of communion. Parliament also approved the Act of Supremacy, establishing ecclesiastical authority with the monarch. Economic Reform<br> Elizabeth's far more important response was to stabilize the English economy following the 1551 collapse of the wool market. To respond to this economic crisis, Elizabeth used her power as monarch to shift the supply-demand curve. She expelled all non-English wool merchants from the empire. Her government placed quotas on the amount of wool that could be produced while also encouraging manors to return to agricultural production. She also started trading directly with the Spanish colonies in direct violation of their tariff regulations. This maritime violation would later result in an attack on England by the Spanish Armada in 1588. Queen Elizabeth was a very popular monarch. Her people followed her in war and peace. She remained unmarried until her death, probably through a reluctance to share any power and preferring a series of suitors. This gave her the name, "the Virgin Queen," and in honor of her, a colony was named "Virginia" a few years after her death. In the aftermath of the Armada's overwhelming defeat and building on the development of a strong fleet started by Henry VIII, England began to gain recognition as a great naval power. Nationalism in England increased tremendously. Thoughts of becoming a colonial power were inspired. These thoughts were aided by the fact that the defeated Spanish lost both money and morale, and would be easy to oppose in the New World. Early Colonial Ventures. Richard Hakluyt In 1584, Richard Hakluyt proposed a strong argument for expansion of English settlement into the new world. With his "Discourse Concerning Western Planting," Hakluyt argued that creating new world colonies would greatly benefit England. The colonies could easily produce raw materials that were unavailable in England. By establishing colonies, England would assure itself of a steady supply of materials that it currently purchased from other world powers. Second, inhabited colonies would provide a stable market for English manufactured goods. Finally, as the economic incentives were not enough, the colonies could provide a home for disavowed Englishmen. Roanoke The English had already begun the exploration of the New World prior to the Armada's defeat. In 1584, Queen Elizabeth granted Sir Walter Raleigh a charter authorizing him to explore the island of Roanoke, which is part of what is now North Carolina. Between 1584 and 1586, Raleigh financed expeditions to explore the island of Roanoke and determine if the conditions were proper for settlement. In 1586, about a hundred men were left on the island. They struggled to survive, being reduced to eating dogs. They were, however, rescued- except for fifteen men whose fate remained a mystery. After another expedition in 1587, another group of men, women, and children- a total of more than one-hundred people- remained on the island. Governor John White of the Roanoke colony discovered from a local Native American tribe that the fifteen men who were not rescued were killed by a rival tribe. While attempting to gain revenge, White's men killed members of a friendly tribe and not the members of the tribe that allegedly killed the fifteen men. Having thus strained relations with the Natives, the settlers could not survive easily. John White decided to return to England in 1587 and return with more supplies. When he returned, England faced war against Spain. Thus delayed, White could not return to Roanoke until 1590. When he did return, White discovered that Roanoke was abandoned. All that gave clue to the fate of the colony was the word "Croatan," the name of a nearby Native American tribe, carved out on to a tree. No attempt was made to discover the actual cause of the disappearance until several years later. There are only theories as to the cause of the loss of Roanoke. There are two major possibilities. Firstly, the settlers may have been killed by the Natives. Second, the settlers may have assimilated themselves into the Native tribes. But there is no evidence that settles the matter beyond doubt. Review Questions. Use the content in this chapter and/or from external sources to answer the following questions. Remember to properly cite any sources used.

US History/English Colonies. Patterns of Colonization. The islands of Great Britain changed greatly in the Renaissance, resulting in the Church of England, the British Civil War, and total transformation of economic, political, and legal systems. Yet through this time, despite pressure from other nations and America's own Natives, a diverse set of English colonies were planted and thrived. These new colonies were funded in three different ways. In one plan, corporate colonies were established by joint stock companies. A joint stock company was a project in which people would invest shares of stock into building a new colony. Depending on the success of the colony, each investor would receive profit based on the shares he had bought. This investment was less risky than starting a colony from scratch, and each investor influenced how the colony was run. These investors often elected their own public officials. (An example of a joint stock company on another continent was the British East India Company.) Virginia was settled in this way. Proprietary colonies were owned by a person or family who made laws and appointed officials as he or they pleased. Development was often a direct result of this ownership. Charles II granted William Penn the territory now known as Pennsylvania. Penn's new colony gave refuge to Quakers, a group of millennial Protestants who opposed the Church of England. (Quakers did not have ministers and did not hold to civil or religious inequality, making them a dangerous element in hierarchical societies.) Penn was an outspoken Quaker and had written many pamphlets defending the Quaker faith. He also invited settlers from other countries and other Protestant minorities, and even some Catholics. Finally, royal colonies were under the direct control of the King, who appointed a Royal Governor. The resulting settlement was not always identical to England. For example, England had broken with Catholicism during the reign of Henry the Eighth, and the Old Faith was seen not only as religious heresy but the prelude to domination by other countries. Yet Maryland's grant of toleration of Catholics was granted as a boon from the British Crown. In 1634, Lord Baltimore appointed George Calvert of England to settle a narrow strip of land north of Virginia and south of Pennsylvania as a Catholic colony via a royal charter. Fifteen years later, in 1649, he signed the Act of Toleration, which proclaimed religious freedom for its colonists. Despite the original charter, Protestants later became the majority faith. After Lord Baltimore's death several years later, Margaret Brent, the wife of an esteemed landowner in Maryland, executed his will as governor of the colony. She defied gender roles in the colonies by being the first woman of non-royal heritage to govern an English colony. Massachusetts Bay Colony. The "Massachusetts Bay Colony", another corporate colony, was founded as a place far from England where its religious dissenters could live. The Puritans, a group of radical Protestants who wanted what they called a return to the faith of the Bible, suffered torture and execution because they disagreed with the official Church of England. In 1620, forty-one Puritans (who called themselves Pilgrims) sailed for the new world. Their own contemporary accounts show that the Pilgrims originally intended to settle the Hudson River region near present day Long Island, New York. Once Cape Cod was sighted, they turned south to head for the Hudson River, but encountered treacherous seas and nearly shipwrecked. They then decided to return to Cape Cod rather than risk another attempt to head south. After weeks of scouting for a suitable settlement area, the Mayflower's passengers finally landed at Plymouth in present-day Massachusetts on December 26, 1620. They called it Massachusetts after the name of the Indian tribe then living there. William Bradford, who was selected as a governor after the death of John Carver, wrote a journal that helps us to better understand the hardships colonists endured, encounters with the Native Americans, and ultimately, the success of the colony. The Pilgrims agreed to govern themselves in the manner set forth in the Mayflower Compact, which signed on the Pilgrims' ship, The Mayflower. After two years they abandoned the communal form of partnership begun under the Compact and in 1623 assigned individual plots of land to each family to work. Ten years later, the joint-stock Massachusetts Bay Company acquired a charter from King Charles of England. The colony of Plymouth was eventually absorbed by Massachusetts Bay, but it remained separate until 1691. A large group of Pilgrims later migrated to the new colony of Massachusetts Bay. In keeping with its mother Church of England, the colony did not provide religious freedom. It only allowed (male) Puritans the right to vote, established Puritanism as the official religion of the colony in The Act of Toleration, and punished people who did not go to their Church. New York. Other countries used the joint-stock company to fund exploration. In 1609, the Dutch East India company discovered a territory on the eastern coast of North America, from latitude 38 to 45 degrees north. This was an expedition in the yacht Halve Maen ("Half Moon") commanded by Henry Hudson. Adriaen Block and Hendrick Christiaensz explored the territory from 1611 until 1614. In March of 1614 the States General, the governing body of the Netherlands, proclaimed exclusive patent for trade in the New World. The States General issued patents for development of New Netherland as a private commercial venture. Ft. Nassau was swiftly built in the area of present day Albany to defend river traffic and to trade with Native Americans. New Netherland became a province of the Dutch Republic in 1624. The northern border was then reduced to 42 degrees north, as the English had encroached north of Cape Cod. According to the Law of Nations, a claim on a territory required not only discovery and charting but settlement. In May 1624 the Dutch completed their claim by landing thirty Dutch families on Noten Eylant, modern Governors Island. In the next few decades incompetent directors-general ran New Netherland. The settlers were attacked by Native Americans, and British and Dutch conflicts seemed destined to destroy the colony. All that changed when Peter Stuyvesant was appointed Director-General in 1647. As he arrived he said, "I shall govern you as a father his children". He expanded the colony's borders. He oversaw conquest of the one settlement of northernmost Europe, New Sweden, in 1655. He resolved the border dispute with New England in 1650. He improved defenses against Native American raids, and the population of the colony went from 500 in 1640 to 9,000 by 1664. But in August of 1664, four English warships arrived in New York Harbor demanding the surrender of the colony. At first, Stuyvesant vowed to fight, but there was little ammunition and gunpowder. He received weak support from the overwhelmed colonists, and was forced to surrender. New Netherland was subsequently renamed "New York", in honor of the British Duke of York. In an attempt to gain supremacy over trade, the English waged war against the Dutch in 1664. The English took control over the Dutch harbor of New Amsterdam on the Atlantic coast of America. James, the brother of King Charles II, received the charter for New Amsterdam and the surrounding Dutch territory. In 1673 the Dutch, lead by Michiel de Ruyter, briefly reoccupied New Netherland again, this time naming it New Orange. After peace was made, ending the Third Anglo-Dutch War, they agreed to return it to the English. Patterns of Colonization in the Other Early Colonies. The territory of Carolina, named after the British King Charles I, was granted as a proprietary colony to eight different nobles. The proprietors divided Carolina into two separate colonies -- "North Carolina" and "South Carolina". Four colonies were formed by division from already extant larger territories. When New Holland was taken to become New York, King James granted a portion of the territory, present-day "New Jersey", to Lord Berkeley and Sir George Cartaret, while retaining present-day New York for himself as a proprietary colony. Sir George had come from the Isle of Jersey, and the new colony was named accordingly. Another portion of the territory became the crown colony Connecticut. This colony was also named for its native tribe of Indians. A corner of Pennsylvania which was not peopled by Quakers separated in 1704 to become the colony of "Delaware". This was given the name of Thomas West, Third Baron De La Warr, a nobleman under Queen Elizabeth and a noted adventurer. "Rhode Island" was a unique experiment in religious and political freedom. Massachusetts banished Roger Williams after he began asserting that Jesus Christ meant for the Church to be separate from the governing authority. This dissenter from the Church of England, and then from the Puritans, became the first American Baptist. After many adventures in other colonies, he bought land from the Narragansett Indians for a new settlement. Providence was meant to be a colony free from religious entanglements and a refuge for people of conscience. He was later followed by Anne Hutchinson. She had outraged Boston divines because she was a woman who preached, and because she believed that one's works were not always tied to grace, unlike the Puritans. She also bought land from the Indians. On this was the settlement subsequently named Portsmouth, and afterward a dissident sister town, Newport. The colony was partially based upon Aquidneck Island, later called Rhode Island for unknown reasons, and the entire establishment eventually took its name from that place. Georgia was another proprietary colony, named after King George I, with a charter granted to James Oglethorpe and others in 1732. It was intended as a "buffer" colony to protect the others from attacks from the Florida Spanish and the Louisiana French. Because of this, Georgia was the only colony to receive funds from the Crown from its founding. The laws in Great Britain put people in prison for debt. Many of these people were shipped from overcrowded jails to freedom in the wilds of Georgia colony. America was already seen as a land of prosperity, and Oglethorpe hoped that the ex-prisoners would soon become honest and rich. However, few of the prisoners of London jails knew how to survive in the new wilderness. Portrait of the British Colonies. The Colonies are often considered as three groups: New England (New Hampshire, Massachusetts, Rhode Island, Connecticut), the Southern Colonies (Maryland, Virginia, the Carolinas, and Georgia), and the Middle Colonies (New York, New Jersey, Pennsylvania and Delaware). Sometimes the Carolinas and Georgia are counted as separate from the Chesapeake Colonies. Each group had geographic and economic characteristics. New England's rocky soil only encouraged small farms, and its agricultural opportunities were limited. Thus it focused on fishing, forestry, shipping, and small industry to make money. Richer land in the Southern colonies was taken over by individual farmers who grasped acreage. This created large plantation farms that grew tobacco, and later cotton. Farms in the Carolinas also farmed sugar, rice, and indigo. In the 17th century, these were farmed by indentured servants, people who would work for a period of years in return for passage to America and land. Many of these servants died before their indentures ended. A group of indentured servants rose up in Bacon's Rebellion in 1676. After Bacon's Rebellion, plantations began using African slaves instead. Even after release from indenture, many of these white people remained in the economic lower classes, though not subject to the slave codes, which became more harsh as time passed, denying almost all liberty to slaves in the southern colonies. By the American Revolution, one in five colonists was an African slave. And the products produced by slavery in the South were consumed and traded by towns in the Middle Colonies and New England. Few people questioned the slave economy. The Middle Colonies had medium-sized farms. These colonies also had people from many different cultures with many different beliefs. Individuals in these states used indentured servants, and later slaves, but there was not the concentration of masses of slave labor found in the Southern colonies. Another distinction lies in religious practices. New England was mostly Congregationalist, with some admixture of Presbyterian congregations and the religious non-conformists who called themselves Baptists. These were all descendants of dissenters before and during the British Civil War. The South was mostly Anglican, cherishing religious and secular traditions and holidays. The Middle Colonies held small groups of people from Holland, German lands, and even Bohemia, and they brought a welter of Catholic and Protestant faiths. Among the whites sent to the colonies by English authorities were many Scots-Irish people from Ulster. These had been Calvinist Protestants in the middle of a Irish Catholic majority, at odds both with them and with England. This minority settled in the frontier region of the Appalachian Mountains and eventually beyond in the Ohio and Mississippi country. In America their desire for land and freedom pushed the colonial boundary westward at little cost to the government, and provided an armed buffer between the eastern settlements and Native American tribes which had been driven away from the seaboard. Colonial frontiersmen endured a very harsh life, building their towns and farms by hand in a dense wilderness amid economic deprivation and native attack. Each colony developed its own areas of edification and amusement, depending upon the local faith and the local capacities. The culture of the South recorded early interest in musical theater, with Charleston, South Carolina and Williamsburg, Virginia as hubs of musical activity. A performance of Richard III, the first professional production of Shakespeare in America, took place in New York City in 1750. And preachers, lecturers, and singers entertained the colonists. Their commonalities were stronger than their differences. All three regions shared a population mostly derived from the British Isles. All had terrible roads, and all had connections to the Atlantic Ocean as a means of transportation. And all were tied to the Atlantic economy. Atlantic merchants used ships to trade slaves, tobacco, rum, sugar, gold, silver, spices, fish, lumber, and manufactured goods between America, the West Indies, Europe and Africa. New York, Philadelphia, Boston, and Charleston were the largest cities and main ports at that time. Early Technology. The first wave of colonists used hand labor to cultivate their farms, and established such land-based crafts such as pottery and tanning. As later ships brought cattle and horses, draft animals became part of the economy. Indentured servants, and then slaves kidnapped from Africa, were imported. This was when larger plantations began to be founded. In the latter part of the eighteenth century small-scale machine-based manufacturing began to appear. Individuals started to dig for coal and iron ore. New England used the latter to begin making building tools and horseshoes. A new textile industry arose, dependent in part upon Southern cotton. Powered by wood or coal and fed by the need for strong metal, household forges pioneered new techniques of iron-making. The blacksmith and the tinsmith became part of large settlements. Colonies started making mechanized clocks, guns, and lead type for printing. Mercantilism, Salutary Neglect and British Interference. The American colonies, entirely new societies separated by an ocean from Great Britain, believed they had the right to govern themselves. This belief was encouraged by Great Britain's Glorious Revolution and 1689 Bill of Rights, which gave Parliament the ultimate authority in government. A policy of relatively lax controls or Salutary Neglect ended in increased British regulation resulting from the policy of mercantilism, and seen through the Lords of Trade and the later Navigation Acts. Mercantilism. Parliament placed controls on colonial trade in obedience to the economic policy of mercantilism. This was the idea that a nation's economic power depended on the value of its exports. A country could use its colonies to create finished goods, rather than raw materials. These could be traded to other countries, thus increasing the strength of the colonizing nation. This policy had been put forth by a Frenchman named Jean-Baptiste Colbert. It seemed tailor-made for Great Britain. Spain had American gold as its economic base, and France had American furs. England had neither of these. But it had American cotton, molasses, and tobacco, as well as its state-of-the-art ships. Prior to the mid-1700's, the colonies had enjoyed a long period of "salutary neglect", where the British largely let the colonies govern themselves. This now ended. The Lords of Trade. In an attempt to enforce mercantilism policies, King Charles II created the Lords of Trade as a new committee on the Privy Council. The Lords of Trade attempted to affect the government of the colonies in a manner beneficial to the English, rather than to the colonists. The Lords of Trade attempted to convert all American colonies to royal ones so that the Crown could gain more power. Under King James II, the successor to Charles II, New York, New Jersey, and the Puritan colonies were combined into the Dominion of New England in 1687. However, the Dominion only lasted a brief time. King James II, a Catholic, was seen as a threat by British Protestants. James was overthrown (he was technically held abdicated by Parliament) in the bloodless Glorious Revolution of 1688. In 1689, James' daughter Mary II and her husband William III took the throne as joint rulers. However, the British Parliament actually held the power. The Dominion of New England was dissolved, the various separate colonies were reestablished, and the Lords of Trade were abandoned (replaced by a Board of Trade, a purely advisory body). Navigation Acts. Beginning in 1660, the Parliament of England passed the Navigation Acts to increase its benefit from its colonies. The Acts required that any colonial imports or exports travel only on ships registered in England, meaning that only England could have the shipping power and the fees derived from them. They forbid the colonies to export tobacco and sugar to any nation other than England. (Tobacco was then used as medicine, and sugar was used to make alcohol, also a medicine.) And the colonies could not import anything manufactured outside England unless the goods were first taken to England, where taxes were paid, and then to the colonies. In the 1730s, The Sugar Act established a tax of six pence per gallon of sugar or molasses imported into the colonies. By 1750, Parliament had begun to ban, restrict, or tax several more products. It tried to curtail all manufacture in the colonies. This provoked much anger among the colonists, despite the fact that their tax burdens were quite low, when compared to most subjects of European monarchies of the same period. Colonists hated the Navigation Acts because they believed they would be more prosperous and rich if they could trade on their own behalf. They also believed that some vital resources would not be found in Britain. Indians in the 1700s. Indians of the Great Plains: Today, the area where the Indians of all the Great Plains lived is located from the Rocky mountains to the Mississippi River. During the 1700s, there were about 30 tribes that lived on the Great Plains. These tribes tended to rely on buffalo as their food source as well as other daily needs, such as clothing. Not only did Indians, specifically women, make their clothing out of buffalo, but also out of deer. Women would soak the deer or buffalo and scrape off the hair of the dead animal. Also, Indian tribes traded with one another. The number of horses an individual owned was a sign of wealth; Indians would trade their horses for food, tools, weapons(such as guns), and hides. Since the tribes spoke many different languages from one another, they had to use sign language to be able to trade with each other. Philadelphia Election Riot. A riot broke out on election day in Philadelphia in 1742 as a result of the Anglican population disagreeing with the Quaker majority. The riot stemmed over a power struggle between the Anglican and Quaker population. The Quakers had a history of political dominance over Philadelphia. The German population backed the Quaker vote because of the Quaker Pacifism which would protect from higher taxes and ultimately the draft. On election day, the Anglicans and sailors fought with the Quakers and Germans. The Quakers were able to seek shelter in the courthouse and complete the election. The Anglican party lost the election and 54 sailors were jailed following the riot. Education. As the three sections of the colonies through the 1700s were made up of people with different interests, they provided differing sorts of education for their children. Although there were commonalities -- a rich family in any of the three regions might send a son to Europe for his education -- people in different colonies tended to educate in differing ways. New England's motives for education were both civil and religious. The good citizen had to know his or her Bible. The Massachusetts General School Law of 1647 stated that if more than 50 families lived in a community, a schoolteacher must be hired. This law gave a justification: "It being one chief project of that old deluder, Satan, to keep men from the knowledge of the Scriptures, as in former times by keeping them in an unknown tongue, so in these latter times by persuading from the use of tongues, that so that at least the true sense and meaning of the original might be clouded and corrupted with love and false glosses of saint-seeming deceivers; and to the end that learning may not be buried in the grave of our forefathers, in church and commonwealth, the Lord assisting our endeavors." This was the Pilgrim ethos, set up in opposition to what they saw as the ignorance imposed by tyrants. Both boys and girls were often taught to read the Bible by their parents, perhaps with the aid of a horn book, an alphabet and syllabary page covered by a protective layer of horn. In addition to being able to read the Bible, a Christian ought to be able to govern in his society. ("His" society: for government was the province of godly, property-holding men, rather than women.) To obtain this youths had to gain a classical education -- that is, one based thoroughly on Latin. The 1647 law was the beginning of the American grammar school, which initially taught Latin, but later included practical subjects such as navigation, engineering, bookkeeping, and foreign languages. Most of the schools opened in the colonial era were private. However, they had been preceded by the first public-supported school, the Boston Latin School, in 1635. It had a rigorous education, and as a result, few students. Harvard was the first university in America, founded in 1636 and originally intended to teach Protestant clergy. Because of the small number of people graduating from the classical curriculum, attendance was low. Some people jumped directly from the classical curriculum to the University, sometimes entering Harvard as young as 14 or 15 years old. Cotton Mather graduated Harvard at 15, an exception only because of his extreme precocity. In private schools, boys and girls learned penmanship, basic Math, and reading and writing English. These fed the various trades, where older children were apprenticed. Girls who did not become servants were often trained for domestic life, learning needlework, cooking, and the several days-long task of cleaning clothes. Like New England, the Middle Colonies had private schools which educated children in reading and writing. However, the basics were rarer. The further west one lived, the less likely one was to be able to go to school, or to read and write at all. Ethnic and religious sub-groups would have their own private schools, which taught their own children their own folk-ways. In none of the colonies was higher education certain. Secondary schools were very rare outside of such major towns as Boston, New York, Philadelphia, and Charleston. The Chesapeake experience was different again. Children could only could only read and write if their parents could. And the South had few schools, of any kind, until the Revolutionary era. Children in wealthy families would study with private tutors. Though wealthy girls might learn 'the womanly arts,' they would not have the same curriculum as their brothers. Martha Washington's granddaughter Eliza Custis was laughed at by her stepfather when "[I] thought it hard they would not teach me Greek and Latin because I was a girl -- they laughed and said women ought not to know those things, and mending, writing, Arithmetic, and Music was all I could be permitted to acquire." Middle class children might learn to read from their parents, and many poor children, as well as all black children, went unschooled. The literacy rates were lower in the South than the North until about the 19th century. In 1693 the College of William & Mary was founded, Virginia's first University. As the 18th century wore on, it specialized not in theology for clergymen but in law. In 1701, the Collegiate College was founded. In 1718 it received funds from a Welsh governor of the British East India Company, Elihu Yale, and was renamed Yale College. These were later joined by several other universities, including Princeton in 1747. In the 18th century, astronomy, physics, modern history and politics took a bigger place in the college curriculum. Some colleges experimented with admitting Native American students in the 18th century, though not African-Americans. In 1640, "The whole Booke of Psalms Faithfully Translated into English Metre", commonly known as the Bay Psalm Book, was printed in Cambridge, Massachusetts. It was the first book written in the new world. The Bay Psalm Book was the first metrical English translation of the Biblical psalms. This famous and influential songbook was succeeded by a whole New England publishing industry. Sometime after 1687 the first "New England Primer" was published as an aid to childhood reading and spelling. An alternative to the classical curriculum emerged in Benjamin Franklin's American Academy, founded in Philadelphia in 1751. This body represented something closer to the modern American high school, offering vocational education. This sort of school later outnumbered the classical secondary school. However, Franklin's Academy was private as well, making such learning open only to those who could afford it. During this period colonists attempted to convert Native Americans to Christianity. Review Questions. 1. Choose one of the following colonies: New York, Virginia, Massachusetts, Georgia. In which of the three areas is it located? Why and how was it initially colonized? How did its immigrants and the religions they adhered to affect it? 2. Why did the British interfere with the colonies?

US History/Road to Revolution. The French and Indian War. "(The following text is from Wikipedia)" The French and Indian War (1754–1763) was the North American chapter of the Seven Years' War. The name refers to the two main enemies of the British, the royal French forces and the various American Indian forces allied with them. This conflict, the fourth such colonial war between the kingdoms of France and Great Britain, resulted in the British conquest of all of New France east of the Mississippi River, as well as Spanish Florida. France ceded control of French Louisiana west of the Mississippi to its Spanish ally, to compensate it for its loss of Florida. By the end of this war France kept only the tiny islands of Saint Pierre and Miquelon north of the Caribbean. These colonies today still allow France access to the Grand Banks. In Great Britain and France, the North American theatre of the Seven Years' War war usually has no special name, and so the entire worldwide conflict is known as the "Seven Years' War" (or the "Guerre de sept ans"). The "Seven Years" refers to events in Europe, from the official declaration of war in 1756 to the signing of the peace treaty in 1763. These dates do not correspond with the actual fighting in North America, where the fighting between the two colonial powers was largely concluded in six years, from the Jumonville Glen skirmish in 1754 to the capture of Montreal in 1760. Elsewhere the conflict is known by several names. In British North America, wars were often named after the sitting British monarch, such as King William's War or Queen Anne's War. Because there had already been a King George's War in the 1740s, British colonists named the second war in King George's reign after their opponents, and thus it became known as the "French and Indian War". This traditional name remains standard in the United States, although it obscures the fact that American Indians fought on both sides of the conflict. American historians generally use the traditional name or the European title (the Seven Years' War), and have also invented other, less frequently used names for the war, including the "Fourth Intercolonial War" and the "Great War for the Empire". Canadian francophones and English speakers both refer to it as the Seven Years' War ("Guerre de Sept Ans") or the War of the Conquest ("Guerre de la Conquête"), as the war in which New France was conquered by the British and became part of the British Empire. This war was also known as the "Forgotten War". Reasons for war. The French and Indian War began less than a decade after France and Great Britain had fought on opposing sides in the European War of the Austrian Succession (1740–1748). One cause for the conflict was territorial expansion. Newfoundland's Grand Banks were fertile fishing grounds and coveted by both sides. Both sides also wanted to expand their territories for trapping furs to trade, and for other pursuits that aided their economic interests. Both the British and the French used trading posts and forts to claim the Ohio Country, the vast territory between the Appalachian Mountains and the Mississippi River, from the Great Lakes to the Gulf of Mexico. English claims resulted from royal grants with no definite western boundaries. La Salle had claimed the Mississippi River for France: its drainage area includes the Ohio River Valley. Both Great Britain and France took advantage of Native American factions to secure these claims, to protect their territories, and to keep the other from growing too strong. A second cause was political & religious ideology. The English Protestant colonists feared papal influence in North America. New France was administered by French governors and Roman Catholic hierarchy. French missionaries included Armand de La Richardie. English history was told as a story of freedom from Catholic (i.e., foreign) influence. French control over North America represented a threat to Great Britain. In their turn, the French feared English anti-Catholicism, in a time when Catholics were still being persecuted under English law. Declaration and Action Anticipating the War. Céloron's expedition. In June 1747 the Governor-General of New France, the Marquis de la Jonquière, ordered Pierre-Joseph Céloron to lead an expedition to the Ohio Country to remove British influence from the area. Céloron was also to confirm allegiance of the Native Americans in the Ohio territory to the French crown. Céloron's expedition consisted of 213 soldiers of the Troupes de la marine (French Marines) transported by twenty-three canoes. The expedition left Lachine on June 15, 1749, and two days later reached Fort Frontenac. It then continued along the shoreline of present-day Lake Erie. At Chautauqua Portage (Barcelona, New York), it moved inland to the Allegheny River. The troop headed south to the Ohio River at present-day Pittsburgh, where Céloron buried lead plates engraved with the French claim to the Ohio Country. Whenever British merchants or fur-traders were encountered by the French, they were informed of the illegality of being on French territory and told to leave the Ohio Country. When the expedition arrived at Logstown, the Native Americans there informed Céloron that they owned the Ohio Country, and they would trade with the British, despite anything the French said. Céloron continued the expedition. At its farthest point south, it reached the junction between the Ohio River and the Miami River, just south of the village of Pickawillany. Here lived the old Chief of the Miami tribe, whom Céloron called "Old Britain." When Céloron arrived at Pickawillany, he informed the elderly Chief of "dire consequences" of continuing to trade with the British. "Old Britain" ignored the warning. After this meeting, Céloron and his expedition began the trip home, reaching Montreal only on November 10, 1749. In his report, Céloron wrote: "All I can say is that the Natives of these localities are very badly disposed towards the French, and are entirely devoted to the English. I don't know in what way they could be brought back." Langlade's expedition. On March 17, 1752, Governor-General de la Jonquière died. His temporary replacement was Charles le Moyne de Longueuil. It was not until July 1, 1752 that Ange Duquense de Menneville arrived in New France to take over the post. In the spring of 1752, Longueuil dispatched an expedition to the Ohio River area. The expedition was led by Charles Michel de Langlade, an officer in the Troupes de la marine. Langlade was given 300 men, some French-Canadians, and others members of the Ottawa tribe. His objective was to punish the Miami of Pickawillany for continuing to trade with the British. At dawn on June 21, 1752, the war party attacked the British trading center at Pickawillany, killing fourteen people of the Miami nation, including "Old Britain." The expedition then returned home. Marin's expedition. In the spring of 1754, Paul Marin de la Malgue was given command of a 2,000 man force of Troupes de la Marine and Aboriginals. His orders were to protect the Ohio from the British. Marin followed the route that Céloron had mapped out four years before. However, where Céloron had buried lead plates, Marin was constructing and garrisoning forts. The first fort that was constructed by Paul Marin was at Presque Isle (Erie, Pennsylvania) on Lake Erie's south shore. He then had a road built to the headwaters of Rivière aux Boeuf (now known as Waterford, Pennsylvania). Marin then constructed a second fort at Le Boeuf, designed to guard the headwaters of the Rivière aux Boeuf. Tanaghrisson's proclamation. On September 3, 1753, Tanaghrisson (d. 1754), Chief of the Mingo, arrived at Fort Le Boeuf. One tradition states that Tanaghrisson hated the French because they had killed and eaten his father. Tanaghrisson told Marin, "I shall strike . . .", threatening the French. The show of force by the French had alarmed the Iroquois in the area. They sent Mohawk runners to William Johnson's manor in Upper New York. Johnson, known to the Iroquois as "Warraghiggey", meaning "He who does big business", had become a respected member of the Iroquois Confederacy in the area. In 1746, Johnson was made a colonel of the Iroquois, and later a colonel of the Western New York Militia. At Albany, New York, there was a meeting between Governor Clinton of New York and Chief Hendrick, as well as other officials from a handful of American colonies. Chief Hendrick insisted that the British abide by their obligations and block French expansion. When an unsatisfactory response was offered by Clinton, Chief Hendrick proclaimed that the "Covenant Chain", a long-standing friendly relationship between the Iroquois Confederacy and the British Crown, was broken. Dinwiddie's reaction. Governor Robert Dinwiddie of Virginia found himself in a predicament. Many merchants had invested heavily in fur trading in Ohio. If the French made good on their claim to the Ohio Country and drove out the British, then the Virginian merchants would lose a lot of money. Dinwiddie could not possibly allow the loss of the Ohio Country to France. In October 1753 he wrote a letter to the commander of the French forces in the Ohio Country, Jacques Legardeur de Saint-Pierre, demanding an immediate French withdrawal. To deliver it he delegated Major "George Washington" of the Virginia militia. Major Washington left for Fort Le Boeuf on the 31st of October, along with his interpreter Jacob Van Braam and several other men. A few days later, Washington and his party arrived at Wills Creek (Cumberland, Maryland). Here Washington enlisted the help of Christopher Gist, a surveyor who was familiar with the area. They arrived at Logstown on November 24, 1753. At Logstown, Washington met with Tanaghrisson, who was angry over the French military encroachment upon his land. Washington convinced Tanaghrisson to accompany his small group to Fort Le Boeuf. On December 12, 1753, Washington and his men reached Fort Le Boeuf. Commander Saint-Pierre invited Washington to dine with him that evening. Over dinner, Washington presented Saint-Pierre with the letter from Dinwiddie. Saint-Pierre was civil in his response, saying, "As to the Summons you send me to retire, I do not think myself obliged to obey it." The French explained to Washington that France's claim to the region was superior to that of the British, as René-Robert Cavelier, Sieur de a Salle (1643–1687) had explored the Ohio Country nearly a century earlier. Washington's party left Fort Le Boeuf early on December 16, 1753. By January 16, 1754, they had arrived in Williamsburg, Virginia. In his report, Washington stated, "The French had swept south." They had constructed and garrisoned forts at Presque Isle, Le Boeuf and Venango. War. The French and Indian War was the last of four major colonial wars between the British, the French, and their Native American allies. Unlike the previous three wars, the French and Indian War began on North American soil and then spread to Europe, where Britain officially declared war on France on May 15, 1756, marking the beginnings of the Seven Years' War in Europe. Native Americans fought for both sides, but primarily alongside the French (with one exception being the Iroquois Confederacy, which sided with the American colonies and Britain). The first major event of the war was in 1754. Lieutenant Colonel George Washington, then twenty-one years of age, was sent to negotiate boundaries with the French, who did not give up their forts. Washington led a group of Virginian (colonial) troops to confront the French at Fort Duquesne (present day Pittsburgh). Washington discovered the French troops at the Battle of Jumonville Glen (about six miles or ten kilometers North-West of soon-to-be-established Fort Necessity). In the ensuing skirmish, a French Officer, Joseph Coulon de Jumonville, was killed. Washington pulled back a few miles and established Fort Necessity. The French forced Washington and his men to retreat. Meanwhile, the Albany Congress was taking place as means to discuss further action. Edward Braddock led a campaign against the French at Fort Duquesne in 1755. Washington was again among the British and colonial troops. Braddock employed European tactics -- bold, linear marches and firing formations -- and employed heavy cannon. This led to disaster at the Monongahela. The French and natives were heavily outmanned and outgunned. But they used superior tactics, taking cover behind trees and bushes to gun down and rout the British. Braddock was killed. Despite four close calls, Washington escaped unharmed and led the survivors in retreat. This stunning British defeat heralded a string of major French victories over the next few years, at Fort Oswego, Fort William Henry, Fort Duquesne, and Carillon, where veteran Montcalm famously defeated five times his number. The sole British successes in the early years of the war came in 1755, at the Battle of Lake George, which secured the Hudson Valley; and in the taking of Fort Beauséjour (which protected the Nova Scotia frontier) by Lieutenant Colonel Robert Monckton. A consequence of this last battle was the subsequent forced deportation of the Acadian population of Nova Scotia and the Beaubassin region of Acadia. In 1756 William Pitt became Secretary of State of Great Britain. His leadership, and France's continued neglect of the North-American theater, eventually turned the tide in favor of the British. The French were driven from many frontier posts such as Fort Niagara, and the key Fortress Louisbourg fell to the British in 1758. In 1759, the Battle of the Plains of Abraham gave Quebec City to the British, who had to withstand a siege there after the Battle of Sainte-Foy a year later. In September of 1760, Pierre François de Rigaud, Marquis de Vaudreuil-Cavagnal, the King's Governor of New France, negotiated a surrender with British General Jeffrey Amherst. General Amherst granted Vaudreuil's request that any French residents who chose to remain in the colony would be given freedom to continue worshiping in their Roman Catholic tradition, continued ownership of their property, and the right to remain undisturbed in their homes. The British provided medical treatment for the sick and wounded French soldiers, and French regular troops were returned to France aboard British ships with an agreement that they were not to serve again in the present war. Summary of the war in America In 1752 the French and their Native allies raided a trading outpost sited at modern day Cleveland rid the area of Pennsylvanians. In 1754 General George Washington attacked French soldiers and then became trapped in his poorly built, Fort Necessity in Great Meadows Pennsylvania and more than one-third of Washingtons's men shortly became casualties. Twenty-two year old Washington and his men surrendered and were allowed to leave back to Virginia. In July 1755, a few miles south of Fort Duquensne in Pennsylvania, the combined forces of French and Natives attacked British colonial troops that were preparing a to assault the fort. The aftermath that ensued would result in a British defeat and General Edward Braddock would be killed. Once London heard of this Britain declared war upon France and formally began the seven years war. After this the British feared that France would attempt to retake Nova Scotia and that the 12,000 French Nova Scotians would break their neutrality, so the British military forced around seven thousand French Nova Scotians from their homeland. This was history's first large-scale modern deportation, the French would be sent from Louisiana to the Caribbean and families would become torn apart. In July of 1758 The British had recaptured the fort at Loiusberg winning control of the St. Lawerence River. This would cut the major French supply route and open up more supply lines for the British. In the fall of 1758 the Shawnee and Delaware Natives accepted peace offerings from the British and the French abandoned Fort Duquesne. A decisive attack would happen in the fall of 1759 when General James Wolfe's forces defeated the French on the Plains of Abraham and thus taking Quebec. A year after this event the British would capture Montreal and the North American stage of the war would be over. Outcome. Though most of the North American fighting ended on September 8, 1760, when the Marquis de Vaudreuil surrendered Montreal — and effectively all of Canada — to Britain (one notable late battle allowed the capture of Spanish Havana by British and colonial forces in 1762), the war officially ended with the signing of the Treaty of Paris on February 10, 1763. The treaty sealed France's loss of all its North American possessions east of the Mississippi except for Saint Pierre and Miquelon islands off Newfoundland. All of Canada was ceded to Britain. France regained the Caribbean islands of Guadeloupe and Martinique, which had been occupied by the British. The economic value of these islands to France was greater than that of Canada at the time, because of their rich sugar crops; and the islands were easier to defend. However, the British were happy to take New France: defense was not an issue, and they had many sources of sugar. Spain gained Louisiana, including New Orleans, in compensation for its loss of Florida to the British. French Canada contained approximately 65,000 French-speaking Roman Catholic residents. Early in the war, in 1755, the British had expelled French settlers from Acadia. (Some of these eventually fled to Louisiana, creating the Cajun population.) Now at peace, and eager to secure control of its hard-won colony, Great Britain made concessions to its newly conquered subjects with the Quebec Act of 1774. The history of the Seven Years' War, particularly the siege of Québec and the death of British Brigadier General James Wolfe, generated a vast number of ballads, broadsides, images, maps and other printed materials, which testify to how this event continued to capture the imagination of the British public long after Wolfe's death in 1759. The European theatre of the war was settled by the Treaty of Hubertusburg on February 15, 1763. The war changed economic, political, and social relations between Britain and its colonies. It plunged Britain into debt, which the Crown chose to pay off with tax money from its colonies. These taxes contributed to the beginning the American Revolutionary War. Proclamation of 1763. "(The following text is taken from the Wikipedia article)" The Royal Proclamation of 1763 was issued October 7, 1763 by George III following Great Britain's acquisition of French territory in North America after the end of the Seven Years' War. The purpose of the proclamation was to make sure Britain could control its new territory for its The Proclamation in essence forbade Americans from settling or buying land west of the Appalachians. Colonists were angry because many already had land in that area. Additionally, the Proclamation gave the Crown a monopoly in land bought from Native Americans. Native land. In the fall of 1763, a royal decree was issued that prohibited the North American colonists from establishing or maintaining settlements west of an imaginary line running down the crest of the Appalachian Mountains. The proclamation acknowledged that Native Americans owned the lands on which they were then residing and white settlers in the area were to be removed. However, provision was made to allow specially licensed individuals and entities to operate fur trading ventures in the proscribed area. There were two motivations for this policy: To avoid warfare with the Indians. Neither side evidenced any affection for the tribes, but Indian conflicts were very expensive, and the British hadn't yet deployed enough soldiers in the West to keep the peace. Some Indians welcomed this policy, believing that separation from the colonies would allow them to resume their traditions. Others realized that the proclamation would, at best, only provide breathing room before the next onslaught of settlers. To concentrate colonial settlements on the seaboard where they could be active parts of the British mercantile system. British trade officials took it as a first priority to populate the recently secured areas of Canada and Florida (referring to the Treaty of Paris), where colonists could reasonably be expected to trade with the mother country. Settlers living west of the Appalachians would be highly self-sufficient and have little opportunity to trade with English merchants. The reaction of colonial land speculators and frontiersmen was immediate and negative. They believed their fight in the recent war had been "rewarded" by the creation of a vast restricted native reserve in the lands they coveted. Most concluded that the proclamation was only a temporary measure: a number ignored it entirely and moved into the prohibited area. Almost from its inception, the proclamation was modified to suit the needs of influential people with interests in the American West, both high British officials and colonial leaders. Beginning in 1764, portions of the Proclamation Line were adjusted westward to accommodate speculative interests. Later, in 1768, the first Treaty of Fort Stanwix formally recognized the surrender of transmontane lands claimed by the Iroquois. The Proclamation of 1763 was a well-intentioned measure. Pontiac’s Rebellion had inflicted a terrible toll on the frontier settlements in North America and the British government acted prudently by attempting to avoid such conflict in the foreseeable future. The colonists, however, were not appreciative and regarded the new policy as an infringement of their basic rights. The fact that western expansion was halted at roughly the same time that other restrictive measures were being implemented, made the colonists increasingly suspicious Almost immediately, many British colonists and land speculators objected to the proclamation boundary, since there were already many settlements beyond the line (some of which had been temporarily evacuated during Pontiac's War), as well as many existing land claims yet to be settled. Indeed, the proclamation itself called for lands to be granted to British soldiers who had served in the Seven Years' War. Prominent American colonists joined with land speculators in Britain to lobby the government to move the line further west. As a result, the boundary line was adjusted in a series of treaties with Native Americans. The Treaty of Fort Stanwix and the Treaty of Hard Labor (both 1768) and the Treaty of Lochaber (1770) opened much of what is now West Virginia and Kentucky to British settlement. Organization of new colonies. Besides regulating colonial expansion, the proclamation dealt with the management of newly ceded French colonies. It established government for four areas: Quebec, West Florida, East Florida, and Grenada. All of these were granted the ability to elect general assemblies under a royally appointed governor or a high council, which could then create laws and ordinances specific to the area in agreement with British and colonial laws. In the meantime, the new colonies enjoyed the same rights as native-born Englishmen, something that British colonists had been fighting over for years. An even bigger affront to the British colonies was the establishment of both civil and criminal courts complete with the right to appeal--but those charged with violating the Stamp or Sugar Act were to be tried in admiralty court, where the defendant was considered guilty until he or she could prove his or her innocence. Legacy. The influence of the Royal Proclamation of 1763 on the coming of the American Revolutionary War (1775–1783) has been variously interpreted. Many historians argue that the proclamation ceased to be a major source of tension after 1768, since the aforementioned treaties opened up extensive lands for settlement. Others have argued that colonial resentment of the proclamation contributed to the growing divide between the colonies and the Mother Country. In the United States, the Royal Proclamation of 1763 ended with the American Revolutionary War, because Great Britain ceded the land in question to the United States in the Treaty of Paris (1783). Afterwards, the U.S. government also faced difficulties in preventing frontier violence, and eventually adopted policies similar to those of the Royal Proclamation. The first in a series of Indian Intercourse Acts was passed in 1790, prohibiting unregulated trade and travel in Native American lands. Additionally, the U.S. Supreme Court case Johnson v. M'Intosh (1823) established that only the U.S. government, and not private individuals, could purchase land from Native Americans. The Royal Proclamation continued to govern the cession of aboriginal land in British North America, especially Upper Canada and Rupert's Land. The proclamation forms the basis of land claims of aboriginal peoples in Canada – First Nations, Inuit, and Metis. The Royal Proclamation of 1763 is thus mentioned in Section Twenty-five of the Canadian Charter of Rights and Freedoms. The Stamp Act and other Laws. In 1764, George Grenville became the British Chancellor of the Exchequer (minister of finance). He allowed customs officers to obtain general writs of assistance, which allowed officers to search random houses for smuggled goods. Grenville thought that if profits from smuggled goods could be directed towards Britain, the money could help pay off debts. Colonists were horrified that they could be searched without warrant at any given moment. Also in 1764, with persuasion from Grenville, Parliament began to impose several taxes on the colonists. The Sugar Act of 1764 reduced the taxes imposed by the Molasses Act, but at the same time strengthened the collection of the taxes. It also provided that British judges, and not juries, would try cases involving that Act. The next year, Parliament passed the Quartering Act, which required the colonies to provide room and board for British soldiers stationed in North America; the soldiers would serve various purposes, chiefly to enforce the previously passed acts of Parliament. Following the Quartering Act, Parliament passed one of the most infamous pieces of legislation: the Stamp Act. Previously, Parliament imposed only external taxes on imports. But the Stamp Act provided the first internal tax on the colonists, requiring that a tax stamp be applied to books, newspapers, pamphlets, legal documents, playing cards, and dice. The legislature of Massachusetts requested a conference on the Stamp Act; the Stamp Act Congress met in October that year, petitioning the King and Parliament to repeal the act before it went into effect at the end of the month, crying "taxation without representation." The act faced vehement opposition throughout the colonies. Merchants threatened to boycott British products. Thousands of New Yorkers rioted near the location where the stamps were stored. In Boston, the Sons of Liberty, a violent group led by radical statesman Samuel Adams, destroyed the home of Lieutenant Governor Thomas Hutchinson. Parliament did indeed repeal the Stamp Act, but additionally passed the Declaratory Act, which stated that Great Britain retained the power to tax the colonists, even without substantive representation. Believing that the colonists only objected to internal taxes, Chancellor of the Exchequer Charles Townshend proposed bills that would later become the Townshend Acts. The Acts, passed in 1767, taxed imports of tea, glass, paint, lead, and even paper. The colonial merchants again threatened to boycott the taxed products, reducing the profits of British merchants, who in turn petitioned Parliament to repeal the Townshend Acts. Parliament eventually agreed to repeal much of the Townshend legislation. But Parliament refused to remove the tax on tea, implying that the British retained the authority to tax the colonies despite a lack of representation. In 1773, Parliament passed the Tea Act, which exempted the British East India Company from the Townshend taxes. Thus, the East India Company gained a great advantage over other companies when selling tea in the colonies. The colonists who resented the advantages given to British companies dumped British tea overboard in the Boston Tea Party in December of 1773. <br>"The Boston Tea Party" In retaliation for the Boston Tea Party, Parliament passed the Coercive Acts, which were in the colonies known as the Intolerable Acts. Parliament reduced the power of the Massachusetts legislature and closed the port of Boston. Also, the Quartering Act was extended to require private individuals to lodge soldiers. Furthermore, Parliament allowed royal officials accused of crimes to be tried by a British, rather than a colonial, jury. First Continental Congress. In order to debate a response to the Intolerable Acts, all American colonies except for Georgia sent delegates to the First Continental Congress at Philadelphia. The Congress met in September 1774 and issued a Declaration of Rights and Grievances. When the Congress adjourned, it stipulated another Congress would meet if King George III did not meet the demands of the Declaration. When the Second Congress did meet, the military hostilities of the Revolutionary War had already begun, and the issue of Independence, rather than a redress of grievances, dominated the debates. Education. Literacy grew for both men and women during the 18th century. In New England and the Middle States, more middle-class girls were sent to school. However, as Science and the requirements for citizenship became more a part of education, girls were excluded from learning these topics. Higher education continued to develop, with the 1746 opening of The College of New Jersey (later known as Princeton), and King's College (now Columbia) in 1754. All of these universities were meant exclusively for White men, though some of the colleges experimented by admitting Native Americans. In the public schools, vocational education expanded. Though what was lost by failing to educate the underclasses was incalculable, we can gauge the lost possibilities through such individuals as Benjamin Banneker and Phillis Wheatley. Mr. Banneker, a self-educated free African-American, observed the stars, wrote his own almanac, and was one of the surveyors of what would later become the District of Columbia. Miss Wheatley, an African-born slave educated and freed by her mistress, wrote a remarkable volume of poems published in the year 1773. Most of these had been published in "The Newport Mercury", edited by Benjamin Franklin's brother James. Questions For Review. 1. What were the reasons for the French and Indian War? 2. What was the strategy of General Braddock against the French at Fort Duquesne? What was the strategy of the defending French and Indian forces? 3. Examine the succession of acts imposed upon the American Colonists in the wake of the war, beginning with the Sugar Act. What was the intended purpose of each act? What was its actual effect?

US History/American Revolution. Background. The British forces might at first glance seem to have every advantage. At the outset of the War they had stocks of cannon and ammunition. The Colonists had single-shot rifles from local forges, guns which took time to load and could easily misfire or explode. When Washington took command of the army in 1775, he learned that there was only enough gunpowder to provide nine rounds of ammunition per man. The British had a large professional army drilled to a pitch like that of Ancient Rome, well-supplied with food, uniforms, and arms. But the American lack of training meant that they did not mass in the European style. Instead they relied on snipers, individuals hidden behind the trees who shot their bullet and then loaded again while their neighbors fired. They had learned this during the French and Indian War. Snipers helped strengthen the American odds. The Beginning of the War (1775 - 1778). Lexington and Concord. The British government commanded General Thomas Gage to enforce the Intolerable Acts and limit rights in Massachusetts. Gage decided to confiscate a stockpile of colonial arms located in Concord. On April 19, 1775, Gage's troops marched to Concord. On the way, at the town of Lexington, Americans who had been warned in advance by Paul Revere and others of the British movements made an attempt to stop the troops. No one knows which side fired the first shot, but it sparked battle on Lexington Green between the British and the Minutemen. Faced against an overwhelmingly superior number of British regular troops in an open field, the Minutemen were quickly routed. Nevertheless, alarms sounded through the countryside. The colonial militias poured in and were able to launch guerrilla attacks on the British while they marched on to Concord. The colonials amassed of troops at Concord. They engaged the British in force there, and they were able to repulse them. They then claimed the contents of the armory. The British retreated to Boston under a constant and withering fire from all sides. Only a reinforcing column with artillery support on the outskirts of Boston prevented the British withdrawal from becoming a total rout. The following day the British woke up to find Boston surrounded by 20,000 armed colonists, occupying the neck of land extending to the peninsula the city stood on. The Battle of Bunker Hill. The action changed from a "battle" to a "siege", where one army bottles up another in a town or a city. (Though in traditional terms, the British were not besieged, since the Royal Navy controlled the harbor and supplies came in by ship.) General Artemas Ward, the head of the Massachusetts militia, had the initial oversight of the siege. He set up headquarters at Cambridge, Massachusetts and positioned his forces at Charlestown Neck, Roxbury, and Dorchester Heights. The 6,000 to 8,000 rebels faced some 4,000 British regulars under General Thomas Gage. Boston and little else was controlled by British troops. General Gage countered the siege on June 17 by attacking the colonists on Breed's Hill and Bunker Hill. Although the British suffered tremendous casualties compared to the colonial losses, the British were eventually able to dislodge the American forces from their entrenched positions. The colonists were forced to retreat when many colonial soldiers ran out of ammunition. Soon after, the area surrounding Boston fell to the British. However, because of the losses they suffered, they were unable to break the siege of the city. Despite the early defeat for the colonists, the battle proved that they had the potential to counter British forces, which were at that time considered the best in the world. The Last Chance For Peace. The Second Continental Congress adopted the Olive Branch Petition, a petition for peace, on July 5, 1775. The Congress affirmed its allegiance to the Crown. It was received in London at the same time as it heard of the Battle For Bunker Hill. The King refused to read the petition or to meet with its ambassadors. Parliament reacted by passing the Prohibitory Act, which banned trade with the colonies. Battle For Boston. Despite the British access to the ships, the town and the army were on short rations. Salt pork was the order of the day, and prices escalated rapidly. While the American forces had some information about what was happening in the city, General Gage had no effective intelligence of rebel activities. On May 25, 1775, 4,500 reinforcements and three new generals arrived in Boston Harbor. The fresh leaders were Major General William Howe and Brigadiers John Burgoyne and Henry Clinton. Gage began planing to break out of the city. On July 3, 1775, George Washington arrived to take charge of the new Continental Army. Forces and supplies came in from as far away as Maryland. Trenches were built at Dorchester Neck, extending toward Boston. Washington reoccupied Bunker Hill and Breeds Hill without opposition. However, these activities had little effect on the British occupation. In the winter of 1775– 1776, Henry Knox and his engineers under order from George Washington used sledges to retrieve sixty tons of heavy artillery that had been captured at Fort Ticonderoga. Knox, who had come up with the idea to use sledges, believed that he would have the artillery there in eighteen days. It took six weeks to bring them across the frozen Connecticut River, and they arrived back at Cambridge on January 24, 1776. Weeks later, in an amazing feat of deception and mobility, Washington moved artillery and several thousand men overnight to take Dorchester Heights overlooking Boston. General John Thomas fortified the area. The British fleet had become a liability, anchored in a shallow harbor with limited maneuverability, and under the American guns on Dorchester Heights. When General Howe saw the cannons, he knew he could not hold the city. He asked that George Washington let them evacuate the city in peace. In return, they would not burn the city to the ground. Washington agreed: he had no choice. He had artillery guns, but did not have the gunpowder. The whole plan had been a masterful bluff. The siege ended when the British set sail for Halifax, Nova Scotia on March 17, 1776. The militia went home, and in April Washington took most of the Continental Army forces to fortify New York City. Ethan Allen and Fort Ticonderoga. The British had considered Fort Ticonderoga a relatively unimportant outpost in a conflict which had up to then been mostly based in Massachusetts. However, a veteran of the French and Indian War, Ethan Allen, had his eye on the fort. Allen had built up a Vermont territorial militia, the Green Mountain Boys, until it was an effective fighting force. Vermont was claimed by the New York colony, but Allen wanted more independence. In April of 1775, Allen was surprised by a visit by Commander Benedict Arnold of the Connecticut Militia. Arnold announced that he had been commissioned to seize the cannons of Fort Ticonderoga. A heated discussion between the two concluded with the agreement that the two militias would combine to attack the fort. This was for the best, for both forces together were small, well short of brigade strength. On May tenth, the combined American forces captured the fort. They seized the arms, including the cannons, which were then hauled by oxen all the way to Boston. Strengthening The Cause. Through the media available in that day, the Revolution promoted the idea of honorable men in revolt against tyranny. Newspapers in North and South published incendiary stories and inspiring engravings. The theater contributed dramatic outcries, including those of Mary Otis Warren. Songs were played and sung to rally flagging spirits. Thomas Paine's 1776. In January of 1776, the Englishman Thomas Paine published the pamphlet "Common Sense". This anti-monarchical publication encouraged American independence, using examples from the Bible and republican virtues to argue that kings were never good for any free state. In late 1776 he began printing his series of pamphlets, "The American Crisis", calling soldiers to mass to the cause of the Revolution. The first of these pamphlets begins with the stirring words, "These are the times that try men's souls." The Declaration of Independence. As military hostilities built up, the Second Continental Congress appointed George Washington as General of the Continental Army. Washington gave up his salary for the position all through the war. (As he was among the richest men in the colonies, he could afford this choice.) In June of 1776, the Second Continental Congress felt it needed a spur for separation from Great Britain. It appointed a Committee of Five to draft a declaration of independence: John Adams, Benjamin Franklin, Robert Livingston, Roger Sherman and Thomas Jefferson. Jefferson became the principal author of this document. Although the British king was no longer principally responsible for his dominion's policy, the Declaration of Independence called him a tyrant. It justified the rights of the rebellion with words the European Enlightenment would have hailed: "We hold these truths to be self-evident, that all men are created equal[.]" The Continental Congress signed the document on July 4, 1776. However, the signatures at this point showed that they wished independence: they could not alone achieve it. Army Bands. One of the attributes of a well-drilled company of soldiers was its military band. The British and Hessian troops drilled to the beat of drums, which carried the rhythm of the march above the noise of musket fire, and provided a way to communicate on the battlefield. "By 1778 soldiers marched at seventy-five 24″ steps per minute in common time and nearly double that (120 steps per minute) when marching in quick time." The music of the fife (a shrill flute) and drum helped build soldier morale. If the Rebellion could not have good supplies, it would at least have high morale. With the "Middle-brook Order", George Washington directed that every officer must provide military music for his troops. This was despite the limited number of instruments. The bands were used to announce the beginning and end of the day, direct troops in battle, and uplift spirits. Popular Music in the Revolution. One of the two major songs of the Revolution was the hymn "Chester", first published in 1770 in "The New England Psalm Singer" and revised in 1778. Its author and composer, William Billings, created a combination of the biblical ("Let tyrants shake their iron rod") and the topical ("Howe and Burgoyne and Clinton too,/ With Prescot and Cornwallis join'd"). Another was the song "Yankee Doodle", adapted from a tune of the Seven Years War. This was originally used by the British to laugh at the provincial manners of the Colonists, but was turned into a theme of the American upstarts. Canada. In September of 1775, the Colonists, led by General Richard Montgomery, invaded Canada. At first the invasion proved successful, with Montgomery capturing Fort St. Jean and the city of Montreal. On December 30 he made the decision to launch an attack onto the British held city of Quebec. It proved disastrous, and Montgomery was killed in battle. This was the last major action in Canada, although Benidict Arnold and a number of other generals did attack the coasts or Canada, or launch raids across the border. The Turning Point of the War. Despite the numerous defeats they faced in the early years of the war, the colonists were able to turn the tide around with several major victories. New York and New Jersey. In July, 1776, General William Howe and thirty-thousand British troops arrived at Staten Island in New York. The large army attacked and defeated General George Washington's American forces in the Battle of Long Island. After nearly having his entire army captured, Washington led a skilled withdrawal out of New York. Eventually the Continental Army was forced to set up camp in Pennsylvania. Howe could have ended the war by pursuing Washington's forces. But Howe was very cautious and took almost no risks. He feared losing too many men so far from home. Britain hired German mercenaries (Hessians) to guard the British fort at Trenton. Howe took advantage of these replacements and decided to wait until spring to attack the Continental Army again. Washington also took advantage of the situation, though from a different perspective. He figured that the Hessians would be weakest on Christmas night, after heavy feasting and drinking. On the night of December 25, 1776, Washington led his troops 9 miles, and across the Delaware River to ambush the Hessians. Crossing the river was difficult. A hail and sleet storm had broken out early in the crossing, winds were strong and the river was full of ice floes. The crossing took 3 hours longer than expected, but Washington decided to continue the attack anyway. As Washington predicted, the mercenaries were completely caught off guard and had little time to respond. Within just a over an hour, on the morning of December 26, the Continental Army had won the Battle of Trenton. The Americans had just 4 wounded and 0 killed against 25 Hessians Killed, 90 wounded and 920 captured. The victory increased the troops' morale and eventually led to re-enlistments. Some historians even speculate Trenton saved the revolution. On January 2, the British came to re-take Trenton, and did so with heavy casualties. Washington once again led a clever withdrawal, and advanced on Princeton. At the Battle of Princeton, the Continental Army attacked the rear-guard of the British Army, and forced them to retreat from New Jersey. During the war, the New World was being devastated by the 1775–1782 North American smallpox epidemic. Having survived the diseased in his youth, and having been warned about the effect the disease may have on the Army by Benjamin Franklin, George Washington wrote he had more dread of the disease crippling the continental army then the British Troops. On February 5, George Washington ordered the first mass inoculation of troops, following large disruptions caused by smallpox outbreaks. The policy was unpopular among soldiers, but stopped the mass infections from continuing. The Battle of Saratoga. In the summer of 1777, British General John Burgoyne and General Howe agreed to attack the colonial Army from two sides and defeat it. Howe marched north, winning the Battles of Brandywine and Germantown and eventually capturing Philadelphia. But Burgoyne was not so fortunate. Delayed by natural traps set up by the Continental Army, his troops slowly marched from Canada to Albany. By September of the year, his forces reached Saratoga, where an enormous American Army attacked the troops. In October, General Burgoyne surrendered all his forces to the Americans. General Howe resigned his post, thwarted despite his victories in Pennsylvania. The Battle of Saratoga proved to be the major turning point in the war. It persuaded France that America had to overthrow Great Britain, and French aid now was introduced to the colonists. The battle was also the last time the British would advance North. By the summer of 1778, following the Battle of Monmouth in New Jersey, all fighting would take place in the South. Defeat of the Iroquois. The Iroquois Confederacy in its zenith had been the equal of the European Powers. But since the French and Indian war it had been in decline. The Tribes of the Confederacy disagreed on who to support in the Revolution. The Onedia and Tuscaroras supported the Americans, while the Mohawk, Onondaga, Cayuga, and the Seneca supported the British. The Confederacy managed to stay together until 1777, when following the Battle of Saratoga, the 4 Tribes supporting the British began to attack American settlements across New York and Pennslyvenia. A back and forth battle followed. The Iroquois would attack American Forts and Towns, then the Americans would burn Iroquois villages. In 1779 George Washington sent General Sullivan to destroy the Iroquois Nation. After defeating the Iroquois at the Battle of Newtown, Sullivan's army then carried out a scorched earth campaign, methodically destroying at least forty Iroquois villages. The devastation created great hardships for the thousands of Iroquois refugees outside Fort Niagara that winter, and many starved or froze to death. The survivors fled to British regions in Canada and the Niagara Falls and Buffalo areas. Thus ended the 700-year history of the Iroquois Confederacy. Conclusion of the War (1778 - 1781). After the loss at Saratoga, the French, traditional rivals of the British, offered their aid in the Revolution. The United States allied itself with France in 1778. Spain and the Dutch Republic also joined the American side, both lending money to the United States and going to war with Britain. Valley Forge. Following the capture of Philadelphia by the British, Washington took his followers to Valley Forge on December 17th, 1777, a defensible nearby area, and built camp for 12,000 soldiers and 400 civilians, then the fourth largest settlement in the colonies. Following the introduction of the Prussian protege of Frederick the Great, Baron Von Steuben to Congress by way of Benjamin Franklin, he was directed to Valley Forge, where he arrived on February 23, 1778. On the Seas. War broke out on the seas as well. Americans granted commissions to "privateers" to attack and destroy all British ships, whether they were military or not. One of the most famous privateers, John Paul Jones, scored several victories at sea for the Americans, even attacking the shores of Britain itself. The War Heads South. An attempted treachery was defeated when its architect, British Major John Andre, was captured in September of 1780. Benedict Arnold, one of the heroes of Fort Ticonderoga, had been placed in charge of Fort Clinton, New York (now called West Point). In response to a bribe, Arnold neglected maintenance of the fortification, and was then preparing to turn the fort over to the British. After he had learned of Andre's arrest he fled to join the British army. Britain turned its attention from the North to the South, where more loyalists lived. They were at first very successful, defeating the Americans at Waxhaws, Charleston, and Camden. Lord Cornwallis, commander of the British forces in the south, was faced with the challenge of chasing down the Americans. Nathanael Greene had split his army into two, leaving one under the control of Daniel Morgan. Morgan drew Banastre Tarleton, who was commanding one half of the British Army, to Cowpens where they were they decisively defeated the British. The other half of the British Army, still under control of Cornwallis, defeated the Americans at the Battle of Guilford Court House. However, it was a bloody victory for Cornwallis and he was forced to withdraw to Yorktown Virginia to regroup. After hearing that the British were in Yorktown, and there was a French Fleet arriving, Washington took the Continental Army, along with French Troops, to Yorktown and surrounded the British. By mid September the town was under siege. Cornwallis was assured by British Commander-in-Chief, Henry Clinton, who was in New York, that he would be relieved shortly. However, the British relief force was defeated by the French fleet. The British continued to hold off for a few more days, but the allied army moved in closer and closer to Yorktown, and their cannons destroyed many of the British defenses. On October 19, 1781, Cornwallis surrendered his entire army, over 7,000 men. Scattered fighting continued, but back in Britain, the British were crushed by this defeat. Parliament voted to cease all offensive operations in "the colonies." Washington took his army to Newburgh, New York, where he stopped a mutiny in the Army. At the conclusion of the war in 1783 large numbers of loyalists and their families relocated to the home country of England and in large part to Canada as well as to other British Colonies. They submitted claims for lost property and lands in America. Many of the claims were not accepted by the English government for lack of evidence of the losses or significantly reduced. The property and lands were acquired by the American communities and then resold to the highest bidders. Due to the climatic effects of a 1782 eruption of an Icelandic volcano, the loyalists also experienced one of the coldest Canadian winters on record which contributed to poor crops in 1783-1784. Starvation, disease and hardship were rampant and many resolved to return to the United States despite the threats of retribution rather than subsist on their meager produce. Treaty of Paris (1783). The British lost hope of crushing the rebellion after Yorktown. They decided to negotiate peace with The United States, France, and Spain. The Treaty of Paris was signed on September 3rd, 1783. In it, the United States was recognized as an independent nation, with boundaries stretching from the Canadian border in the North, to the Mississippi River to the West, and the northern border of Florida in the South. Britain was forced to return Florida to Spain, but could still hold Canada. Congress was told to advise the states to restore property lost or stolen from the Loyalists. (However, many Loyalists had fled during the Revolution, and many of them did not return to claim their property.) Religion & the Revolution. Catholics in the Revolution. The complex situation of Catholicism in Great Britain had results in its Colonies. At the time of the American revolution, Catholics formed approximately 1.6% of the total American population of the original 13 colonies. If Catholics were seen as potential enemies of the British state, Irish Catholics, subject to British rule, were doubly-damned. In Ireland they had been subject to British domination. In America Catholics were still forbidden from settling in some of the colonies. Although the head of their faith dwelt in Rome, they were under the official representation of the Catholic Bishop of the London diocese, one James Talbot. When War began, Bishop Talbot declared his faithfulness to the British Crown. (If he had done otherwise, Catholics in England would have been in trouble. Anti-Catholic sentiment still ran high.) He forbade any Colonial priest to serve Communion. This made practice of the faith impossible. This created sympathy for the Colonial rebels. The Continental Army's alliance with the French increased sympathy for the faith. When the French fleet arrived in Newport, Rhode Island, the colony repealed the Act of 1664 and allowed citizenship to Catholics. (This anticipated the provision of the Constitutional Bill of Rights which would strike anti-Catholic laws from the books.) After the war, the Pope created an American Bishop, John Carroll -- a descendant of the same Carrolls who had helped found Maryland -- and an American Diocese communicating directly with Rome. From Anglicanism to Episcopalianism. On the one hand the colonial Church of England was an organ of the British government and a collaborator with it. Its clergy swore allegiance to the King. Several colonial governments paid monies to the local Anglican Church. Although other faiths were allowed in those states, the Anglican was considered the Official (Established) Church, putting pressure on other denominations. Still, several Revolutionaries, including Thomas Jefferson, rented their pews in a Church of England building. (Jefferson's own faith was Low Church, and he disagreed with the miracles in Christianity.) Significant meetings of the rebellion were held in Church of England buildings. But after the war, the Church needed to find a new role. Some of the Loyalist clergy went north to Canada. Others were allowed to remain after swearing an oath to the new government. The formerly Established Church was no more: even before the creation of the Constitution, with its separation of Church and State, Americans did not want to pay any extra fees. The Book of Common Prayer, the form of worship in that Church, was pragmatically revised for the new Episcopal Church so that people prayed for "Civil Rulers," instead of the King. But many Church buildings were closed, and there was now room for other denominations to flourish in Virginia and other states. The Early Government of the New United States. [Copied from Wikipedia] The Articles of Confederation, formally the Articles of Confederation and Perpetual Union, was an agreement among the 13 founding states that established the United States of America as a confederation of sovereign states and served as its first constitution. Its drafting by the Continental Congress began in mid-1776, and an approved version was sent to the states for ratification in late 1777. The formal ratification by all 13 states was completed in early 1781. Even when not yet ratified, the Articles provided domestic and international legitimacy for the Continental Congress to direct the American Revolutionary War, conduct diplomacy with Europe and deal with territorial issues and Native American relations. Nevertheless, the weakness of the government created by the Articles became a matter of concern for key nationalists. [Whom?] Questions for Review. 1. Who were these authors/composers, and what were they known for? (Mary Otis Warren, Thomas Jefferson, Thomas Paine, William Billings.) 2. How do the battles of Lexington and Concord show the early strengths and weaknesses of the American fighters? 3. Examine a copy of the Declaration of Independence in relation to this and the previous chapters. How does its rhetoric (choice of words) address the concerns of the American rebellion? How does it deviate from actual events to make a point?

US History/Friction Between States. Ideas and Questions of the Time. The overriding question throughout the decade preceding the Civil War was, “Should slavery be allowed in the new territories of the United States?” Before 1848, the question had been hypothetical; however, with the new lands acquired during the Mexican War, it was time for America to make a firm decision regarding the expansion of slavery. The central ideas dominating the debate were: The Wilmot Proviso. On August 8, 1846, Representative David Wilmot, a Pennsylvania Democrat, presented a proposal expressing that “slavery nor involuntary servitude shall ever exist in any part of any territory obtained from Mexico.” The Wilmot Proviso was never accepted as law, but it at long last put the issue forth on the political table. The Calhoun Resolutions. John C. Calhoun, the South Carolina statesman, responded with the Calhoun Resolutions, which said that Congress had no right to stop any citizen with slaves in their possession from taking those slaves into one of the territories. If they did so, the Fifth Amendment, which states that no person can be “deprived of life, liberty, or property, without due process of law,” would be violated. While this was not made formal legislation either, this belief became the standard in most of the south. Popular Sovereignty. A third option, which appealed to many moderates, most prominently Stephen A. Douglas of Illinois, was the idea of popular sovereignty. This was the idea of letting the settlers of a territory themselves decide whether slavery was to be allowed in it, by voting on state constitutions and other such measures. The primary merit of this initiative was that it took the debate out of Congress, which quickly grew tired of the issue, and put it into the hands of people it truly affected. There was also an unspoken understanding that most of the territories would end up being free, as most settlers that were already in those areas did not bring their slaves with them. Compromise of 1850. America looked to the Senate for an answer to the question of slavery within the territories. Henry Clay, nicknamed the "Great Compromiser," constructed a compromise: California was admitted as a free state, but all other territories in the Mexican Cession were allowed to choose between becoming a free territory or a slave territory. Also, as part of the Compromise, the slave trade was banned in the District of Columbia, and a Fugitive Slave Act was passed to allow the capture of fugitive slaves. The Fugitive Slave Act was a very controversial measure. Previously, many in the North felt that slavery merely occurred in the South and that they had nothing to do with it. But under the Fugitive Slave Act, Northerners were required to help return runaway slaves. Thus, the Northerners felt that they were being dragged into aiding the institution of slavery. Several Northern states passed laws prohibiting their officials from aiding the enforcement of the Act. While the admission of California as a free state gave the free states the majority in Congress, the pro-slavery measures in the Fugitive Slave Act made the Compromise seem more favorable to the South. Uncle Tom’s Cabin. Harriet Beecher Stowe’s "Uncle Tom’s Cabin", published in 1852, is often called “the book that started the Civil War.” The melodramatic story of the evil overseer Simon Legree and his slaves Eliza and Uncle Tom painted an accurate picture of the horrors of slavery, and gave rise to much abolitionist feeling in the North. However, the effects were not easily visible from the start: because the country was growing tired of the sectional bickering over slavery, it took a while for the story to becoming embedded in the American imagination. Nat Turner. Nat, commonly called Nat Turner, (October 2, 1800 – November 11, 1831) was an American slave whose slave rebellion in Southampton County, Virginia, was the most remarkable instance of black resistance to enslavement in the antebellum southern United States. His methodical slaughter of white civilians during the uprising makes his legacy controversial, but he is still considered by many to be a heroic figure of black resistance to oppression. At birth he was not given a surname, but was recorded solely by his given name, Nat. In accordance with a common practice, he was often called by the surname of his owner, Samuel Turner. Election of 1852. In one of the less spectacular elections in American history, Senator Franklin Pierce of the Democratic party defeated General Winfield Scott of the Whig party. The Whigs tried to rely on Scott’s heroics as a general during the Mexican war to get him elected, a strategy that proved unsuccessful. Pierce, of New Hampshire, ended up being largely an ineffective president, trying and failing to please both the North and the South. The Kansas-Nebraska Act and its Effects. Throughout this time, plans were underway for a transcontinental railroad. A question arose as to what Eastern city should be the main terminus. Senator Stephen Douglas of Illinois hoped to advance his own state’s interests by making Chicago the railroad hub. To do this, he suggested a piece of legislation known as the “Kansas-Nebraska Act,” requiring recognition of two new territories, Kansas and Nebraska, west of Missouri and Iowa, respectively. These territories would both help his railroad and solve the overdue issue of the territories in the remainder of the Louisiana Purchase. But to get the Kansas-Nebraska Act passed, he would have to get the support of Southerners, who wanted a railroad along a more southern route. For this reason, Douglas included in the Act the provision of popular sovereignty in the territories. This blatantly violated the Missouri Compromise of 1821, which stated that slavery would be prohibited above the 36º30’ line. Douglas therefore opened himself up to the verbal barrage of protests from the North, who denounced the cancellation of the Missouri Compromise as unfair. Yet the Act passed, to the indignation of many Northerners, with the support of President Pierce. The North. Many in the North figured that if the Missouri Compromise was not an unbreakable law, neither was the Fugitive Slave Act, leading to many demonstrations against it. Boston witnessed the most remarkable of these, leading to many New Englanders turning against Pierce for his support of the Kansas-Nebraska Act. Political Parties. The Whig party essentially buckled under the pressure of the Kansas-Nebraska Act, with the North condemning it and the South supporting it. Whigs from the North joined some Democrats and Free Soilers that united under the general principle of the Wilmot Proviso, eventually calling themselves the Republican Party and offering its first presidential candidate, John C. Fremont in 1856. Rachel v. Walker. Rachel v. Walker was a lawsuit involving a slave who, in 1834, sued for her freedom from John Walker in the Supreme Court of Missouri, and won. This result was cited in 1856 in the famous Dred Scott v. Sandford case before the Supreme Court of the United States.[1] Dred Scott. The question of the constitutionality of Congressional Compromises was decided by the Supreme Court in 1856. In "Scott v. Sanford", the Court ruled against a slave, Dred Scott, who had sued to become free. The Court ruled 7-2 that Scott remained a slave, and there were nine written opinions. The Chief Justice of the United States, Roger Taney, decided that blacks were so inferior that they could not be citizens of the United States, and that, consequently, they could not sue for his freedom (a state issue)in diversity in federal court, and therefore the court lacked jurisdiction. Nevetheless (the biggest "nevertheless" in American history) in a supererogatory effort to settle the question of slavery once and for all, the Marylander Taney ruled that the Missouri Compromise (which had banned the expansion of slavery into the territories north of Missouri) among other laws, was unconstitutional because it restricted the Constitutional right to own property. Many felt that Taney had committed a legal error in his decision. First, Taney had ruled that Scott had no right to sue. The case should have ended there. Taney had ruled on the constitutionality of the Missouri Compromise, which had, under Taney's own ruling that Scott had no right to sue, no bearing upon the case. Thus, the outrage against the Dred Scott decision was increased even more. John Brown’s Raid. John Brown, an extreme abolitionist known for fighting in Bloody Kanasas, came to the federal arsenal at Harper’s Ferry, Virginia for his last fight. He planned to take over the arsenal, give weapons to the slaves that would support him, and make a center of black power in the Appalachian Mountains that would support slave uprisings in the south. The raid did not go as planned. Brown did take over the arsenal and took a couple of hostages, but ended up being assaulted by Virginia militia and U.S. Marines under the command of Col. Robert E. Lee of the US 2nd Cavalry. He was tried, convicted, and hanged for treason to the State of Virginia. However, his raid left a profound impact. John Brown became a martyr for the abolitionist cause during the Civil War. In the South, his actions gave cause to rumors of Northern conspiracy supporting slave insurrections, engendering further suspicion of outsiders in the South. A later Northern marching song sang “John Brown’s body lies a-mouldering in the grave, but his soul is marching on.” Lincoln. <br> " Lincoln campaign poster" In 1860, four major candidates ran for President. The Whigs, adopting the name "Constitutional Union", nominated Tennessean Senator John Bell. The Northern Democrats nominated Senator Stephen Douglas of Illinois and the Southern Democrats nominated the Vice President John Breckenridge of Kentucky. The more united Republican party nominated Abraham Lincoln, who spoke out against expansion of slavery. Though he assumed that, under the constitution, Congress could not outlaw slavery in the South, he assured all that he would work to admit only free states to the US. Due to divisions between the parties, Lincoln won the election by carrying every Northern State. Douglas won Missouri, Bell the Upper South, and Breckenridge the Deep South. The South was outraged. The North had a far larger population than the South, and thus had more electoral votes. The South had been out voted.

US History/Preface. This textbook is based on the College Entrance Examination Board test in Advanced Placement United States History. The test is a standard on the subject, covering what most students in the United States study in high school and college, so we treat it as the best reference. The text was reorganized and edited in November 2008 to be closer to the content and organization the college board requires. The content was carefully chosen for significance and interest. We welcome reader feedback and suggestions for improvement. Enjoy! The AP Course Description can be found here.

GCSE Science/Circuits Part2. GCSE Science/Electricity Now we have learned Ohm's Law we can start applying it to some circuits. The test circuits below can be used to investigate how the voltage across a component varies with the current flowing through the component. Either circuit can be used. The one on the left is easiest to set up, the one on the right is easiest to use once it is set up, but does require you to use the rheostat as a potential divider. Note that the voltmeter is in parallel with the component and the ammeter is in series with it.This is necessary so that the ammeter and voltmeter do not interfere with the circuit in anyway. An ideal meter does not change either the current or the voltage. The wire should be "resistance wire", such as nichrome. Ordinary copper wire would short circuit the power pack and blow the pack's fuse. Set up either circuit and then by turning the voltage setting on the power pack and the slider on the rheostat, adjust the current to read 0.1 A. Take a reading of the voltage. Repeat for 0.2 A, 0.3 A up to 1.0 A. Repeat the readings but this time go from 1.0 A to 0.9 A and so on down to 0.1 A. Set your results out in a table like this. Now plot the average voltage against the current on graph paper. You should find the points all fall approximately on a straight line. The slope of the line =Voltage/Current. This is the resistance. Below is a typical voltage/current graph for a wire. Note that all the points fall approximately on a straight line. The slope of the line is 1.1 V/A. Therefore the resistance of this wire is 1.1 Ω All "Ohmic" components have a constant resistance like this. However, "non-Ohmic" components (that is, components that do not obey Ohm's law) do not have such a resistance. A bulb, for example, has a resistance that increases as the current flowing through it goes up, because the filament is heating up. A current-voltage graph for a bulb would be a curve. Q1) Plot a current/voltage graph for the following set of data for a 12V filament bulb. Answers | «Current, Voltage, Resistance | Parallel and series circuits»

Algebra/Complex Numbers. Complex numbers are the extension of the real numbers, i.e., the number line, into a number plane. They allow us to turn the rules of plane geometry into arithmetic. Complex numbers have fundamental importance in describing the laws of the universe at the subatomic level, including the propagation of light and quantum mechanics. They also have practical uses in many fields, including signal processing and electrical engineering. Introduction. Currently, we are able to solve many different kinds of equations for formula_1 , such as formula_2 , or formula_3 , or formula_4 . In each of these cases the solution for formula_1 is a real number: respectively 5, 4/3, and -10. However, there is no real number "x" that satisfies the equation formula_6 , since the square of any real number is nonnegative. Conceptually it would be nice to have some kind of number to be the solution of formula_6 . This "number" would not be a real number, however, and we refer to such a number as an "imaginary" number. Now, is this really the reason? Well - Definitely not! This mistake occurs in many teaching books from the attempts to "solve problems by force", as we could explain psychologically. This has nothing to do with reality, and gives the false feeling that mathematicians are "Cranks" full of to much spare time on their hands with nothing to do. The reason, be surprised, has to do with a problem called Cubic functions. We then extend the real number system to accommodate this special number. It turns out that there will be two imaginary solutions of the equation formula_6 . One of them will be called formula_9 and, following the normal rules for arithmetic, the other solution is formula_10 . We may be inclined to say that formula_11 . That would, however, be incorrect solely because in words this says that "the square root of -1 is formula_9" , but there is no basis for preferring formula_9 over formula_10 (or vice versa) as the square root of -1. Rather, the two square roots have equal standing. We say that all numbers of the form a +bformula_9 , where formula_16 and formula_17 are any real numbers, is the set of "complex" numbers, and we denote this set formula_18 . The real numbers formula_19 may be considered to be the subset of complex numbers formula_20 for which b = 0. Complex numbers can be added, subtracted, multiplied, and divided (except by 0). We will explore some of the properties of these numbers later. There are in fact two commonly used definitions of complex numbers, but they are immediately seen to be logically equivalent. For a negative root like formula_21 , we split the number into two parts such that one part is formula_22 like formula_23 which leads to formula_24 Definition 1. A complex number is an expression of the form "x + yi", in which "x" and "y" are real numbers and "i" is a new number, called the imaginary unit, for which expressions the normal rules of calculation apply together with the extra rule: "i2=-1". Definition 2. A complex number is a pair of real numbers "(x,y)", satisfying the properties: In both cases a complex number consists of two real numbers "x" and "y". The real number "x" is called the real part and the real number "y" the imaginary part of the complex number. From the properties we deduce that complex numbers of the form (x,0) behave just like the real numbers, so we identify (1,0) with 1 and hence (x,0) with x. Furthermore we see that: It is common use to write "i" instead of (0,1), so: Any complex number "(x,y)" may now be written as "x + yi". Some examples. A "complex number" is a number that is in the form formula_30 , where "a" and "b" are real numbers. We say that "a" is the "real" part of z and write formula_31, and that "b" is the "imaginary" part of z, and write formula_32 A number of the form "b"i is sometimes called a "pure imaginary" number, as it has no real part. The pure imaginary numbers are also complex numbers, because "b"i = 0 + "b"i. In the same way, all real numbers are also complex numbers, because "a" = "a" + 0i. So the set of complex numbers includes real numbers, pure imaginary numbers, and the sums of reals and pure imaginaries. Here are some examples Notice that the number 2 is a complex number and a real number. This fact is clearer if we write 2 = 2 + 0i. Any complex number may be written in three main forms, which we will explore later. The form "x" + "y"i is known as the "Cartesian" form. Complex numbers and matrices. Complex numbers can be identified with a certain set of "matrices". If we think of the 2×2 identity matrix as the number 1, and we think of formula_9 which we introduced above as the matrix then the complex number formula_35 then has the form Properties. Complex numbers obey most of the properties of real numbers. Take two complex numbers, formula_37 and formula_38. Addition. How can we add these two complex numbers? We don't even have to think about formula_9 as being "special" in any way, just treat it as any other symbol and proceed by the standard rules of algebra, grouping along the way. We obtain: If one uses the matrix analogy above, regular matrix addition works to add complex numbers in the same way. Verify for yourself that this is true. Subtraction. Subtraction proceeds just as before. Multiplication. By the normal rules, taking into account that formula_42, we find: If one uses the matrix analogy above, regular matrix multiplication works to multiply complex numbers in the same way. Verify for yourself that this is true. Conjugates. The "conjugate" of a complex number formula_44, written formula_45, is the same number with the sign of the imaginary part changed: the conjugate of "a" + "b"i = "a" - "b"i (and vice versa). Let us examine what happens when we have a complex number "z" = "a" + "b"i, what is the product of "z" and its conjugate? Notice the imaginary parts cancel out, so the product is a "real number". This will aid us greatly in the division of a complex number, as we will see. Notice also that this is the "sum" of two squares, analogous to the difference of two squares. Matrix transposition behaves as conjugation if one uses the matrix analogy. Division. How do we compute the quotient of two complex numbers? It is not difficult. Let the quotient be: then cross multiplication gives: hence and So we have to solve two linear equations. Solution: and Note that this is complete nonsense unless formula_53. In fact, it is easy to see that the pair of linear equations have a solution exactly when this is true, i.e., when c and d are not both zero. Or in other words, when formula_54 as a complex number. Thus we can divide by a complex number "only" when it is non-zero. Luckily there is a little trick to speed up this computation. We multiply the denominator with a well chosen number as to make it real. We "realize the denominator" by multiplying with the conjugate of the denominator; a complex number times its conjugate is a real number: hence: Note that in the multiplication and division of complex numbers, we usually work out the whole problem instead of just memorizing the equation of the answer. The reader will note that we use here the familiar trick from algebra of multiplying by the number 1 in a particularly convenient form: formula_57. (We leave it to the reader to verify that any non-zero complex number divided by itself is in fact equal to 1.) Exponents and Roots. Because formula_58, real numbers can be raised to imaginary numbers. Imaginary and complex numbers cannot be raised to imaginary or complex numbers, as imaginary and complex numbers have no natural logarithms. Example: formula_59 Because formula_60, imaginary numbers can be root degrees. Problem set. Given the above rules, answer the following questions. Note: Use sqrt(x) for formula_61 <quiz display=simple points="2/2"> (7 + 2i) + (11 - 6i) = { 18_19 } + { -4_19 } i (8 - 3i) - (6i) = { 8_19 } + { -9_19 } i (9 + 4i)(3 - 16i) = { 91_19 } + { -132_19 } i 3i formula_62 9i = { -27_19 } + { 0_19 } i formula_63{ 1/5|0.2_19 } + { 2/5|0.4_19 } i formula_64{ [11sqrt(3) - 12]/19 (i)|[11sqrt(3)-12]/19 (i) _19 } + { [44 + 3sqrt(3)]/19 (i)|[44+3sqrt(3)]/19 (i) _19 } i formula_65{ x/(x^2 + y^2) (i)|x/(x^2+y^2) (i) _19 } + { -y(x^2 + y^2) (i)|-y(x^2+y^2) (i) _19 } i </quiz> The Argand Plane. We can represent complex numbers "geometrically" as well. Every complex number can be represented in the form z=x+iy (so x=Re(z) and y=Im(z)). Then we can represent z in the xy-plane by the point (x,y). Notice that this is a one-to-one relationship: for each complex number, we have one corresponding point in the plane, and for each point in the plane there corresponds one complex number. When we use the xy-plane in this way to represent complex numbers, we call the plane the "Argand plane". We will refer to the "y" axis as the imaginary axis, and the "x" axis as the real axis. Notice that a purely imaginary number is represented in the Argand plane by a point on the imaginary axis. A purely real number is represented by a point on the real axis. Here is an example of the Argand plane. There are two complex numbers drawn in the plane; viz., 1 + i, -2 - i. Their sum is plotted on the graph, -1. The red and blue lines demonstrate how geometrically, a parallelogram can be constructed, and their apex forms their sum. Modulus and argument. On this diagram we can see the number 3 + 4i. The red line is the distance away from the origin (the number 0 + 0i). The gray line represents the distances away from the respective axes. We can see that the red line makes an angle θ from the real axis. It is clear that almost all complex numbers have this distance away from the origin and that almost all complex numbers make an angle away from the real axis. We give these two qualities special names; the distance away from the origin is known as the "modulus" of the complex number, and the angle θ is known as the "argument" of the complex number. We write the modulus of a complex number z by |z|, and the argument of the complex number as arg z. We can calculate the modulus and argument by basic trigonometry. Calculating the modulus. In the above example, we have the number 3 + 4i. We can form a triangle in the Argand plane with base 3 and height 4. By Pythagoras we can find the length of the hypotenuse by formula_66. And thus, the length of the hypotenuse is thus the modulus of the complex number, and it is 5 for 3+4i. Generalization. If "z" = "x" + "y"i, |"z"| is clearly formula_67. Equivalently, formula_68. Calculating the argument. We have the same triangle as we had in calculating the modulus. Remember from trigonometry that tan θ is the ratio of the height over the base. So, for 3 + 4i, we have tan θ = 4/3, and thus θ = arctan 4/3 = 0.9... With complex numbers, we always take two things: Note that arg 0 is undefined. Generalization. If "z" = "x" + "y"i, arg "z" is clearly arctan (y/x), or, equivalently, arg "z" = arctan (Im("z")/Re("z")). The polar form. We are now able to calculate the modulus and argument of a complex number, where these two numbers are able to uniquely describe every number in the Argand plane. Using these two characteristics of complex numbers, we are now able to formulate a new way of writing these numbers. Note that in the above diagram, we obtain a triangle that describes the complex number 3 + 4i. Clearly, we can do this for all complex numbers in the Argand plane (except for 0). To simplify our work, let us look at numbers in the circle of unit length equidistant from 0. From trigonometry, we can parameterize all the points on a circle in the Cartesian plane by (cos θ, sin θ). In complex number notation we can say that all numbers on this unit circle are in the form cos θ+i sin θ. This works well on the unit circle, but how does this generalize to describing "all" numbers on the plane? We simply make the circle larger or smaller to encompass the number; this is done by multiplying by the modulus. So then, we obtain the polar form "r"(cos θ + i sin θ) = "z", where "r" is the modulus. Euler's formula. A very significant result in the area of complex numbers is Euler's formula. It basically asserts that This statement can be verified through a rearrangement of the of the cosine and sine functions. Note that conjugate complex numbers have an opposing argument. 2e2i and 2e-2i are conjugate pairs. Proofs. Using Taylor series. Here is a proof of Euler's formula using expansions as well as basic facts about the powers of "i": The functions "e""x", cos("x") and sin("x") (assuming "x" is real) can be written as: and for complex "z" we "define" each of these function by the above series, replacing "x" with "iz". This is possible because the radius of convergence of each series is infinite. We then find that The rearrangement of terms is justified because each series is absolutely convergent. Taking "z" = "x" to be a real number, gives the original identity as Euler discovered it.formula_77 Using calculus. Define the complex number "z" such that Differentiating "z" with respect to "x": Using the fact that "i"2 = -1: Separating variables and integrating both sides: where C is the constant of integration. To finish the proof we have to argue that it is zero. This is easily done by substituting x = 0. But z is just equal to: thus So now we just exponentiate Corollaries. A number of significant results follow as corollaries to Euler's result. de Moivre's theorem. De Moivre's theorem is useful in calculating powers of complex numbers. It states that This follows clearly (from the laws of exponents) if we rewrite the theorem in the form Equivalent trigonometric forms. From the cosine/sine form of the complex number, we can rewrite the cosine and sine function in terms of exponentials. Relation of e, formula_91, i, 1, and 0. By substituting π into the formula, we obtain the following result: formula_92 The actual mathematical relevance of this equation is actually very little. It is known more for its relation of the many branches of mathematics: e comes from calculus, π from geometry, i comes from algebra, 1 is the multiplicative identity, and 0 is the additive identity. It is also known for its simple mathematical aesthetic. Forming trigonometric identities. The aforementioned equivalent trigonometric forms, combined with the Binomial theorem, allow us to create some trigonometric identities that would be difficult to form in any other way. These identities can be used to simplify integral problems. Cosine/sine powers. How can we simplify, say, (cos "x")5? Let us look at a simple example for motivation. First, rewrite as 1/25 (eix+e-ix)5 By the Binomial theorem, Replacing a with ei"x"/2 and b with e-i"x"/2, we obtain Procedure. We can summarize from the above example the general procedure: To simplify an expression in the form: the procedure is: Cosine/sine multiples. We can also form identities in the form: Let's look at another example to see how it's done. Example. Let's expand sin(3"x"). Recall de Moivre's theorem stating We will use this fact to expand out the left side. For ease of manipulation, it may be easier to let "c" = cos("x"), and "s"=sin("x"). Then use the Binomial theorem again to expand out: Collect real and imaginary parts Now, this is of course equal to cos(3"x")+i sin (3"x"). So, substituting back cos("x") for "c" and similarly for sin("x"), we can equate real and imaginary parts, and we get and we get for free. NB: In the cosine expansion, one could write sin("x")2 as 1-cos("x")2 to obtain a formula consisting completely of cosines. (analogously one could write the sine expansion using only sines) External links. This is incomplete and a draft, additional information is to be added.

Latin/Lesson 11-Translation. Lesson 20, as a bit of a reward is a little translation exercise from the Gospel of Saint Luke. Exercise 1 Vocabulary coming soon, at the moment consult your dictionary Respondens Simon dixit: "Aestimo quia is, cui plus donavit". At ille dixit ei: "Recte iudicasti". Et conversus ad mulierem, dixit Simoni: "Vides hanc mulierem? Intravi in domum tuam: aquam pedibus meis non dedisti; haec autem lacrimis rigavit pedes meos et capillis suis tersit. Osculum mihi non dedisti haec autem, ex quo intravi non cessavit osculari pedes meos. Oleo caput meum non unxisti; haec autem unguento unxit pedes meos. Propter quod dico tibi: Remissa sunt peccata eius multa, quoniam dilexit multrum: cui autem minus dimittitur, minus diligit." Dixit autem ad illam: "Remissa sunt peccata tua". Et coeperunt, qui simul accumbebant, dicere intra se: "quis est hic, qui etiam peccata dimittit?". Dixit autem ad mulierem: Fides tua te salvam fecit; vade in pace!". Et factum est deinceps, et ipse iter faciebat per civitatem et castellum praedicans et evangelizans regnum Dei, et Duodecim cum illo, et mulieres aliquae, quae erant curatae ab spiritibus malignis et infirmitatibus, Maria, quae vocatur Magdalene, de qua daemonia septem exierant, et Ioanna uxor Chuza procuratoris Herodis, et Sussanna et aliae multae, quae ministrabant eis de facultatibus suis.

Latin/Lesson 6-Translation. Congratulations! You have completed the Introductory Latin course! To finish off, you can look at an exciting section from Caesar's Civil Wars Book II stanza 10–12. Exercise 1 Skill: Translation from Latin source "Vocabulary", coming soon Ubi ex ea turri, quae circum essent opera, tueri se posse confisi sunt, musculum pedes LX longum ex turrim murumque perducerent, facere instituerunt cuius musculi haec erat forma. Duae primum trabes in solo aeque longae distantes inter se pedes IIII collocantur, inque eis columellae pedum in altitudinem V defiguntur. Has inter se capreolis molli fastigio coniungunt, ubi tigna, quae musculi tegendi causa ponant, collocentur. Eo super tigna bipedalia iniciunt eaque laminis clabisque religant. Ad extremum musculi tectum trabesque extremas quadratas regulas IIII patentes digitos difigunt, quae lateres, qui super musculo struantur, contineant. Ita fastigato atque ordinatim structo, ut trabes erant in capreolis collocatae. lateribus lutoque musculus, ut ab igni, qui ex muro iaceretur, tutus esset, contegitus. Super lateres coria inducuuntur, ne canalibus aqua immissa lateres diluere posset. Coria autem, ne rursus igni ac laidibus corrumpantur, centonibus conteguntur. Hoc opus omne tectum vineis ad ipsam turrim perficiunt subitoque inoopinantibus hostibus machinatione navali, phalangis subiectis, ad turrim hostium admovent, ut aedificio iungatur. Quo malo perterriti subito oppiindani saxa quam maxima possunt vectibus promovent praecipitataque muro in musculum devolvunt. Ictum firmitas materiae sustinet, et quicquid incidit fastigio musculi elabitur. Id ubi vident, mutant consilium: cupas taeda ac pice refertas incendunt easque de muro musculum devolvunt. Involutae labuntur, delapsae ab lateribus longuriis furcisque abopere removentur. Interim sub musculo milites vectibus infima saxa turris hostium, quibus fundamenta continebantur convellunt. Musculus ex turri latericia a nostris telis tormentisque defenditur; hostes ex muro ac turribus submoventur: non datur libera muro defendendi facultas. Compluribus iam lapidibus ex ea, quae suberat, turri subductis repentina ruina pars eius turrisconcidit, pars reliqua consequens procumbebat: cum hostes urbis direptione perterriti inermes cum infulis se porta foras universi proripiunt, ad legatos atque exercitum supplices manus tendunt.

Latin/Lesson 3-Translation. For your pleasure, I present to you a selection of poems from Catullus. Tips for translation: soon. Exercise 1 Skill: Reading Latin poetry I Cui dono lepidum novum libellum arido modo pumice expolitum? Corneli, tibi : namque tu solebas meas esse aliquid putare nugas, iam tum cum ausus es unus Italorum omne aevum tribus explicare chartis doctis, Juppiter, et laboriosis. quare habe tibi quicquid hoc libelli, qualecumque, quod, o patrona virgo, plus uno maneat perenne seclo. Exercise 2 Skill: Reading Latin poetry V Vivamus, mea Lesbia, atque amemus rumoresque senum severiorum omnes unius aestimemus assis. soles occidere et redire possunt. nobis, cum semel occidit brevis lux nox est perpetua una dormienda. da mi basia mille, deinde centum, dein mille altera, dein secunda centum deinde usque altera mille, deinde centum; dein, cum milia multa fecerimus conturbabimus illa, ne sciamus, aut nequis malus invidere possit, cum tantum sciat esse basiorum. Exercise 3 Skill: Reading Latin poetry XVI Pedicabo ego vos et irrumabo, Aureli pathice et cinaede Furi, qui me ex versiculis meis putastis, quod sunt molliculi, parum pudicum, nam castum esse decet pium poetam ipsum, versiculos nihil necessest. qui tum denique habent salem ac leporem. si sunt molliculi ac parum pudici et quod pruriat incitare possunt, non dico pueris, sed hi s pilosis, qui duros nequeunt moveere lumbos. vos, quod milia multa basiorum legistis, male me marem putatis? pedicabo ego vos et irrumabo. Exercise 4 Skill: Reading Latin poetry XCVII Non (ita me di ament) quicquam referre putavi, utrumne os an culum olgacerem Aemilio. nilo mundius hoc, niloque immundior ille, verum etiam culus mundior et melior, nam sine dentibus est: os dentis sesquipedalis, gingivas, vero ploxeni habet veteris, praeterea rictum qualem diffissus in aestu meientis mulae cunnus habere solet. hic futuit multas et se facit esse venustum, et non pistrino traditur atque asino? quem siqua attingit, non illam posse putemus aegroti culum lingere carnificis?

GCSE Science/Parallel and series circuits. GCSE Science/Electricity You will have already studied series and parallel circuits before, so should be familiar with what a series and parallel circuit is and their basic properties.But in this module we will be looking at them in a little more detail. We will apply Ohm's law to see how we can work out the resistance of a whole circuit that is made up of a large number of components. Before we begin You might want to try some revision questions. Follow the link then come back here when you are finished. GCSE Science/Parallel and series circuits revision questions. Resistors in Series Circuits. As we know, in a series circuit the current in all parts of the circuit is the same and the current has a one way system. The current depends on the applied voltage and the number of and nature of other components in the circuit. Consider two resistors in a series circuit with a battery. As you might expect the total resistance in this circuit is higher than the resistance of each resistor, because the battery has to "push" the charge through both resistors one after the other. So the total potential difference of the supply is "shared" between the two resistors. Think about what is happening to the current as it flows around the circuit. There are no branches, nowhere for the electric current to escape to, so obviously the same current must flow through both resistors. Let's call this current I. The total resistance for the whole circuit is very simple. It's just R1 plus R2. Formula for resistance of two resistors in series. RTotal = R1 + R2 The total resistance in a series circuit is the sum of the resistances of all the components. Using this formula we can calculate the voltage across each resistor. But it could depend on how many resistors there are. Example: Calculating voltages in a series circuit. Question: Suppose R1 = 1Ω and R2= 4Ω. If the battery supplies 2.5 Volts what is the voltage across each resistor. Answer: First use the total resistance of the circuit to work out how much current is flowing through the circuit. Step 1: Work out the total resistance Step 2: Use Ohms's law to calculate the current in the circuit. Decide which resistance to use. Now we know how much current is flowing through both resistors, we can work out the voltage across each resistor. Step 3: Use Ohm's law to calculate the voltage across each resistor: Resistors in Parallel Circuits. Parallel circuits are a bit more complicated than series circuits, because they contain a branch - the electric current will take more than one route. Look at the diagram. At point X the current splits into 2 paths, and flows through both resistor R1 and resistor R2. It may not split in equal amounts. When several(two or more) components are connected in parallel branches, the voltage (potential difference) across each parallel branch is the same. And this is the same as the voltage across the battery. The current through each component is the same as if it were the only component present. So the total current flowing through the battery is the sum of the currents flowing through each branch. Here is the formula for the currents flowing through a parallel circuit. IMain = I1 + I2 Because the voltage is the same for all branches, the branch with the lowest resistance has the highest current flowing through it. Because there are more paths for the charge to flow along, the total resistance is less than either of the two paths on their own. And therefore (with the same battery) the current is bigger. To find out the resistance of the whole circuit , we can't just add together the resistors as we did in the series circuit, we have to apply Ohm's law to each branch of the circuit. Imagine we replaced the resistors with bulbs. You should now be able to answer the following questions from your previous knowledge. If you answered the above questions correctly you should find this next section easy! Example: Calculating the resistance of several resistors in parallel. It's best to break the process down into a number of simple steps. Some books may give you a formula to use, but you shouldn't use any formula without understanding where it comes from (otherwise you are likely to remember it incorrectly or apply it inappropriately). By using a simple step by step method instead you can get a feel for why it works, and you will be far less likely to make a mistake in the exam. Step1 considering each branch on its own, as if the other branch didn't exist use Ohm's law to work out the current flowing through each branch. Step 2 Add the currents together to find out the total amount of current flowing through the whole circuit. Step 3 Apply Ohm's law again to work out the total resistance of the circuit. Example. Suppose V=2V R1 = 1Ω and R2= 1Ω. Applying Ohm's law to the branch containing R1 gives I1=V/R1 =2/1 =2A Applying Ohm's law to the branch containing R2 gives I2=V/R2 =2/1 =2A Total current = I1+I2 = 4A Applying Ohm's law again, to the whole circuit. RTotal =V/Itotal = 2/4 =0.5Ω Notice that the resistance of the whole circuit is "lower" than the resistance of either branch! Practice questions. Answers | Three useful components»

Spanish/Exercises/Personal Pronouns - Solutions. Soluciones a los ejercicios.<br> "(Solutions to the exercises)" Pronombres personales.<br> "(Personal pronouns.)" Ejercicio 1.<br> Rellena los espacios en blanco con los pronombres personales correctos en español. "Exercise 1."<br> "Fill the blank spaces with the correct Spanish personal pronous." Ejercicio 2.<br> Rellena los espacios en blanco con los pronombres personales correctos en español. "Exercise 2."<br> "Fill the blank spaces with the correct Spanish personal pronouns." Enlace a los Ejercicios "Link to exercises" Enlace a la lección 1 "Link to Lesson 1."

Spanish/Exercises/Regular Verbs - Solutions. Soluciones a los ejercicios. "Solutions to the exercises" "Fill in the blank". Por favor, rellena los espacios en blanco con la forma correcta del verbo: "Please, fill in the blank with the correct form of the verb:" 1. Nosotros aprendemos español. "We learn Spanish." 2. Yo compro un libro. "I buy a book." 3. Carmen y Roberto viajan a Mexico. "Carmen and Roberto travel to Mexico." 4. Ana habla ingles. "Ana speaks English." 5. Tú bebes una cerveza. "You drink a beer." 6. Susana escribe una carta. "Susana writes a letter." 7. Los niños estudian para el examen. "The children study for the exam." 8. Fernando y Lucas cantan una cancion. "Fernando and Lucas sing a song." 9. Tú lees un libro. "You read a book." 10. Vosotros subís las escaleras. "You (plural) climb the stairs." Enlace a los Ejercicios "Link to exercices" Enlace a la lección 3 "Link to the lesson 3."

Botany/Introduction discussion. Further Discussion. The questions posed in Chapter 1. Introduction are discussed further on this page. Remember, some questions are intended to be thought-provoking and more than one answer may be "correct". Users are encouraged to expand upon the discussions here. 1-1. "Do you think the "scientific method" is something only a scientist would use?" The "scientific method" is something that is taught, so we might question just how natural or intuitive an approach it is. Think about how you discovered answers to interesting or difficult questions as a child. You might have first sought the opinion of an expert (like your dad, right?). That is the first step used by a scientist as well. Scientists learn to seek the expertise of others that have asked similar questions and come up with at least partial answers. This does not require contacting other scientists; more often it is a matter of becoming very familiar with the literature (the written and published record) on the subject of interest. Scientists rarely formulate "hypotheses" without first learning all they can about a subject from what has been published already. In effect, they learn how to put their question at the very forefront of knowledge about a subject. There are so many questions to be answered in science that no one would want to expend a lot of energy asking and answering questions to mysteries already solved. Of course learning is different. Asking questions and seeking answers from books, journals, and other sources is a valid approach to this first step of learning, and one you and any scientist would have in common. Formulating a proper question or a hypothesis is perhaps the most difficult step. Recall that the hypothesis is not really a question but an answer. The question is the wonder about something; the hypothesis is a testable answer to that question. It is not THE answer, just a reasonable one posed in such a way that an experiment can be conducted to ascertain its validity. You may see this step expressed as "making a guess"; but consider that after he or she has completed the step described above—learning everything written about a subject—the scientist is in a position to make a pretty good guess. This step could be difficult for the scientist because he or she must have in mind one or more experiments to conduct to test the hypothesis. This step may be difficult for you for the same reason, and because it probably feels odd to answer a question before investigating it. The hypothesis step is included in the scientific method to promote intellectual honesty and to allow others to better understand a scientist's reasoning when reviewing what was done and how a conclusion was reached. Compare these scenarios: Or In the absence of any further report from this technician, only the second procedure provides any information to the next technician faced with a second, similar bomb. He at least knows what not to do! Note also that the hypothesis is falsifiable. Testing demonstrated whether an intact red wire was or was not needed for detonation (apparently it controlled the undetonated state). Framing the hypothesis thusly: "the red wire serves a purpose" cannot be proven false; what test could you devise to satisfactorily demonstrate it has no purpose? It may in fact have no purpose (not in the example above), but eliminating by testing every possible purpose under the sun is an unsatisfactory approach. 1-3. When you catch a cold a virus has infected your body. "Why do you think there is reason to question whether the virus is living or not?" After all, if you took some ricinin (a plant poison), you would get very sick, but no one would suggest the toxin were alive or that the plant had entered your body. Ricinin is an alkaloid and, along with the toxalbumin ricin (a plant protein), constitute extremely toxic substances found in the seeds of the castor bean ("Ricinus communis") plant. Were you to ingest several raw seeds, you would experience nausea and vomiting, stomachache, bloody diarrhea, headache, cold sweat, sleepiness, disorientation, fever, shortage of breath, seizures, and possibly collapse and death. While there are a number of different ways that a virus could enter your body, the most common would be breathing in virus particles while in the presence of an infected person. The outcome of such exposure could be pretty much the same as that described for ricinin ingestion, depending upon the type of virus and your body's ability to respond appropriately to the "infection". Or, perhaps the infection you "catch" is cholera—the "Vibrio cholerae" bacterium. These bacteria are typically ingested in drinking water contaminated by improper sanitation. Again, you might display many of the same symptoms described, including the really unpleasant part about dying. The point here is to consider which of these problems constitute an "attack" by another living organism and which represent simply a poisoning of your living body by a non-living chemical. You cannot use the resulting symptoms as an indication because...; well, because they are just symptoms: what you "feel" as your body reacts to the chemical or biological attack. In the case of ricin, this protein inhibits protein synthesis within the cells of the body. Organ damage results. "Vibrio cholerae" in the body produce a chemical that results in a loss of fluid and salts across the lining of the gut. The resulting diarrhea allows the bacterium to spread to other people under unsanitary conditions, and can result in death due to dehydration (an inability to retain water). So both the non-living chemical and the living bacterium cause illness by toxicity to our bodily functions. You should recognize one pretty significant difference between an illness caused by a living organisms and an illness caused by a non-living, but toxic, chemical. In the latter case, the severity of our symptoms will be pretty much dependent upon the dose of toxin we ingest. There will be just so much chemical entering the body, and the damage should be proportional to that amount. In the case of the bacterium, something like a million cells need to be ingested to result in an infection, but once established, the living organism is a tiny factory that cranks out toxin and reproduces more identical factories (more cells) that themselves produce toxin. So the dose of toxin we get from the bacterial infection is not obviously limited. Living cells metabolize (break down and produce chemicals for various purposes) and reproduce (increase their numbers). In essence, this is what is meant by an infection: another life form has taken up residence in or on our body, and is utilizing organic substances that are a part of our life processes to carry out its life functions, to further its existence and numbers. In the case of chlorea, the bacterium has some nasty habits that make us very ill; but there are a number of other bacteria ("Escherichi coli", for example) that live in perfect harmony within or digetive tract and help us digest food. So not every "alien" that invades our body necessarily causes an infection. « Chapter 1

Lojban/Dates. There are two systems of naming months in use: one based on the zodiac, and one based on numbers. The place structure is "x1 is foomonth in year x2 in calendar x3"; this is not according to jvojva but makes it easy to specify dates as "the day nth of the foomonth of the year mmmm". There are also systems of naming the days of the week based on Oriental elements and numbers. Note that Sunday in Lojban is either day seven or day zero, depending on your perspective.

Lojban/Directions. < Lojban N north berti B 0°00' NbE north by east bersunberberti BDBB 11°15' NNE north northeast bersunberti BDB 22°30' NEbN northeast by north bersunberstuna BDBD 33°45' NE northeast berstuna BD 45°00' NEbE northeast by east bersunsunberti BDDB 56°15' ENE east northeast bersunstuna BDD 67°30' EbN east by north bersunsunstuna BDDD 78°45' E east stuna D 90°00' EbS east by south nansunsunstuna NDDD 101°15' ESE east southeast nansunstuna NDD 112°30' SEbE southeast by east nansunsunsnanu NDDN 123°45' SE southeast nanstuna ND 135°00' SEbS southeast by south nansunynanstuna NDND 146°15' SSE south southeast nansunsnanu NDN 157°30' SbE south by east nansunynansnanu NDNN 168°45' S south snanu N 180°00' SbW south by west nansicnansnanu NVNN 191°15' SSW south southwest nansicysnanu NVN 202°30' SWbS southwest by south nansicnanstici NVNV 213°45' SW southwest nanstici NV 225°00' SWbW southwest by west nansicysicysnanu NVVN 236°15' WSW west southwest nansicystici NVV 247°30' WbS west by south nansicysicystici NVVV 258°45' W west stici V 270°00' WbN west by north bersicysicystici BVVV 281°15' WNW west northwest bersicystici BVV 292°30' NWbW northwest by west bersicysicyberti BVVB 303°45' NW northwest berstici BV 315°00' NWbN northwest by north bersicyberstici BVBV 326°15' NNW north northwest bersicyberti BVB 337°30' NbW north by west bersicyberberti BVBB 348°45'

Lojban/Le ninmu cu te dunda le ninmu le gerku. Lojban. le ninmu cu te dunda le gerku<br> .uinaicaidai zo'e na prami le ninmu<br> .i .a'ucu'idai le ninmu cu na junri zo'e<br> .i .u'icu'idai le ninmu na cmila<br> .i .iucu'idai le ninmu cu na prami zo'e<br> .i .a'odai le nanmu cu klama le ninmu la kentykis.<br> .i .i'odai le nanmu cu dunda le gerku le ninmu<br> .i .oidai le nanmu cu klama la kentykis. le ninmu<br> .i .uiru'edai le gerku cu prami le ninmu<br> .i .a'uru'edai le ninmu cu junri le gerku<br> .i .u'idai le ninmu cu cmila<br> .i .iucaidai le ninmu cu prami le gerku<br> English. The Woman Receives a Dog<br> Sadness! The woman is not loved.<br> Disinterest! The woman doesn't have a gravity for anything.<br> No amusement! The woman doesn't laugh.<br> No love! The woman doesn't love.<br> Hope! The man goes to the woman from Kentucky.<br> Appreciation! The man gives the dog to the woman.<br> Complaint! The man goes to Kentucky from the woman.<br> A little happiness! The dog loves the woman.<br> A little interest! The woman has a gravity for the dog.<br> Amusement! The woman laughs.<br> Lots of love! The woman loves the dog.

US History/New Nation. The Articles of Confederation. "(The following text is taken from Wikipedia)" The Articles of Confederation and Perpetual Union, also the Articles of Confederation, was the governing constitution of the alliance of thirteen independent and sovereign states styled "United States of America." The Article's ratification (proposed in 1777) was completed in 1782, legally uniting the states by compact into the "United States of America" as a union with a confederation government. Under the Articles (and the succeeding Constitution) the states retained sovereignty over all governmental functions not specifically deputed to the confederation. The final draft of the Articles was written in the summer of 1777 and adopted by the Second Continental Congress on November 15, 1777 in York, Pennsylvania after a year of debate. In practice the final draft of the Articles served as the "de facto" system of government used by the Congress ("the United States in Congress assembled") until it became "de jure" by final ratification on March 1, 1781; at which point Congress became the Congress of the Confederation. The "Articles" set the rules for operations of the "United States" confederation. The confederation was capable of making war, negotiating diplomatic agreements, and resolving issues regarding the western territories; it could mint coins and borrow inside and outside the United States. An important element of the Articles was that Article XIII stipulated that "their provisions shall be inviolably observed by every state" and "the Union shall be perpetual." This article was put to the test in the American Civil War. The Articles were created by the chosen representatives of the states in the Second Continental Congress out of a perceived need to have "a plan of confederacy for securing the freedom, sovereignty, and independence of the United States." Although serving a crucial role in the attainment of nationhood for the thirteen states, a group of reformers, known as "federalists", felt that the Articles lacked the necessary provisions for a sufficiently effective government. Fundamentally, a federation was sought to replace the confederation. The key criticism by those who favored a more powerful central state (i.e. the federalists) was that the government (i.e. the Congress of the Confederation) lacked taxing authority; it had to request funds from the states. Another criticism of the Articles was that they did not strike the right balance between large and small states in the legislative decision making process. Due to its "one-state, one-vote" plank, the larger states were expected to contribute more but had only one vote. The Articles were replaced by the United States Constitution on June 21, 1788. Background. The political push for the colonies to increase cooperation began in the French and Indian Wars in the mid 1750s. The opening of the American Revolutionary War in 1775 induced the various states to cooperate in seceding from the British Empire. The Second Continental Congress starting 1775 acted as the confederation organ that ran the war. Congress presented the Articles for enactment by the states in 1777, while prosecuting the American Revolutionary war against the Kingdom of Great Britain. Ratification. Congress began to move for ratification of the Articles in 1777: "The articles can always be candidly reviewed under a sense of the difficulty of combining in one general system the various sentiments and interests of a continent divided into so many sovereign and independent communities, under a conviction of the absolute necessity of uniting all our councils and all our strength, to maintain and defend our common liberties..." The document could not become officially effective until it was ratified by all of the thirteen colonies. The first state to ratify was Virginia on December 16, 1777. The process dragged on for several years, stalled by the refusal of some states to rescind their claims to land in the West. Maryland was the last holdout; it refused to go along until Virginia and New York agreed to cede their claims in the Ohio River valley. A little over three years passed before Maryland's ratification on March 1, 1781. Article summaries. Even though the Articles of Confederation and the Constitution were established by many of the same people, the two documents were very different. The original five-paged Articles contained thirteen articles, a conclusion, and a signatory section. The following list contains short summaries of each of the thirteen articles. Still at war with the Kingdom of Great Britain, the colonists were reluctant to establish another powerful national government. Jealously guarding their new independence, members of the Continental Congress created a loosely-structured unicameral legislature that protected the liberty of the individual states. While calling on Congress to regulate military and monetary affairs, for example, the Articles of Confederation provided no mechanism to force the states to comply with requests for troops or revenue. At times, this left the military in a precarious position, as George Washington wrote in a 1781 letter to the governor of Massachusetts, John Hancock. The end of the war. The Treaty of Paris (1783), which ended hostilities with Great Britain, languished in Congress for months because state representatives failed to attend sessions of the national legislature. Yet Congress had no power to enforce attendance. Writing to George Clinton in September 1783, George Washington complained: Function. The Articles supported the Congressional direction of the Continental Army, and allowed the 13 states to present a unified front when dealing with the European powers. As a tool to build a centralized war-making government, they were largely a failure, but since guerrilla warfare was correct strategy in a war against the British Empire's army, this "failure" succeeded in winning independence. Under the articles, Congress could make decisions, but had no power to enforce them. There was a requirement for unanimous approval before any modifications could be made to the Articles. Because the majority of lawmaking rested with the states, the central government was also kept limited. Congress was denied the power of taxation: it could only request money from the states. The states did not generally comply with the requests in full, leaving the confederation chronically short of funds. Congress was also denied the power to regulate commerce, and as a result, the states fought over trade as well. The states and the national congress had both incurred debts during the war, and how to pay the debts became a major issue. Some states paid off their debts; however, the centralizers favored federal assumption of states' debts. Nevertheless, the Congress of the Confederation did take two actions with lasting impact. The Land Ordinance of 1785 established the general land survey and ownership provisions used throughout later American expansion. The Northwest Ordinance of 1787 noted the agreement of the original states to give up western land claims and cleared the way for the entry of new states. Once the war was won, the Continental Army was largely disbanded. A very small national force was maintained to man frontier forts and protect against Indian attacks. Meanwhile, each of the states had an army (or militia), and 11 of them had navies. The wartime promises of bounties and land grants to be paid for service were not being met. In 1783, Washington defused the Newburgh conspiracy, but riots by unpaid Pennsylvania veterans forced the Congress to leave Philadelphia temporarily. Signatures. The Second Continental Congress approved the Articles for distribution to the states on November 15 1777. A copy was made for each state and one was kept by the Congress. The copies sent to the states for ratification were unsigned, and a cover letter had only the signatures of Henry Laurens and Charles Thomson, who were the president and secretary to the Congress. But, the "Articles" at that time were unsigned, and the date was blank. Congress began the signing process by examining their copy of the "Articles" on June 27 1778. They ordered a final copy prepared (the one in the National Archives), and that delegates should inform the secretary of their authority for ratification. On July 9, 1778, the prepared copy was ready. They dated it, and began to sign. They also requested each of the remaining states to notify its delegation when ratification was completed. On that date, delegates present from New Hampshire, Massachusetts, Rhode Island, Connecticut, New York, Pennsylvania, Virginia and South Carolina signed the Articles to indicate that their states had ratified. New Jersey, Delaware and Maryland could not, since their states had not ratified. North Carolina and Georgia also didn't sign that day, since their delegations were absent. After the first signing, some delegates signed at the next meeting they attended. For example, John Wentworth of New Hampshire added his name on August 8. John Penn was the first of North Carolina's delegates to arrive (on July 10), and the delegation signed the "Articles" on July 21 1778. The other states had to wait until they ratified the "Articles" and notified their Congressional delegation. Georgia signed on July 24, New Jersey on November 26, and Delaware on February 12 1779. Maryland refused to ratify the "Articles" until every state had ceded its western land claims. On February 2, 1781, the much-awaited decision was taken by the Maryland General Assembly in Annapolis. As the last piece of business during the afternoon Session, "among engrossed Bills" was "signed and sealed by Governor Thomas Sim Lee in the Senate Chamber, in the presence of the members of both Houses… an Act to empower the delegates of this state in Congress to subscribe and ratify the articles of confederation" and perpetual union among the states. The Senate then adjourned "to the first Monday in August next." The decision of Maryland to ratify the Articles was reported to the Continental Congress on February 12. The formal signing of the "Articles" by the Maryland delegates took place in Philadelphia at noon time on March 1, 1781 and was celebrated in the afternoon. With these events, the Articles entered into force and the United States came into being as a united, sovereign and national state. Congress had debated the "Articles" for over a year and a half, and the ratification process had taken nearly three and a half years. Many participants in the original debates were no longer delegates, and some of the signers had only recently arrived. The "Articles of Confederation and Perpetual Union" were signed by a group of men who were never present in the Congress at the same time. The signers and the states they represented were: Presidents of the Congress. The following list is of those who led the Congress of the Confederation under the "Articles of Confederation" as the presidents of the United States in Congress Assembled. Under the Articles, the president was the presiding officer of Congress, chaired the Cabinet (the Committee of the States) when Congress was in recess, and performed other administrative functions. He was not, however, a "chief" executive in the way the successor "President of the United States" is a chief executive, but all of the functions he executed were under the auspices and in service of the Congress. "For a full list of presidents of the Congress Assembled and presidents under the two Continental Congresses before the Articles, see President of the Continental Congress." Revision and replacement. In May 1786, Charles Pinckney of South Carolina proposed that Congress revise the Articles of Confederation. Recommended changes included granting Congress power over foreign and domestic commerce, and providing means for Congress to collect money from state treasuries. Unanimous approval was necessary to make the alterations, however, and Congress failed to reach a consensus. In September, five states assembled in the Annapolis Convention to discuss adjustments that would improve commerce. Under their chairman, Alexander Hamilton, they invited state representatives to convene in Philadelphia to discuss improvements to the federal government. Although the states' representatives to the Constitutional Convention in Philadelphia were only authorized to amend the Articles, the representatives held secret, closed-door sessions and wrote a new constitution. The new Constitution gave much more power to the central government, but characterization of the result is disputed. Historian Forrest McDonald, using the ideas of James Madison from "Federalist 39", describes the change this way: Historian Ralph Ketcham comments on the opinions of Patrick Henry, George Mason, and other antifederalists who were not so eager to give up the local autonomy won by the revolution: According to their own terms for modification (Article XIII), the Articles would still have been in effect until 1790, the year in which the last of the 13 states ratified the new Constitution. The Congress under the Articles continued to sit until November 1788, overseeing the adoption of the new Constitution by the states, and setting elections. Historians have given many reasons for the perceived need to replace the articles in 1787. Jillson and Wilson (1994) point to the financial weakness as well as the norms, rules and institutional structures of the Congress, and the propensity to divide along sectional lines. Rakove (1988) identifies several factors that explain the collapse of the Confederation. The lack of compulsory direct taxation power was objectionable to those wanting a strong centralized state or expecting to benefit from such power. It could not collect customs after the war because tariffs were vetoed by Rhode Island. Rakove concludes that their failure to implement national measures "stemmed not from a heady sense of independence but rather from the enormous difficulties that all the states encountered in collecting taxes, mustering men, and gathering supplies from a war-weary populace." The second group of factors Rakove identified derived from the substantive nature of the problems the Continental Congress confronted after 1783, especially the inability to create a strong foreign policy. Finally, the Confederation's lack of coercive power reduced the likelihood for profit to be made by political means, thus potential rulers were uninspired to seek power. When the war ended in 1783, certain special interests had incentives to create a new "merchant state," much like the British state people had rebelled against. In particular, holders of war scrip and land speculators wanted a central government to pay off scrip at face value and to legalize western land holdings with disputed claims. Also, manufacturers wanted a high tariff as a barrier to foreign goods, but competition among states made this impossible without a central government. Historical importance. The Articles are historically important for two major reasons: "i)" they were the first constitution or governing document for the United States of America and "ii)" they legally established a union of the thirteen founding states; a Perpetual Union. Early on, tensions developed surrounding the Union, not least because of the fact that with the US Constitution the basis of government was changed from that of confederation to federation. Thomas Jefferson and John C. Calhoun were in their time leading proponents of guaranteeing the constitutional rights of states in federal legislation. Over time, a legal view developed that if the union violated the constitutional rights of states they might rightfully seceed. A significant tension in the 19th century surrounded the expansion of slavery (which was generally supported in agricultural Southern states and opposed in industrial Northern states). As the secessionist view gained support in the South, the opposing view in the North was that since the U.S. Constitution declared itself to be "a more perfect union" than the Articles, it too must be perpetual, and also could not be broken without the consent of the other states. This view was promoted by Daniel Webster and Abraham Lincoln. In 1861, these constitutional contracts were cited by President Lincoln against any claims by the seceding states that unilaterally withdrawing from the Union and taking federal property within those states was legal. The Northwest Ordinance. The Congress established the Northwest Territory around the Great Lakes between 1784 and 1787. In 1787, Congress passed the Northwest Ordinance banning slavery in the new Territory. Congressional legislation divided the Territory into "townships" of six square miles each and provided for the sale of land to settlers. The Northwest Territory would eventually become the states of Ohio, Wisconsin, Indiana, Illinois and Michigan. Problems with the Confederation. The Confederation faced several difficulties in its early years. Firstly, Congress became extremely dependent on the states for income. Also, states refused to require its citizens to pay debts to British merchants, straining relations with Great Britain. France prohibited Americans from using the important port of New Orleans, crippling American trade down the Mississippi river. Shays' Rebellion. Due to the post-revolution economic woes, agitated by inflation, many worried of social instability. This was especially true for those in Massachusetts. The legislature's response to the shaky economy was to put emphasis on maintaining a sound currency by paying off the state debt through levying massive taxes. The tax burden hit those with moderate incomes dramatically. The average farmer paid a third of their annual income to these taxes from 1780 to 1786. Those who couldn't pay had their property foreclosed and were thrown into crowded prisons filled with other debtors. But in the summer of 1786, a revolutionary war veteran named Daniel Shays began to organize western communities in Massachusetts to stop foreclosures, with force, by prohibiting the courts from holding their proceedings. Later that fall, Shays marched the newly formed "rebellion" into Springfield to stop the state supreme court from gathering. The state responded with troops sent to suppress the rebellion. After a failed attempt by the rebels to attack the Springfield arsenal, and other small skirmishes, the rebels retreated and then uprising collapsed. Shays retreated to Vermont by 1787. While Daniel Shays was in hiding, the government condemned him to death on the charge of treason. Shays pleaded for his life in a petition which was finally granted by John Hancock on June 17, 1788. With the threat of treason behind him, Shays moved to New York and died September 25, 1825 U.S. presidents before George Washington. Who was the first president of the United States? Ask any school child and they will readily tell you "George Washington." And of course, they would be correct—at least technically. Washington was inaugurated on April 30, 1789, and yet, the United States continually had functioning governments from as early as September 5, 1774, and operated as a confederated nation from as early as July 4, 1776. During that nearly fifteen-year interval, Congress—first the Continental Congress and then later the Confederation Congress—was always moderated by a duly elected president. This officer was known as the "President of the Continental Congress", and later as the "President of the United States, in Congress Assembled". However, the office of President of the Continental Congress had very little relationship to the office of President of the United States beyond the name. The president of the United States is the head of the executive branch of government, while the president of the Continental Congress was merely the chair of a body that most resembled a legislature, although it possessed legislative, executive, and judicial powers. The following brief biographies profile these "forgotten presidents." Peyton Randolph of Virginia (1723–1775) When delegates gathered in Philadelphia for the first Continental Congress, they promptly elected the former King's Attorney of Virginia as the moderator and president of their convocation. He was a propitious choice. He was a legal prodigy—having studied at the Inner Temple in London, served as his native colony's Attorney General, and tutored many of the most able men of the South at William and Mary College—including the young Patrick Henry. His home in Williamsburg was the gathering place for Virginia's legal and political gentry—and it remains a popular attraction in the restored colonial capital. He had served as a delegate in the Virginia House of Burgesses, and had been a commander under William Byrd in the colonial militia. He was a scholar of some renown—having begun a self-guided reading of the classics when he was thirteen. Despite suffering poor health served the Continental Congress as president twice, in 1774 from September 5 to October 21, and then again for a few days in 1775 from May 10 to May 23. He never lived to see independence, yet was numbered among the nation's most revered founders. Henry Middleton (1717–1784) America's second elected president was one of the wealthiest planters in the South, the patriarch of the most powerful families anywhere in the nation. His public spirit was evident from an early age. He was a member of his state's Common House from 1744 to 1747. During the last two years he served as the Speaker. During 1755 he was the King's Commissioner of Indian Affairs. He was a member of the South Carolina Council from 1755 to 1770. His valor in the War with the Cherokees during 1760–1761 earned him wide recognition throughout the colonies—and demonstrated his leadership abilities while under pressure. He was elected as a delegate to the first session of the Continental Congress and when Peyton Randolph was forced to resign the presidency, his peers immediately turned to Middleton to complete the term. He served as the fledgling coalition's president from October 22, 1774, until Randolph was able to resume his duties briefly beginning on May 10, 1775. Afterward, he was a member of the Congressional Council of Safety and helped to establish the young nation's policy toward the encouragement and support of education. In February 1776 he resigned his political involvements in order to prepare his family and lands for what he believed was inevitable war—but he was replaced by his son Arthur who eventually became a signer of both the Declaration of Independence and the Articles of Confederation, served time as an English prisoner of war, and was twice elected Governor of his state. John Hancock (1737–1793) The third president was a patriot, rebel leader, merchant who signed his name into immortality in giant strokes on the Declaration of Independence on July 4, 1776. The boldness of his signature has made it live in American minds as a perfect expression of the strength and freedom—and defiance—of the individual in the face of British tyranny. As President of the Continental Congress during two widely spaced terms—the first from May 24 1775 to October 30 1777 and the second from November 23, 1785, to June 5, 1786—Hancock was the presiding officer when the members approved the Declaration of Independence. Because of his position, it was his official duty to sign the document first—but not necessarily as dramatically as he did. Hancock figured prominently in another historic event—the battle at Lexington: British troops who fought there April 10, 1775, had known Hancock and Samuel Adams were in Lexington and had come there to capture these rebel leaders. And the two would have been captured, if they had not been warned by Paul Revere. As early as 1768, Hancock defied the British by refusing to pay customs charges on the cargo of one of his ships. One of Boston's wealthiest merchants, he was recognized by the citizens, as well as by the British, as a rebel leader—and was elected President of the first Massachusetts Provincial Congress. After he was chosen President of the Continental Congress in 1775, Hancock became known beyond the borders of Massachusetts, and, having served as colonel of the Massachusetts Governor's Guards he hoped to be named commander of the American forces—until John Adams nominated George Washington. In 1778 Hancock was commissioned Major General and took part in an unsuccessful campaign in Rhode Island. But it was as a political leader that his real distinction was earned—as the first Governor of Massachusetts, as President of Congress, and as President of the Massachusetts constitutional ratification convention. He helped win ratification in Massachusetts, gaining enough popular recognition to make him a contender for the newly created Presidency of the United States, but again he saw Washington gain the prize. Like his rival, George Washington, Hancock was a wealthy man who risked much for the cause of independence. He was the wealthiest New Englander supporting the patriotic cause, and, although he lacked the brilliance of John Adams or the capacity to inspire of Samuel Adams, he became one of the foremost leaders of the new nation—perhaps, in part, because he was willing to commit so much at such risk to the cause of freedom. Henry Laurens (1724–1792) The only American president ever to be held as a prisoner of war by a foreign power, Laurens was heralded after he was released as "the father of our country," by no less a personage than George Washington. He was of Huguenot extraction, his ancestors having come to America from France after the revocation of the Edict of Nantes made the Reformed faith illegal. Raised and educated for a life of mercantilism at his home in Charleston, he also had the opportunity to spend more than a year in continental travel. It was while in Europe that he began to write revolutionary pamphlets—gaining him renown as a patriot. He served as vice-president of South Carolina in 1776. He was then elected to the Continental Congress. He succeeded John Hancock as President of the newly independent but war beleaguered United States on November 1, 1777. He served until December 9, 1778, at which time he was appointed Ambassador to the Netherlands. Unfortunately for the cause of the young nation, he was captured by an English warship during his cross-Atlantic voyage and was confined to the Tower of London until the end of the war. After the Battle of Yorktown, the American government regained his freedom in a dramatic prisoner exchange—President Laurens for Lord Cornwallis. Ever the patriot, Laurens continued to serve his nation as one of the three representatives selected to negotiate terms at the Paris Peace Conference in 1782. John Jay (1745–1829) America's first Secretary of State, first Chief Justice of the Supreme Court, one of its first ambassadors, and author of some of the celebrated Federalist Papers, Jay was a Founding Father who, by a quirk of fate, missed signing the Declaration of Independence—at the time of the vote for independence and the signing, he had temporarily left the Continental Congress to serve in New York's revolutionary legislature. Nevertheless, he was chosen by his peers to succeed Henry Laurens as President of the United States—serving a term from December 10, 1778, to September 27, 1779. A conservative New York lawyer who was at first against the idea of independence for the colonies, the aristocratic Jay in 1776 turned into a patriot who was willing to give the next twenty-five years of his life to help establish the new nation. During those years, he won the regard of his peers as a dedicated and accomplished statesman and a man of unwavering principle. In the Continental Congress Jay prepared addresses to the people of Canada and Great Britain. In New York he drafted the State constitution and served as Chief Justice during the war. He was President of the Continental Congress before he undertook the difficult assignment, as ambassador, of trying to gain support and funds from Spain. After helping Franklin, Jefferson, Adams, and Laurens complete peace negotiations in Paris in 1783, Jay returned to become the first Secretary of State, called "Secretary of Foreign Affairs" under the Articles of Confederation. He negotiated valuable commercial treaties with Russia and Morocco, and dealt with the continuing controversy with Britain and Spain over the southern and western boundaries of the United States. He proposed that America and Britain establish a joint commission to arbitrate disputes that remained after the war—a proposal which, though not adopted, influenced the government's use of arbitration and diplomacy in settling later international problems. In this post Jay felt keenly the weakness of the Articles of Confederation and was one of the first to advocate a new governmental compact. He wrote five Federalist Papers supporting the Constitution, and he was a leader in the New York ratification convention. As first Chief Justice of the Supreme Court, Jay made the historic decision that a State could be sued by a citizen from another State, which led to the Eleventh Amendment to the Constitution. On a special mission to London he concluded the "Jay Treaty," which helped avert a renewal of hostilities with Britain but won little popular favor at home—and it is probably for this treaty that this Founding Father is best remembered. Samuel Huntington (1732–1796) An industrious youth who mastered his studies of the law without the advantage of a school, a tutor, or a master—borrowing books and snatching opportunities to read and research between odd jobs—he was one of the greatest self-made men among the Founders. He was also one of the greatest legal minds of the age—all the more remarkable for his lack of advantage as a youth. In 1764, in recognition of his obvious abilities and initiative, he was elected to the General Assembly of Connecticut. The next year he was chosen to serve on the Executive Council. In 1774 he was appointed Associate Judge of the Superior Court and, as a delegate to the Continental Congress, was acknowledged to be a legal scholar of some respect. He served in Congress for five consecutive terms, during the last of which he was elected President. He served in that office from September 28, 1779 until ill health forced him to resign on July 9, 1781. He returned to his home in Connecticut—and as he recuperated, he accepted more Councilor and Bench duties. He again took his seat in Congress in 1783, but left it to become Chief Justice of his state's Superior Court. He was elected Lieutenant Governor in 1785 and Governor in 1786. According to John Jay, he was "the most precisely trained Christian jurists ever to serve his country." Thomas McKean (1734–1817) During his astonishingly varied fifty-year career in public life he held almost every possible position—from deputy county attorney to President of the United States under the Confederation. Besides signing the Declaration of Independence, he contributed significantly to the development and establishment of constitutional government in both his home state of Delaware and the nation. At the Stamp Act Congress he proposed the voting procedure that Congress adopted: that each colony, regardless of size or population, has one vote—the practice adopted by the Continental Congress and the Congress of the Confederation, and the principle of state equality manifest in the composition of the Senate. And as county judge in 1765, he defied the British by ordering his court to work only with documents that did not bear the hated stamps. In June 1776, at the Continental Congress, McKean joined with Caesar Rodney to register Delaware's approval of the Declaration of Independence, over the negative vote of the third Delaware delegate, George Read—permitting it to be "The unanimous declaration of the thirteen United States." And at a special Delaware convention, he drafted the constitution for that State. McKean also helped draft—and signed—the Articles of Confederation. It was during his tenure of service as President—from July 10, 1781 to November 4, 1782—when news arrived from General Washington in October 1781 that the British had surrendered following the Battle of Yorktown. As Chief Justice of the supreme court of Pennsylvania, he contributed to the establishment of the legal system in that State, and, in 1787, he strongly supported the Constitution at the Pennsylvania Ratification Convention, declaring it "the best the world has yet seen." At sixty-five, after over forty years of public service, McKean resigned from his post as Chief Justice. A candidate on the Democratic-Republican ticket in 1799, McKean was elected Governor of Pennsylvania. As Governor, he followed such a strict policy of appointing only fellow Republicans to office that he became the father of the spoils system in America. He served three tempestuous terms as Governor, completing one of the longest continuous careers of public service of any of the Founding Fathers. John Hanson (1715–1783) He was the heir of one of the greatest family traditions in the colonies and became the patriarch of a long line of American patriots—his great grandfather died at Lutzen beside the great King Gustavus Aldophus of Sweden; his grandfather was one of the founders of New Sweden along the Delaware River in Maryland; one of his nephews was the military secretary to George Washington; another was a signer of the Declaration; still another was a signer of the Constitution; yet another was Governor of Maryland during the Revolution; and still another was a member of the first Congress; two sons were killed in action with the Continental Army; a grandson served as a member of Congress under the new Constitution; and another grandson was a Maryland Senator. Thus, even if Hanson had not served as President himself, he would have greatly contributed to the life of the nation through his ancestry and progeny. As a youngster he began a self-guided reading of classics and rather quickly became an acknowledged expert in the juridicalism of Anselm and the practical philosophy of Seneca—both of which were influential in the development of the political philosophy of the great leaders of the Reformation. It was based upon these legal and theological studies that the young planter—his farm, Mulberry Grove was just across the Potomac from Mount Vernon—began to espouse the cause of the patriots. In 1775 he was elected to the Provincial Legislature of Maryland. Then in 1777, he became a member of Congress where he distinguished himself as a brilliant administrator. Thus, he was elected President in 1781. He served in that office from November 5, 1781 until November 3, 1782. He was the first president to serve a full term after the full ratification of the Articles of Confederation—and like so many of the Southern and New England Founders, he was strongly opposed to the Constitution when it was first discussed. He remained a confirmed anti-federalist until his untimely death. Elias Boudinot (1741–1802) He did not sign the Declaration, the Articles, or the Constitution. He did not serve in the Continental Army with distinction. He was not renowned for his legal mind or his political skills. He was instead a man who spent his entire career in foreign diplomacy. He earned the respect of his fellow patriots during the dangerous days following the traitorous action of Benedict Arnold. His deft handling of relations with Canada also earned him great praise. After being elected to the Congress from his home state of New Jersey, he served as the new nation's Secretary for Foreign Affairs—managing the influx of aid from France, Spain, and Holland. The in 1783 he was elected to the Presidency. He served in that office from November 4, 1782 until November 2, 1783. Like so many of the other early presidents, he was a classically trained scholar, of the Reformed faith, and an anti-federalist in political matters. He was the father and grandfather of frontiersmen—and one of his grandchildren and namesakes eventually became a leader of the Cherokee nation in its bid for independence from the sprawling expansion of the United States. Thomas Mifflin (1744–1800) By an ironic sort of providence, Thomas Mifflin served as George Washington's first aide-de-camp at the beginning of the Revolutionary War, and, when the war was over, he was the man, as President of the United States, who accepted Washington's resignation of his commission. In the years between, Mifflin greatly served the cause of freedom—and, apparently, his own cause—while serving as the first Quartermaster General of the Continental Army. He obtained desperately needed supplies for the new army—and was suspected of making excessive profit himself. Although experienced in business and successful in obtaining supplies for the war, Mifflin preferred the front lines, and he distinguished himself in military actions on Long Island and near Philadelphia. Born and reared a Quaker, he was excluded from their meetings for his military activities. A controversial figure, Mifflin lost favor with Washington and was part of the Conway Cabal—a rather notorious plan to replace Washington with General Horatio Gates. And Mifflin narrowly missed court-martial action over his handling of funds by resigning his commission in 1778. In spite of these problems—and of repeated charges that he was a drunkard—Mifflin continued to be elected to positions of responsibility—as President and Governor of Pennsylvania, delegate to the Constitutional Convention, as well as the highest office in the land—where he served from November 3, 1783, to November 29, 1784. Most of Mifflin's significant contributions occurred in his earlier years—in the First and Second Continental Congresses he was firm in his stand for independence and for fighting for it, and he helped obtain both men and supplies for Washington's army in the early critical period. In 1784, as president, he signed the treaty with Great Britain which ended the war. Although a delegate to the Constitutional Convention, he did not make a significant contribution—beyond signing the document. As Governor of Pennsylvania, although he was accused of negligence, he supported improvements of roads, and reformed the State penal and judicial systems. He had gradually become sympathetic to Jefferson's principles regarding states' rights; even so, he directed the Pennsylvania militia to support the Federal tax collectors in the Whiskey Rebellion. In spite of charges of corruption, the affable Mifflin remained a popular figure. A magnetic personality and an effective speaker, he managed to hold a variety of elective offices for almost thirty years of the critical Revolutionary period. Richard Henry Lee (1732–1794) His resolution "that these United Colonies are, and of right ought to be, free and independent States", approved by the Continental Congress July 2, 1776, was the first official act of the United Colonies that set them irrevocably on the road to independence. It was not surprising that it came from Lee's pen—as early as 1768 he proposed the idea of committees of correspondence among the colonies, and in 1774 he proposed that the colonies meet in what became the Continental Congress. From the first, his eye was on independence. A wealthy Virginia planter whose ancestors had been granted extensive lands by King Charles II, Lee disdained the traditional aristocratic role and the aristocratic view. In the House of Burgesses he flatly denounced the practice of slavery. He saw independent America as "an asylum where the unhappy may find solace, and the persecuted repose." In 1764, when news of the proposed Stamp Act reached Virginia, Lee was a member of the committee of the House of Burgesses that drew up an address to the King, an official protest against such a tax. After the tax was established, Lee organized the citizens of his county into the Westmoreland Association, a group pledged to buy no British goods until the Stamp Act was repealed. At the First Continental Congress, Lee persuaded representatives from all the colonies to adopt this non-importation idea, leading to the formation of the Continental Association, which was one of the first steps toward union of the colonies. Lee also proposed to the First Continental Congress that a militia be organized and armed—the year before the first shots were fired at Lexington; but this and other proposals of his were considered too radical—at the time. Three days after Lee introduced his resolution, in June of 1776, he was appointed by Congress to the committee responsible for drafting a declaration of independence, but he was called home when his wife fell ill, and his place was taken by his young protégé, Thomas Jefferson. Thus Lee missed the chance to draft the document—though his influence greatly shaped it and he was able to return in time to sign it. He was elected President—serving from November 30, 1784 to November 22, 1785 when he was succeeded by the second administration of John Hancock. Elected to the Constitutional Convention, Lee refused to attend, but as a member of the Congress of the Confederation, he contributed to another great document, the Northwest Ordinance, which provided for the formation of new States from the Northwest Territory. When the completed Constitution was sent to the States for ratification, Lee opposed it as anti-democratic and anti-Christian. However, as one of Virginia's first Senators, he helped assure passage of the amendments that, he felt, corrected many of the document's gravest faults—the Bill of Rights. He was the great uncle of Robert E. Lee and the scion of a great family tradition. Nathaniel Gorham (1738–1796) Another self-made man, Gorham was one of the many successful Boston merchants who risked all he had for the cause of freedom. He was first elected to the Massachusetts General Court in 1771. His honesty and integrity won his acclaim and was thus among the first delegates chose to serve in the Continental Congress. He remained in public service throughout the war and into the Constitutional period, though his greatest contribution was his call for a stronger central government. But even though he was an avid federalist, he did not believe that the union could—or even should—be maintained peaceably for more than a hundred years. He was convinced that eventually, in order to avoid civil or cultural war, smaller regional interests should pursue an independent course. His support of a new constitution was rooted more in pragmatism than ideology. When John Hancock was unable to complete his second term as President, Gorham was elected to succeed him—serving from June 6, 1786 to February 1, 1787. It was during this time that the Congress actually entertained the idea of asking Prince Henry—the brother of Frederick II of Prussia—and Bonnie Prince Charlie—the leader of the ill-fated Scottish Jacobite Rising and heir of the Stuart royal line—to consider the possibility of establishing a constitutional monarch in America. It was a plan that had much to recommend it but eventually the advocates of republicanism held the day. During the final years of his life, Gorham was concerned with several speculative land deals which nearly cost him his entire fortune. Arthur St. Clair (1734–1818) Born and educated in Edinburgh, Scotland, during the tumultuous days of the final Jacobite Rising and the Tartan Suppression, St. Clair was the only president of the United States born and bred on foreign soil. Though most of his family and friends abandoned their devastated homeland in the years following the Battle of Culloden—after which nearly a third of the land was depopulated through emigration to America—he stayed behind to learn the ways of the hated Hanoverian English in the Royal Navy. His plan was to learn of the enemy's military might in order to fight another day. During the global conflict of the Seven Years' War—generally known as the French and Indian War—he was stationed in the American theater. Afterward, he decided to settle in Pennsylvania where many of his kin had established themselves. His civic-mindedness quickly became apparent: he helped to organize both the New Jersey and the Pennsylvania militias, led the Continental Army's Canadian expedition, and was elected Congress. His long years of training in the enemy camp was finally paying off. He was elected President in 1787—and he served from February 2 of that year until January 21 of the next. Following his term of duty in the highest office in the land, he became the first Governor of the Northwest Territory. Though he briefly supported the idea of creating a constitutional monarchy under the Stuart's Bonnie Prince Charlie, he was a strident Anti-Federalist—believing that the proposed federal constitution would eventually allow for the intrusion of government into virtually every sphere and aspect of life. He even predicted that under the vastly expanded centralized power of the state the taxing powers of bureaucrats and other unelected officials would eventually confiscate as much as a quarter of the income of the citizens—a notion that seemed laughable at the time but that has proven to be ominously modest in light of our current governmental leviathan. St. Clair lived to see the hated English tyrants who destroyed his homeland defeated. But he despaired that his adopted home might actually create similar tyrannies and impose them upon themselves. Cyrus Griffin (1736–1796) Like Peyton Randolph, he was trained in London's Inner Temple to be a lawyer—and thus was counted among his nation's legal elite. Like so many other Virginians, he was an anti-federalist, though he eventually accepted the new Constitution with the promise of the Bill of Rights as a hedge against the establishment of an American monarchy—which still had a good deal of currency. The Articles of Confederation afforded such freedoms that he had become convinced that even with the incumbent loss of liberty, some new form of government would be required. A protégé of George Washington—having worked with him on several speculative land deals in the West—he was a reluctant supporter of the constitutional ratifying process. It was during his term in the office of the presidency—the last before the new national compact went into effect–that ratification was formalized and finalized. He served as the nation's chief executive from January 22, 1788 until George Washington's inauguration on April 30, 1789.

Spanish/Exercises/Articles. ^Lesson 2^ "Fill in the blank". Por favor, rellena los espacios en blanco con el articulo correcto: "Please, fill in the blank with the correct article:" 1. ____ mesa "(a table)" 2. ____ caballos "(some horses)" 3. ____ gato "(the cat)" 4. ____ ciudad "(the city)" 5. ____ casas "(some houses)" 6. ____ hijos "(the sons)" 7. ____ hijas "(the daughters)" 8. ____ perro "(a dog)" Soluciones a los ejercicios "Solutions to exercices" ^Lesson 2^

Spanish/Exercises/Telling Time. ^Lesson 2^ Translate the following into Spanish. Soluciones a los ejercicios "Solutions to exercices" ^Lesson 2^

GCSE Science/Three useful components. GCSE Science/Electricity This page looks at three components that are used in electrical circuits. The three components in question are: The diode, the thermistor, and the light dependent resistor. You will see how the components work and how they are used. The Diode. A diode is a device that allows current to flow in one direction but not in the reverse direction. Its circuit symbol consists of a triangle pointing in the direction that current "is" allowed to flow with a line at the point, inside a circle. Diodes are useful for stopping current flowing in the "wrong" direction. Above is a current voltage graph for a typical diode. Note that the diode needs a small voltage (about 0.6V) to work. Below 0.6V in the forward direction very little current flows. At or above 0.6V the resistance drops dramatically and a huge current can flow. In the reverse direction, virtually no current flows no matter how large the voltage is. (Eventually, when the voltage gets high enough, the diode "breaks down" and current is able to flow in the reverse direction. For normal diodes however this "break down voltage" is very high and can be ignored. A diode that is connected in reverse to use the break down effect is called a Zener diode. It is used to provide voltage control in power supplies (called the Zener voltage).) Diodes are useful for turning AC current into DC current (AC/DC converters are called rectifiers). In AC the electricity flows back and forth in cycles. Mains electricity is AC. It cycles 50 times every second. This is fine for something like a lightbulb, where the bulb does not care in which direction the electricity flows. Some devices however can only work off DC. A toy electric train for example would not go with AC. The current would be saying "go forwards", "go backwards" over and over again 50 times a second! With a diode in the circuit the "negative" part of the cycle is stopped. The graph on the left shows AC current. Note that the current cycles positive, negative, positive, and so on. The electricity is flowing to and fro. Putting the current through a diode has the result seen on the right. The positive part of the cycle in unaffected, but the negative is wiped out. The current goes positive, zero, positive. The Thermistor. A thermistor is a just a resistor whose resistance depends on temperature. Most thermistors have lower resistance when the temperature is high. They are used in circuits which are temperature dependent. For example, fire alarms, the temperature gets too high; the alarm sounds. The LDR. A light dependent resistor is a resistor whose resistance depends on the amount of light shining on it. Its resistance gets less the more light shines on it. It can be used in circuits that are light dependent. For example, switching circuits for street lights. The ambient light gets too low; the lamp turns on. It is also known as a photoresistor from photo, the Latin for light. Questions. Safety in Mains circuits»

GCSE Science/Safety in Mains circuits. GCSE Science/Electricity Mains electricity is potentially dangerous. There are, however, safety features included in plugs. This module looks at how to wire a plug correctly. The three pin plug. Nowadays most appliances are sold with moulded plugs already fitted. Nevertheless, it is still important to understand the correct wiring of a plug because enough of the old plugs still exist. It is also the case when you bring in equipments overseas. British Standard compliant adaptors are not always available for such non-UK plugs. You are very likely to need to change a plug at some time in your life. In the UK mains electricity is 230 V. (In Hong Kong, it is 220 V.) If you were to touch a live wire a current would flow through your body to the ground. This current may be enough to kill you. The cable from the appliance usually consist of three wires, an earth and two other wires, live and neutral, which carry the current to and from the power station (live is from the power station and neutral is back to the power station). The wires are made of copper surrounded by an insulation casing. The casing is made of plastic and is coloured: The three wires are covered by an outer sheath made of plastic. Q1) Use your knowledge of insulators and conductors to explain The plug has the following features: Q2) Why are the pins made of brass and why is the case plastic? The purpose of the parts of a plug. The live and neutral wires. The live and neutral wires carry the current around the circuit. Mains current is A.C. (alternating current); this means that it is going backward and forwards in cycles (clockwise and anticlockwise around the circuit). The frequency of the cycle is 50 hertz (50 times per second). This cycling of current is achieved by varying the voltage on the line wire from about +325V to – you to the earth. This is where the earth wire is included, for your safety. The earth wire connects the case of the appliance out down the flex to the earth pin on its plug. This connection goes into the socket, then inside the wiring of your house down to the earth through the earthing system (not necessarily plumbing). If the live wire were to touch the case a huge current would flow through the earth wire. This would probably blow the fuse and break the circuit (see next section). However even if the fuse doesn't blow the current would still prefer to flow through a wire with low resistance than a human body with relatively higher resistance. Thus the earth wire helps protect you if you touch the case of an appliance that is "live". The earth pin on a plug is longer than the live and neutral pins. This ensures that the earth pin always connects with the socket first. All sockets have shutters which prevent access to the live contacts when there is no plug in the socket. On some sockets these shutters are operated by the earth pin pushing the shutter mechanism down to uncover the line and neutral socket contacts, on other sockets there is a mechanism which opens the shutters when the two live pins are inserted simultaneously, and on other sockets when all three pins are inserted simultaneously. The fuse. A fuse is simply a very thin wire. The wire has quite a low melting point. As current flows through the wire it heats up. If too large a current flows, it melts, breaking the circuit. Fuses are used to protect the flexible lead between the plug and the appliance. If too large a current flows through a lead it may overheat or catch fire. Fuses are unlikely to act quickly enough to prevent human electrocution – their main purpose is to prevent fires due to large currents. Fuses are rated according to how much current they can carry before melting. In plugs fuses are usually 3A (red), 5A (black), or 13A (brown). The correct fuse is the one that matches the current rating of the lead. All plug fuses must comply to British Standard BS1362. The rating and "BS1362" should be explicitly marked on such fuses. Q4) A table lamp usually carries a current of 0.5A. What fuse should be put in the plug: 3A, 5A, or 13A? Q5) An iron usually carries a current of 5.2A. What fuse should be put in the plug: 3A, 5A, or 13A? Q6) A kettle is protected by an earth wire and a 13A fuse. The line wire comes loose and touches the side of the kettle. The fuse blows. Explain why. Q7) Explain why the fuse is always located on the line wire and not the neutral wire? Q8) Describe and Explain what happens in the following scenarios: Answers | «Three useful components | Power»

Botany/Plant structure laboratory. "I'm experimenting here with the practicality of having laboratory excercises as part of the Botany Study Guide" Comments invited. Chapter 3. Plant Structure Laboratory. Leaves. <br> Examine this 'marsh purslane' plant and determine the following about its leaves: 3-1. "Leaf arrangement is": <br> 3-2. "Which of the following describes the leaves": 3-3. "Only one of the following statements is true": « Chapter 3 "Answers to Laboratory Questions:"

Discrete Mathematics/Number theory. Introduction. 'Number theory' is a large encompassing subject in its own right. Here we will examine the key concepts of number theory. Unlike real analysis and calculus which deals with the dense set of real numbers, number theory examines mathematics in discrete sets, such as N or Z. If you are unsure about sets, you may wish to revisit ../Set theory/. Number Theory, the study of the integers, is one of the oldest and richest branches of mathematics. Its basic concepts are those of divisibility, prime numbers, and integer solutions to equations -- all very simple to understand, but immediately giving rise to some of the best known theorems and biggest unsolved problems in mathematics. The Theory of Numbers is also a very interdisciplinary subject. Ideas from combinatorics (the study of counting), algebra, and complex analysis all find their way in, and eventually become essential for understanding parts of number theory. Indeed, the greatest open problem in all mathematics, the Riemann Hypothesis, is deeply tied into Complex Analysis. But never fear, just start right into "Elementary Number Theory", one of the warmest invitations to pure mathematics, and one of the most surprising areas of applied mathematics! Divisibility. Note that in R, Q, and C, we can "divide" freely, except by zero. This property is often known as "closure" -- the quotient of two rationals is again a rational, etc.. However, if we move to performing mathematics purely in a set such as Z, we come into difficulty. This is because, in the integers, the result of a division of two integers might not be another integer. For example, we can of course divide 6 by 2 to get 3, but we "cannot" divide 6 by 5, because the fraction 6/5 is not in the set of integers. However we can introduce a new relation where division is defined. We call this relation "divisibility", and if formula_1 is an integer, we say: Formally, if there exists an integer formula_10 such that formula_11 then we say that formula_2 divides formula_3 and write formula_14. If formula_2 does not divide formula_3 then we write formula_17: Proposition. The following are basic consequences of this definition. Let a, b, and c be integers: Quotient and divisor theorem. For any integer "n" and any "k" > 0, there is a unique "q" and "r" such that: Here n is known as dividend. We call "q" the "quotient", "r" the "remainder", and "k" the "divisor". It is probably easier to recognize this as division by the algebraic re-arrangement: Modular arithmetic. What can we say about the numbers that divide another? Pick the number 8 for example. What is the remainder on dividing 1 by 8? Using the division theorem above We have a notation for the remainders, and can write the above equations as We can also write These notations are all short for So "x" ≡ 1 (mod 8), for example, is the same as saying Observe that the remainder here, in comparing it with the division algorithm is 1. "x" ≡ 1 (mod 8) asks what numbers have the remainder 1 on division by 8? Clearly the solutions are "x"=8×0+1, 8×1+1... = 1, 9, ... Often the entire set of remainders on dividing by "n" - which we say "modulo n" - are interesting to look at. We write this set Zn. Note that this set is finite. The remainder on dividing 9 by 8 is 1 - the same as dividing 1 by 8. So in a sense 9 is really "the same as" 1. In fact, the relation "≡" is an equivalence relation. We call this relation "congruence". Note that the equivalence classes defined by congruence are precisely the elements of Zn. We can find some number "a" modulo "n" (or we say "a" congruent to "n") by finding its decomposition using the division algorithm. Addition, subtraction, and multiplication work in Zn - for example 3 + 6 (mod 8) = 9 (mod 8) = 1 (mod 8). The numbers do look strange but they follow many normal properties such as commutativity and associativity. If we have a number greater than "n" we often reduce it modulo "n" first - again using the division algorithm. For example if we want to find 11+3 mod 8, its often easier to calculate 3 + 3 (mod 8) rather than reducing 14 mod 8. A trick that's often used is that, say, if we have 6 + 7 (mod 8) we can use "negative" numbers instead so the problem becomes -2 + -1 = -3 = 5 (mod 8). We often use the second notation when we want to look at equations involving numbers modulo some "n". For example, we may want to find a number "x" such that We can find solutions by trial substitution (going through all the numbers 0 through 7), but what if the moduli are very large? We will look at a more systematic solution later. Note: we often say that we are working in Zn and use equals signs throughout. Familiarize yourself with the three ways of writing modular equations and expressions. The Consistency of Modular Arithmetic. Let formula_18 denote an arbitrary base. Given an arbitrary integer formula_19, the sequence of integers formula_20 are all congruent to each other modulo formula_21: formula_22 In modular arithmetic, two integers formula_19 and formula_24 that are congruent modulo formula_21 (formula_26) both "represent" the same quantity from formula_27. It should be possible to substitute an arbitrary integer formula_19 in place of integer formula_24 provided that formula_26. This means that: Number Bases. Converting between various number bases is one of the most tedious processes in mathematics. The numbers that are generally used in transactions are all in base-10. This means that there are 10 digits that are used to describe a number. These ten digits are {0,1,2,3,4,5,6,7,8,9}. Similarly, base-4 has 4 digits {0,1,2,3} and base-2 has two digits {0,1}. Base two is sometimes referred to as Binary. There are also bases greater than 10. For these bases, it is customary to use letters to represent digits greater than 10. An example is Base-16 (Hexadecimal). The digits used in this base are {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}. In order to convert between number bases, it is critical that one knows how to divide numbers and find remainders. To convert from decimal to another base one must simply start dividing by the value of the other base, then dividing the result of the first division and overlooking the remainder, and so on until the base is larger than the result (so the result of the division would be a zero). Then the number in the desired base is the remainders read from end to start. The following shows how to convert a number (105) which is in base-10 into base-2. Answer : 1101001 After finishing this process, the remainders are taken and placed in a row (from bottom to top) after the final quotient (1101001, in this example) is shown as the base-2 equivalent of the number 105. To sum up the process, simply take the original number in base 10, and divide that number repeatedly, keeping track of the remainders, until the quotient becomes less than the numerical value of the base. This works when converting any number from base-10 to any base. If there are any letters in the base digits, then use the letters to replace any remainder greater than 9. For example, writing 11(of base-10) in base 14. Answer: B As 11 is a single remainder, it is written as a single digit. Following the pattern {10=A, 11=B, 12=C...35=Z}, write it as B. If you were to write "11" as the answer, it would be wrong, as "11" Base-14 is equal to 15 in base-10! In order to convert from a number in any base back to base ten, the following process should be used: Take the number 3210 (in base-10). In the units place (100), there is a 0. In the tens place (101), there is a 1. In the hundreds place (102), there is a 2. In the thousands place (103), there is a 3. The formula to find the value of the above number is: 3×103 + 2×102 + 1×101 + 0×100 = 3000 + 200 + 10 + 0 = 3210. The process is similar when converting from any base to base-10. For example, take the number 3452 (in base-6). In the units place (60), there is a 2. In the sixths place (61) there is a 5. In the thirty-sixths place (62), there is a 4. In the 216th place (63), there is a 3. The formula to find the value of the above number (in base-10) is: 3×63 + 4×62 + 5×61 + 2×60 = 648 + 144 + 30 + 2 = 824. The value of 3452 (base-6) is 824 in base-10. A more efficient algorithm is to add the left-most digit and multiply by the base, and repeat with the next digit and so on. ((3 * 6 + 4) * 6 + 5) * 6 + 2 = 824 The processes to convert between number bases may seem difficult at first, but become easy if one practices often. Prime numbers. Prime numbers are the building blocks of the integers. A prime number is a positive integer greater than one that has only two divisors: 1, and the number itself. For example, 17 is prime because the only positive integers that divide evenly into it are 1 and 17. The number 6 is not a prime since more than two divisors 1, 2, 3, 6 divide 6. Also, note that 1 is not a prime since 1 has only one divisor. Some prime numbers. The prime numbers as a sequence begin Euclid's Proof that There are Infinitely Many Primes. The Greek mathematician Euclid gave the following elegant proof that there are an infinite number of primes. It relies on the fact that all non-prime numbers --- composites --- have a unique factorization into primes. Euclid's proof works by contradiction: we will assume that there are a finite number of primes, and show that we can derive a logically contradictory fact. So here we go. First, we assume that that there are a finite number of primes: Now consider the number M defined as follows: There are two important --- and ultimately contradictory --- facts about the number M: Thus, we have shown that M is divisible by a prime p that is not on the finite list of all prime. And so there must be an infinite number of primes. These two facts imply that M must be divisible by a prime number bigger than pn. Thus, there cannot be a biggest prime. Note that this proof does not provide us with a direct way to generate arbitrarily large primes, although it always generates a number which is divisible by a new prime. Suppose we know only one prime: 2. So, our list of primes is simply p1=2. Then, in the notation of the proof, M=1+2=3. We note that M is prime, so we add 3 to the list. Now, M = 1 +2 *3 = 7. Again, 7 is prime. So we add it to the list. Now, M = 1+2*3*7 = 43: again prime. Continuing in this way one more time, we calculate M = 1+2*3*7*43 = 1807 =13*139. So we see that M is not prime. Viewed another way: note that while 1+2, 1+2*3, 1+2*3*5, 1+2*3*5*7, and 1+2*3*5*7*11 are prime, 1+2*3*5*7*11*13=30031=59*509 is not. Testing for primality. There are a number of simple and sophisticated primality tests. We will consider some simple tests here. In upper-level courses we will consider some faster and more sophisticated methods to test whether a number is prime. Inspection. The most immediate and simple test to eliminate a number n as a prime is to inspect the units digit or the last digit of a number. If the number n ends in an even number 0, 2, 4, 6, 8 we can show that number n cannot be a prime. For example, take n = 87536 = 8753(10) + 6. Since 10 is divisible by 2 and 6 is divisible by 2 then 87536 must be divisible by 2. In general, any even number can be expressed in the form n = a*10 + b, where b = 0, 2, 4, 6, 8. Since 10 is divisible by 2 and b is divisible by 2 then n = a*10 + b is divisible by 2. Consequently, any number n which ends in an even number such as 7777732 or 8896 is divisible by 2 so n is not a prime. In a similar type of argument, if a number n ends in a 5 we can show the number n cannot be a prime. If the last digit of n, call it b, is a 5 we can express n in the form n = a*10 + b, where b = 5. Since 10 is divisible by 5 and b = 5 is divisible by 5 then n = a*10 + b is divisible by 5. Hence, any number n which ends in a 5 such as 93475 is divisible by 5 so n is not a prime. Thus, if a number greater than 5 is a prime it must end with either a 1, 3, 7, or 9. Note that this does not mean all numbers that end in a 1, 3, 7, or 9 are primes. For example, while the numbers 11, 23, 37, 59 are primes, the numbers 21 = 3*7, 33 = 3*11, 27 = 3*9, 39 = 3*13 are not primes. Consequently, if a number ends in a 1, 3, 7, or 9 we have to test further. Trial Division Method. To test if a number n that ends in a 1, 3, 7, or 9 is prime, we could simply try the smallest prime number and try to divide it in n. If that doesn't divide, we would take the next largest prime number and try again etc. Certainly, if we took all primes numbers in this manner that were less than n and we could not divide n then we would be justified in saying n is prime. However, it can be shown that you don't have to take all primes smaller than n to test if n is prime. We can stop earlier by using the Trial Division Method. The justification of the Trial Division Method is if a number n has no divisors less than or equal to formula_41 then n must be a prime. We can show this by contradiction. Let us assume n has no divisors less than or equal to formula_41. If n is not a prime, there must be two numbers a and b such that formula_43. In particular, by our assumption formula_44 and formula_45. But then formula_46. Since a number can not be greater than itself the number n must be a prime. Trial Division Method is a method of primality testing that involves taking a number n and then sequentially dividing it by primes up to formula_41. For example, is 113 prime? formula_48 is approximately 10.63... We only need to test whether 2, 3, 5, 7 divide 113 cleanly (leave no remainder, i.e., the quotient is an integer). So we need not look at any more primes such as 11, 13, 17 etc. less than 113 to test, since 2, 3, 5, 7 does not divide 113 cleanly, 113 is prime. Notice that after rejecting 2 and 3 as a divisor, we next considered the next prime number 5 and not the next number 4. We know not to consider 4 because we know 2 does not divide 113. If 2 cannot divide 113 then certainly 4 cannot because if 4 divided 113 and since 2 divides 4 then 2 would divide 113. So we only use the next cheapest available prime to test not the next consecutive number. If we test 91 we get, So we know since 7 divides 91, 91 is not a prime. Trial division is normally only used for relatively small numbers due to its inefficiency. However this technique has the two advantages that firstly once we have tested a number we know for sure that it is prime and secondly if a number is not prime it also gives us the number's factors. To obtain a few small primes, it may be best to use the Sieve of Eratosthenes than to test each number sequentially using trial division. The Sieve of Eratosthenes method is basically a process of finding primes by elimination. We start by taking a list of consecutive numbers say 1 to 100. Cross out the number 1 because the number is not prime. Take the next least uncrossed off number which is 2 and circle it. Now cross out all multiples of 2 on the list. Next take the next least uncircled number which is 3. Circle the number 3 and cross out all multiples of 3. The next least uncircled number should be 5 since 4 is a multiple of 2 and should have been crossed off. Circle the number 5 and cross out all multiples of 5. The next least uncircled number should be a 7 since 6 is a multiple of 2. Circle the 7 and mark off all multiples of 7. Now the next uncrossed off number should be 11 since 8,9,10 is a multiple of 2, 3, and 2. If we continue in this manner what is left is the circled numbers which are primes. But notice we can actually stop now and circle all the unmarked numbers after crossing off multiples of 7 because of the result that since formula_49 any number less than 100 which is not prime must be divisible by 2, 3, 5, or 7. The Fundamental Theorem of Arithmetic. The Fundamental Theorem of Arithmetic is an important theorem relating to the factorization of numbers. The theorem basically states that every positive integer can be written as the product of prime numbers in a unique way (ignoring reordering the product of prime numbers). In particular, The Fundamental Theorem of Arithmetic means any number such as 1,943,032,663 is either a prime or can be factored into a product of primes. If a number such as 1,943,032,663 can be factored into primes such as 11×13×17×19×23×31×59 it is futile to try to find another different combination of prime numbers that will also give you the same number. To make the theorem work even for the number 1, we think of 1 as being the product of zero prime numbers. More formally, Here are some examples. A proof of the Fundamental Theorem of Arithmetic will be given after Bezout's identity has been established. LCM and GCD. Two characteristics we can determine between two numbers based on their factorizations are the "lowest common multiple", the "LCM" and "greatest common divisor", the "GCD" (also "greatest common factor", "GCF") LCM. The lowest common multiple, or the least common multiple, for two numbers a and b is the smallest number designated by LCM(a,b) that is divisible by both the number a and the number b. We can find LCM(a,b) by finding the prime factorization of a and b and choosing the maximum power for each prime factor. In another words, if the number a factors to formula_50, and the number b factors to formula_51, then LCM(a,b) = formula_52 where formula_53 for "i" = "1 to n". An example, let us see the process on how we find lowest common multiple for 5500 and 450 which happens to be 49500. First, we find the prime factorization for 5500 and 450 which is Notice the different primes we came up for both the number 5500 and the number 450 are 2, 3, 5, and 11. Now let us express 5500 and 450 completely in a product of these primes raised to the appropriate power. The LCM(5500,450) is going to be in the form 2? 3? 5? 11?. All we now have to do is find what the powers of each individual prime will be. So now we compare the power of each prime for 5500 and 450. Let us consider the powers of the first prime 2. In the number 5500, the prime 2 is raised to the second power and in the number 450, prime 2 is raised to the first power. Since the maximum between 2 and 1 for the power of the prime 2 is 2, we use 2 for the power of the prime 2. Now let us consider the powers of the prime 3. In the number 5500, the prime 3 is raised to the zero power and in the number 450 the prime 3 is raised to the second power. Since the maximum between 0 and 2 for the power of the prime 3 is 2, we use 2 for the power of the prime 3. Similarly, let us consider the powers of the next prime 5. In the number 5500, the prime 5 is raised to the third power and in the number 450 the prime 5 is raised to the second power. Since the maximum between 3 and 2 for the power of the prime 5 is 3, we use 3 for the power of the prime 5. Finally, let us consider the powers of the prime 11, the last prime on our list. In the number 5500, the prime 11 is raised to the first power and in the number 450 the prime 11 is raised to the zero power. Since the maximum between 1 and 0 for the power of the prime 11 is 1, we use 1 for the power of the last prime 11. Consequently, the product of our results is LCM(5500,450)=22 32 53 111 = 49500. GCD. The greatest common divisor for two numbers a and b is the biggest number designated by GCD(a,b) that divides both the number a and the number b. In a similar process to finding LCM(a,b), we can find GCD(a,b) by finding the prime factorization of a and b but choosing the minimum power for each prime factor instead. In other words, if the number a factors to formula_50, and the number b factors to formula_51, then GCD(a,b) = formula_52 where formula_57 for "i" = "1 to n". An example, let us see the process on how we find the greatest common divisor for 5500 and 450 which happens to be 50. First, we find the prime factorization for 5500 and 450 which is Notice the different primes we came up for both the number 5500 and the number 450 are 2, 3, 5, and 11. Now let us express 5500 and 450 completely in a product of these primes raised to the appropriate power. The GCD(5500,450) is going to be in the form 2? 3? 5? 11?. All we now have to do is find what the powers of each individual prime will be. So now we compare the power of each prime for 5500 and 450. Let us consider the powers of the first prime 2. In the number 5500, the prime 2 is raised to the second power and in the number 4</syntaxhighlight> 50, prime 2 is raised to the first power. Since the minimum between 2 and 1 for the power of the prime 2 is 1, we use 1 for the power of the prime 2. Now let us consider the powers of the prime 3. In the number 5500, the prime 3 is raised to the zero power and in the number 450 the prime 3 is raised to the second power. Since the minimum between 0 and 2 for the power of the prime 3 is 0, we use 0 for the power of the prime 3. Similarly, let us consider the powers of the next prime 5. In the number 5500, the prime 5 is raised to the third power and in the number 450 the prime 5 is raised to the second power. Since the minimum between 3 and 2 for the power of the prime 5 is 2, we use 2 for the power of the prime 5. Finally, let us consider the powers of the prime 11, the last prime on our list. In the number 5500, the prime 11 is raised to the first power and in the number 450 the prime 11 is raised to the zero power. Since the minimum between 1 and 0 for the power of the prime 11 is 0, we use 0 for the power of the last prime 11. Consequently, the product of our results is GCD(5500,450)=21 30 52 110 = 50. The Euclidean algorithm. The Euclidean algorithm is such that we can find the gcd of two numbers without finding the factorization*. The Euclidean algorithm consists of only addition and multiplication, and uses the above properties of gcd as its basis. An example. We will see how this works by calculating gcd(458,44) First, divide 458 by 44 and obtain the remainder: Now suppose that a number is a common divisor of 458 and 44. Then it must also be a divisor of 18. To see this, rearrange the above equation to: When this equation is divided by a common divisor of 44 and 458, an integer is obtained on the left, and so must also be obtained on the right. This, by definition, means that the number is also a divisor of 18. By the same reasoning, any common divisor of 18 and 44 is also a divisor of 458. Since all of the common divisors of 458 and 44 are equal to common divisors of 44 and 18, then in particular the greatest common divisors are equal. So we have gcd(458,44)=gcd(44,18) The next step in the algorithm is to divide 44 by 18 and find the remainder. Repeat this process; keep dividing the previous divisor by the previous remainder: Our gcd is the last remainder before the zero, in this case, 2. This is because the reasoning that proved gcd(458,44)=gcd(44,18) applies at every step, so gcd(458,44)=gcd(44,18)=gcd(18,8)=gcd(8,2)=gcd(2,0)=2. The Matrix Method. We can construct a matrix that provides an alternative method for calculating the greatest common divisor. In its general form, the matrix is formula_58 Recall that one way to write the gcd of two numbers is as an integral linear combination. If we are finding the gcd, for example, we could represent it as "as + bt", where "a" and "b" are the two numbers we are comparing, and "s" and "t" are integers. We also know that "b = aq + r" where "r" is the remainder upon division of "b" by "a". After we subtract row 2 from row 1, we get formula_59 If r_2 is nonzero, we must continue the process; this time, subtracting row 1 from row 2. We continue this process until one of the " r's " has been reduced as far as possible. We now have our gcd. The numbers that are in that row, where the 1 and the 0 used to be, represent "t" and "s", respectively. Let us now look at a computational example. formula_60 We see that it would be trivial at this point to go any further; we would just end up with row-2 containing a zero where "a" used to be. So we look at row-1 and remember that the "1" represents our remainder, 1(=t) multiplies "b" and -14(=s) multiplies "a" such that formula_61 This can be checked by the Euclidean algorithm that gcd(7,99)=1. The extended Euclidean algorithm. What happens if we try and reverse the process of the Euclidean algorithm by substituting back? Back-substitution is rather tedious and prone to error, so here is a faster method. Draw up a table with four columns, label these from left to right "q", "r", "u", "v". For convenience label a column "i" representing the step we're currently up to. Place "a" and "b" with the greater of these on top in the column "r", and place 1s and 0s accordingly: formula_62 Now iterate downwards by taking the quotient of "b"/"a" and putting it in the next space in the "q" column, then of "b"-"aq" in the "r" column. To update "u" and "v", take Indeed, you are looking for "u" and "v" such that a"u" + b"v" = gcd (a,b). At some point, gcd (a,b) is in fact the remainder at the ith stage, so you might as well compute ui and vi such that a"u"i + b"v"i = ri, at EACH stage. Deriving the recurrences found above results from these three equations (the second equation is Euclid's algorithm's basic property, the other two are constraints we set to attain our desired goal): The trick is to then appropriately express ri-2. Stop writing when you obtain a 0 in the "r" column. Finding then, gcd(450,44) (this is the same as gcd(44,450) ) formula_63 The bold number is the gcd. Observe (9)×450+(-92)×44=2 Clearly these "u" and "v" are very special. What can we say about the general case? Bezout's identity. In the above case we have 9×450+(-92)×44=gcd(450,44). So the greatest common divisor of 450 and 44 can be written as a linear combination of 450 and 44 with integer coefficients. This turns out to be true of any pair of integers. This result is known as "Bezout's Identity" and can be stated as follows: "Proof" The numbers "u" and "v" can either be obtained using the tabular methods or back-substitution in the Euclidean Algorithm. Proof of the Fundamental Theorem of Arithmetic. One use of Bezout's identity is in a proof of the Fundamental Theorem of Arithmetic. Before this is proven, two other results are needed: Lemma 1: If a prime number, "p", divides a product of two integers, formula_72, then it must divide "a" or "b" (or both). Lemma 2: If a prime number, "p", divides a product of integers, formula_75, then it must divide at least one of the factors. Fundamental Theorem of Arithmetic: Any positive integer, "n", can be expressed as a product of primes. This product is unique up to the order in which the terms appear. Partitioning the Divisors of Products. The Fundamental Theorem of Arithmetic can also be derived from the following lemma: Lemma: Given integers formula_2, formula_3, and formula_93, if formula_93 divides formula_72 (denoted by formula_96), then there exist integers formula_97 and formula_21 such that formula_99 and formula_100 and formula_101. In other words, an integer that divides a product can itself be factored into a product where each factor divides the corresponding factor from formula_72. This means that no new primes are "created" when formula_2 and formula_3 are multiplied together. This Lemma follows from the Fundamental Theorem of Arithmetic and Bezout's identity, but here a more direct proof will be given. Proof: If any of formula_2, formula_3, or formula_93 is formula_108, then the Lemma is trivial. In addition, if any of formula_2, formula_3, or formula_93 is negative, then if the Lemma holds for the absolute values formula_112, formula_113, and formula_114, then it is trivial to show that the Lemma holds for formula_2, formula_3, and formula_93. It will now be assumed that formula_2, formula_3, and formula_93 are all strictly positive integers. Form an formula_121 array formula_122 of integers that has formula_2 columns and formula_3 rows. formula_125 will denote the integer at column formula_19 and row formula_24. Fill the array by sweeping the array row by row starting with row 1, with each row swept starting from column 1. During this "raster" sweep of formula_122, assign values to formula_125 using the following cyclical pattern: formula_130. In essence, formula_125 is the unique integer from the range formula_132 such that formula_133. Since formula_96, it is the case that formula_135 and formula_136. As previously indicated, the "raster sweep" through array formula_122 is a cyclical progression through the entries of formula_122 where column index formula_19 cycles around formula_140, and every time formula_19 transitions from formula_2 to formula_143, row index formula_24 advances by one step around the cycle formula_145. In the image below, the grid formula_122 where formula_147; formula_148; and formula_149 is depicted both explicitly and using a brickwork pattern. Array formula_122 can be endlessly replicated and used to form the infinite array formula_151. For arbitrary integers formula_152 and formula_153, the block of entries in formula_151 formed by columns formula_155 to formula_156 and rows formula_157 to formula_158 is a copy of formula_122. For arbitrary integers formula_19 and formula_24, the entry formula_162 of formula_151 is the unique integer from the range formula_132 such that formula_165. Given any column formula_19 and row formula_24, the entry formula_162 of formula_151 located at formula_170 is the unique integer from formula_171 such that formula_165. Given an arbitrary displacement column displacement formula_173 and row displacement formula_174, the difference formula_175 is separated from formula_176 by a multiple of formula_93. This gives the entries of formula_151 the following symmetries: The columns of formula_151 that contain formula_143 are spaced evenly due to the aforementioned symmetry. Let formula_97 denote the smallest positive integer such that every formula_198 column contains formula_143. The rows of formula_151 eventually repeat (not allowing any column shifts) with a period of formula_21. A row does not appear twice in a single cycle due to the symmetry of formula_151. Row formula_143 is identical to row formula_214 so it must be the case that formula_3 is an integer multiple of the period formula_21: formula_101. It will now be proven that formula_99 by showing that a sub-block of formula_151 that consists of formula_97 columns and formula_21 rows contains every integer from formula_171 exactly once. To clarify notation, given the column indices formula_31 where formula_224, and the row indices formula_32 where formula_226, then formula_227 will denote the sub-block of formula_151 consisting of columns formula_229 through to formula_230, and rows formula_231 through to formula_232. Since a row can be uniquely determined from a single cell and the rows only repeat with a period of formula_21, any block formula_234 will contain exactly formula_21 unique entries. Columns that contain formula_143 occur with a period of formula_97. Due to the symmetry of formula_151, given any integer formula_239, columns that contain formula_240 occur with a period of formula_97. Any block formula_242 will contain exactly formula_243 unique entries. Given any integer formula_239, integer formula_240 will occur in every formula_198 column, and within that column, in every formula_247 cell. Any block formula_242 will contain formula_240. Any block formula_242 will contain every integer from formula_171 exactly once. So therefore formula_99. formula_253. Solving linear modular equations - back to Bezout. Bezout's identity above provides us with the key to solving equations in the form Coprime case - gcd("a", "m") is 1. Consider the case where but with gcd("a", "m")=1 Because of Bezout's identity When we calculate "u", this number is special. Say if we have the equation 4 and 21 are coprime since gcd(4,21)=1. Now 1=4*16+(-3)*(21). Our "u" in this case is 16. Observe now that 4*16=64. 64 (mod 21) = 1. This number "u" is very special - it is known as the "multiplicative inverse". It is the number "u" on multiplication by "a" gives 1 mod "m". Bezout's identity on calculating gcd("a", "m") will always give you the multiplicative inverse of "a" modulo "m". The multiplicative inverse of "a" is often written "a"-1 but note that this does not mean 1/"a" since we have seen in the first sections that we can not always divide in the integers. Note that in Z"p" there is one number "without" a multiplicative inverse - 0. It may be useful to exclude 0 when considering modular arithmetic, so instead of having to say Z"p"\{0} all the time, we merely write Z"p"*. Now since we have the magic multiplicative inverse, our problem becomes relatively easy to solve. 4-1=16 in Z21 and now, on multiplying throughout by 16 (since 4×16=1 because 16 is 4's multiplicative inverse mod 21). 11×16=176 and using a calculator or using the division theorem we obtain which is our solution! Verify - 8×4 = 32 = 11 (mod 21). The general case. Consider the general case where with no restrictions on "a", "b" and "m". Firstly we calculate gcd("a", "m") again to obtain "d". Now "d" is a "divisor" since the "d" in gc"d" means greatest common divisor. So we can now divide "a" and "m" - but what about "b"? Since we have calculated the gcd of "a" and "m" but not "b" we have no guarantees that "d" will divide "b". This then becomes a condition that the equation has no solution. Now we have reduced the problem to the previous coprime case because gcd("a"/"d", "m"/"d")=1 with "d" as above. However we do not have 1 solution any more - this is true because we have reduced the solution to being "x" = "c" (mod "m"/"d") and we must bring the solution back mod "m". This will be come clearer in the examples. Let's work through some examples. Example 1. Solve 4"x" ≡ 3 (mod 20). Firstly, gcd(4, 20) = 4. 4 does not divide 3 and we have no solution. Example 2. Solve 9"x" ≡ 6 (mod 15). gcd(9, 15) = 3 and 3 does divide 6 and we have 3 solutions. Now, divide through by 3 to obtain gcd(3, 5) = 1 = 3 × 2 + -1 × 5 So the inverse of 3 mod 5 is 2. Now we obtain the solution Now in Z15 we must obtain the two extra solutions 9 and 14 mod 15 - 9 mod 5 = 4 and 14 mod 5 = 4. Generally we can say that if we have the solution to the reduced equation "x", the general solution is "x"+("m"/"d")"k" for "k"={0, 1, .., "d"-1}. Chinese Remainder Theorem. Very often congruence relations are required to hold simultaneously. Given positive integer bases formula_254 and formula_255 and arbitrary integers formula_2 and formula_3 where formula_258 and formula_259, a common question is what integers formula_19 satisfy the following congruence relations simultaneously: formula_261 The Chinese Remainder Theorem dictates that when formula_262, for any choice of formula_263 and formula_264 there exists a unique integer formula_265 such that: In essence, when formula_254 and formula_255 are coprime, there is a 1-to-1 correspondence between ordered pairs from formula_271 and the set formula_272. Proof 1. Proof: To begin, observe that formula_273 and formula_274 so it is possible to pair each formula_275 with a unique ordered pair formula_276 and vice-versa. Given any formula_275, integer formula_93 can be reduced modulo formula_254 to get an integer formula_280, and can be reduced modulo formula_3 to get an integer formula_282. Integers formula_2 and formula_3 satisfy: formula_285 It is not obvious that for any choice of formula_286 that there exists a unique formula_275 such that formula_288 Let formula_122 denote an infinite array with two rows indexed by formula_290, and an infinite number of columns indexed by formula_291. formula_125 will denote the entry of formula_122 at column formula_19 and row formula_24. formula_125 is the unique integer from formula_297 where formula_298. Given column indices formula_31 where formula_224, then formula_301 will respectively denote the sub-blocks formed by columns formula_229 through to formula_230 and row sets formula_304. Partition formula_122 into the series of formula_306 blocks formula_307 where block formula_308 is formula_309. Row 1 of block formula_310 will always be the sequence formula_311. Row 2 of block formula_310 can be uniquely determined by its first entry, formula_313 since formula_314. The blocks only differ by row 2, and row 2 for each block is uniquely determined by its first entry formula_313. formula_316 and formula_317 so formula_318. This implies that the first entry of row 2 for the next block can be uniquely determined from the first entry of row 2 for the current block. Since each block is uniquely determined from the previous block, the row 2 pattern for each block will repeat after a regular period of formula_319 blocks: formula_320. Let set formula_321 denote the total range of values attained by formula_322. It is the case that formula_323. Let formula_324 be the minimum positive difference between any two elements from formula_325. The cyclical nature of the elements from formula_325 makes it easy to show that any element formula_327 is congruent to a multiple of formula_324 modulo formula_255. In essence: formula_330. Since formula_324 is the minimum positive difference between any two elements of formula_325, both formula_254 and formula_255 are multiples of formula_324 (in fact, formula_336). Since formula_337, it must be the case that formula_338. This implies that formula_339 and that formula_340. A total of formula_255 blocks are encountered before any repetition occurs in array formula_122, and therefore all formula_343 possible columns occur exactly once in a column period of formula_343 in array formula_122. This establishes the Chinese Remainder Theorem. formula_253 Proof 2. A second (more intuitive) proof can be derived by constructing a mesh to depict the space formula_347. This mesh is a rectangular array of points with formula_254 columns and formula_255 rows. The columns are indexed from left to right by formula_350, and the rows are indexed from bottom to top by formula_351. Most importantly, the mesh will "wrap around" in the horizontal and vertical dimensions. This means that moving to the right from column formula_352 will return you to column formula_108; moving to the left from column formula_108 will send you to column formula_352; moving up from row formula_356 will return you to row formula_108; and moving down from row formula_108 will send you to row formula_356. The mesh has formula_343 points, and the horizontal and vertical coordinates of each point are the remainders from dividing an integer formula_19 by formula_254 and formula_255 respectively. For convenience, given an arbitrary dividend formula_19, formula_365 and formula_366 will denote the remainders after formula_19 is divided by formula_254 and formula_255 respectively. If the dividend formula_19 is incremented by formula_143, then the coordinate formed by the remainders moves to the right by one step, and up by one step, wrapping around if necessary. formula_372 corresponds to the coordinate formula_373. Increasing formula_19 in steps of formula_143 will trace a ray that originates from formula_373 and moves one step to the right and one step up each interation, wrapping around if necessary. The images below give examples of this ray for formula_377 and for formula_378. In the images below, a copy of column 0 and row 0 appears at the right and top of the mesh respectively to illustrate the wrap around property. When formula_378, formula_254 and formula_255 are not coprime and fail to satisfy the conditions of the Chinese remainder theorem. The ray forms diagonal "stripes" in the mesh, and if these stripes are all equally spaced by formula_143, then the ray passes through every point in the mesh exactly once proving that every remainder pair is possible and hence the Chinese remainder theorem. When formula_378, formula_254 and formula_255 are not coprime and fail to satisfy the conditions of the Chinese remainder theorem, hence the ray does not hit every mesh point. The wrap around property of the mesh makes the mesh "symmetric" in both the horizontal and vertical dimensions, which means that if the wrap around "seams" were moved to any column and row where the ray passes through the lower left corner, then the ray is completely unchanged. This requires that the stripes be equally spaced. Let formula_324 denote this equal spacing, and it will be shown that formula_387 and formula_388. The ray passes through row formula_108 every formula_324 steps to the right. The ray passes through formula_373, and the wrap around property implies that moving formula_254 steps to the right returns to this same intersection point. This can only occur if formula_387. By a similar argument formula_388. If formula_254 and formula_255 are coprime, then formula_338, the stripes are evenly spaced by formula_143, every remainder pair is possible, and the Chinese remainder theorem is therefore true. formula_253

Spanish/Exercises/Questions. ^Lesson 5^ Yes/No Questions. Form the corresponding yes/no question: 1. Ellos tienen hambre. 2. Nosotros estudiamos español. 3. Fernando es alto. Specific Questions. Put in the correct question word: 4. ¿_________ estás? - Estoy bien. 5. ¿__________ es el hombre alto? 6. ¿_________ hermanos tienes? 7. ¿__________ está España? - Está en Europa. 8. ¿_________ es tu cumpleaños? 9. ¿_________estudias español? - Porque es muy interesante. Soluciones a los ejercicios "Solutions to exercices" ^Lesson 5^

GCSE Science/Electrical Power. GCSE Science/Electricity The reason electricity has become so popular over the last 100 years or so is because it is a very good way of moving "energy" from one place to another. When you buy a light bulb is usually rated in watts. The watt is a unit of "power". In this unit you are going to lean some equations rating current voltage, energy and power and apply the equations. Definition of power. Power is defined as the rate of energy flow. Its unit is the watt — one watt is one joule per second. In electrical circuits the power can be found by multiplying the current and voltage together. One way of remembering this is to use an equation triangle like the one below. Memorize the positions of the symbols. "P" is power, "V" is voltage and "I" is current. If you want to know the power, cover its symbol up and what you have left is "I"×"V", or current times voltage. Want to know the voltage? Cover it up and what you have left is "P"÷"I", or power divided by current. Where does the equation "P" equals "VI" come from? From the definition above power is energy "E" per unit time "t". ( how many joules per second) So where does "P" = "IV" come from? To find out we look at what "I" and "V" are defined as. "I" is electrical current. It is the amount of charge "Q" flowing past any point every sec. The voltage also determines the current, so the power is directly proportional to the voltage and the current. We know that from the definition of the volt, if 1 amp flows for 1 second, with a 1 volt potential difference, 1 joule of energy is used up per second, and therefore the power is 1 Watt. Examples. Michael plugs a 100 W light bulb into the mains, what is the resistance of the bulb? To find the resistance we need to know the current, to find the current we use the equation for power.Covering up the "I" in the triangle gives: Now we can use this in the equation for resistance. How much charge flows through this bulb in 15 seconds? We use the definition of current, to work this out. "I" = "C"/"t" So "C" ="It" = (0.435 A)(15 s) = 6.53 coulombs (C) How much electrical energy is converted into heat and light energy in 15 s? For this we use the equation for power in its energy per second form. "P" = "E"/"t" So "E" = "Pt" = (100 W)(15 s) = 1500 joules (J) Q1) Put Ohm's law into a triangle like the one above. Q2) If a current of 3 A flows through a 12 V heater, how much energy will it transfer in half an hour? How much charge will have flowed through the heater in the same time? Q3) In the USA mains voltage is only 120 V. If a 60 W light bulb is connected to the mains in the USA, what current flows through it ? Q4)What current would flow through the same bulb if plugged into the mains in the UK (230 V) and what would be the power? Before we go on to looking at power transmission in the power lines of the national grid, we need to look at how energy is generated. We'll come back to this topic later on, after we look at the next module, which is on the magnetic effects of current. Summary Answers |«Safety | Electromagnetism»

Cell Biology/Endoplasmic Reticulum. Cell Biology | ../Parts of the cell/ | ../Organelles/ Endoplasmic Reticulum | Mitochondria and Chloroplasts » The endoplasmic reticulum (endoplasmic="within the cytoplasm", reticulum="little net"; short : ER) is an important organelle in all eukaryotic cells. Prokaryotic organisms do not have organelles and thus do not have an ER. It's base structure and composition is similar to the plasma membrane, though it is an extension of the nuclear membrane. The ER is the site of the translation and folding of and transport of proteins that are to become part of the cell membrane (e.g., transmembrane receptors and other integral membrane proteins) as well as proteins that are to be secreted or "exocytosed" from the cell (e.g., digestive enzymes). The ER consists of an extensive membrane network of tubes and cisternae (sac-like structures). The membrane encloses a space, the cisternal space (or internal lumen) from the cytosol. This space is acting as a gateway. Parts of the ER membrane are continuous with the outer membrane of the nuclear envelope, and the cisternal space of the ER is continuous with the space in between the two layers of the nuclear envelope. Parts of the ER are covered with ribosomes (which assemble amino acids into proteins based on instructions from the nucleus). Their rough appearance under electron microscopy led to their being called rough ER (RER), other parts are free of ribosomes and are called smooth ER (SER). The ribosomes on the surface of the rough ER insert the freshly produced proteins directly into the ER, which processes them and then passes them on to the Golgi apparatus (Fig. 1). Rough and smooth ER differ not only in appearance, but also in function. While the rough ER manufactures and transports proteins destined for membranes and secretion, the smooth ER has functions in several metabolic processes. It takes part in the synthesis of various lipids (e.g., for building membranes) and steroids (e.g., hormones), and also plays an important role in carbohydrate metabolism, detoxification of the cell, and calcium storage. Proteins that are transported by the ER and from there throughout the cell are marked with an address tag that are called a signal sequence. Günter Blobel was awarded the 1999 Nobel Prize in Physiology or Medicine for his discovery of these signal sequences in 1975. The N-terminus (one end) of a polypeptide chain (e.g., a protein) contains a few amino acids that work as an address tag, which are removed when the polypeptide reaches its destination. Proteins that are destined for places outside the ER are packed into transport vesicles and moved along the cytoskeleton towards their destination. Endoplasmic Reticulum | Mitochondria and Chloroplasts » Cell Biology | ../Parts of the cell/ | ../Organelles/

Latin/Lesson 4-Ablative. The Ablative Case. The ablative case in Latin has 9 main uses: The different uses of the ablative will be dealt progressively. For a summary of all forms of the ablative, please consult the Appendix. Grammar Part 5: The Power of the Ablative Case. Ablative generally indicates position in time and/or space (i.e. when and where). It can also indicate the idea of ways of getting to a location, abstractly or concretely. Ablative of Means. Exercise. How would you translate "I made the toga by hand"? Answer. Answer: "Togam manu feci". In this case, the word "manu" is in the ablative (see fourth declension list) and thus means "by hand." Exercise. I have my wisdom by means of my teacher. Answer. Answer: "Habeo sapientiam magistro." Ablative of Time. How would you say: "I will arrive at the 5th hour." 'at the 5th hour' is indicating position of time. Thus, it can be put into the ablative case, giving: adveniam quinta hora In general, therefore, in order to say "In the morning", "At nine O'clock," or "In the tenth year," use ablative. It is generally used to refer to a specific time in which something has, does, or will occur. Example: I will leave in the night. Hint: Future tense can be looked up in the appendices of this Wikibook! Hint: to leave- discedo, discedere; night- nox, noctis(This is a third declension word!) Answer. Answer: Discedam nocte. Note the simplicity in which Latin translates the six words into simply two. The ending based language completely negates the need for the words "I," "will," "in," and "the." Ablative of Place. "Naves navigabant mari." The ships were sailing on the sea. The ablative is also useful for showing the location of things, in general where you would use the words on, in, or at. There is an exception for the slightly more archaic locative, which is used with the words "domi" (from "domus, domus, f.", home), "ruri" (from "rus, ruris, n.", country [as opposed to city]), and "Romae" (from "Roma, Romae, f.", Rome), as well as with the names of towns, cities and small islands. Latin has its own way of handling prepositions depending on the nouns and their cases in the sentence, including the versatile "in", which can take many different meanings depending upon the case of the object. Ablative with prepositions. Here are a few prepositions that can take the ablative (for a fuller list, see the lesson on adverbs and prepositions in the previous chapter): As a general rule, when motion is implied, use the accusative instead. Example 3. "Servus ex agris venit." Note: "Ager" ("ager, agri, m.", field) must take an ablative suffix to match the preceding preposition, in this case "e"/"ex". Incidentally, both "ager" and "campus" mean "field," but "ager", like its English derivative "agriculture", connotes a farming field, while "campus" (think "camping" or "college campus") means "open field." The "Campus Martius" was a large field in Rome used for military training. The Vocative Case. While you will rarely need to ask Lupus where the bathroom is in Latin, you may find yourself reading either quotes or letters in which a person is being directly addressed. The case it will be in is the vocative. For example, "Hail, Augustus" will appear in Latin as Ave Auguste, and not Ave Augustus. Each declension has its own form of the vocative singular and plural. They are listed in the table below. Furthermore, in all but the second declension, the nominative and vocative are exactly the same! Examples. The basic form of the imperative is created by dropping the "re" off of the infinitive form of the verb, as in: Amare, which becomes Ama; at least in the singular active form, which is all that these exercises require. More can be found about this subject in the chapter on verbs.

Latin/Appendix A. The pronunciation of Church Latin might be easier, for an average European, than Classical Latin. The way introduced here reflect the medieval way. C is pronounced as [ts] or [tS] before e, i, y, ae, or oe G is alway hard, except before e, i, or y, then soft (like j in jut) H is not pronounced. QU might become [k] rather than [kv] or [kw].

Botany/Kinds of plants. Chapter 7 Chapter 7. Plant Systematics The Kinds of Plants. The total number of species of plants is tremendous. Any attempt at representing their great diversity requires a system of ordering or arranging the many plant types—hopefully a system that itself contributes to our knowledge and understanding. We could take the straightforward approach of listing all plants alphabetically by their common name, or perhaps by their species name. This index approach would be handy, but would not tell us much about the plants themselves. We would have to know the plants whose names are included for the list itself to have any meaning to us. However, botanists developed a hierarchical system based on the fact—considering a variety of characteristics—that some plants are clearly more similar to each other than to other plants. Arranging all of the world's plants (and animals and minerals) by similarities to each other was an idea first promoted by Carolus Linnaeus. Categorizing is an important process by which we humans gain understanding of the world around us, and something we all do to some degree as part of our observation of things and events that we encounter. In biology, as the concept of evolution was formulated, it became obvious that this concept could be the basis for categorization. If plants that are similar in form are indeed closely related—at least more closely related than plants that are dissimilar in form—then a system of classification could be devised that reflected these relationships. This approach has important implications. Related plants have common properties, a fact that can be exploited in agriculture and other practical botanical fields. Initially, botanists had but one approach: physical examination. The careful examination (and detailed description) of plant structures allowed for arranging each species within a system that placed all more or less similar plants (in certain "important" features) together. This approach is not as easy as it sounds, but played off of and contributed to the expansion of descriptive botany in the 18th and 19th centuries. One problem that became evident is that as species evolved, unrelated plants could come to resemble each other in many respects. After all, form and function are closely related. Within similar habitats (say deserts), species of very distantly related plants might well evolve towards a similar form. Species do not have (or certainly did not have over geological time) unrestricted access to all places on the planet and species distribution is then an important part of interpreting the evolutionary process. As species evolved, they did so within the constraints to dispersion that existed at the time. This fact provides an important clue: unrelated but similar plants are likely to be distributed far from each other on the Earth's surface; and the corollary: plants that have similar structures but have widely separated distributions, may not be so closely related in an evolutionary sense. At this point it is worthwhile to consider some examples. There are many succulent plants, as this form (typically thick, fleshy stems and/or leaves; often reduction or complete loss of leaves) incorporates adaptations necessary for a plant to survive very dry conditions. Non-botanists are tempted to classify all such plants as types of cacti. In fact, cacti evolved in the New World (the Americas), yet there are many succulents (and many plants that resemble cacti) that are not native to the New World, and evolved independently on the African continent. A large group of such plants are known as the euphorbs.

Internet Technologies/History of the Web. The Web grew out of a project at CERN, beginning around 1989, where Tim Berners Lee and Robert Cailliau built the prototype system that became the core of what is now the World Wide Web. The original intent of the system was to make it easier to share research papers among colleagues. The original name of the first prototype was Enquire Within Upon Everything, after a famous 19th century reference work of how-tos. Berners-Lee released files describing his idea for the "World Wide Web" onto the Internet on August 6, 1991.

Internet Technologies/The Web. The World Wide Web (the "Web" or "WWW" for short) is a hypertext system that operates over the Internet. To view the information, you use a software program called a web browser to retrieve pieces of information (called "documents" or "web pages") from web servers (or "web sites") and view them on your screen. You can then follow hyperlinks on the page to other documents or even send information back to the server to interact with it. The act of following hyperlinks is often called "surfing" the web. Looking further at web browsers, a web browser is an application program that accesses the World Wide Web, which then searches for wanted information on the Internet. The first web browser named Mosaic was developed in the early 1990s. The ease of information access provided by web browsers greatly added to the popularity of the Internet. Companies and individual users alike can use a browser to access untold amounts of information, and its as easy to find as clicking a mouse. The four most popular web browsers are Internet Explorer, Chrome, Firefox, and Netscape. Tight competition has caused for continual improvement in the programs and associated technologies. Web browsers are loaded with ease-of-use features and are customizable to an individual user’s preference. URLs, HTTP and HTML. The core functionality of the Web is based on three standards: the "Uniform Resource Locator" (URL), which specifies how each page of information is given a unique "address" at which it can be found; "Hyper Text Transfer Protocol" (HTTP), which specifies how the browser and server send the information to each other; and "Hyper Text Markup Language" (HTML), a method of encoding the information so it can be displayed on a variety of devices. Tim Berners-Lee now heads the World Wide Web Consortium, which develops and maintains these standards and others that enable computers on the Web to effectively store and communicate all kinds of information. Beyond text. The initial "www" program at CERN only displayed text, but later browsers such as Pei Wei's Viola (1992) added the ability to display graphics as well. Marc Andreessen of NCSA released a browser called "Mosaic for X" in 1993 that sparked a tremendous rise in the popularity of the Web among novice users. Andreesen went on to found Mosaic Communications Corporation (now Netscape Communications, a unit of AOL Time Warner). Additional features such as dynamic content, music and animation can be found in modern browsers. Frequently, the technical capability of browsers and servers advances much faster than the standards bodies can keep up with, so it is not uncommon for these newer features to not work properly on all computers, and the web as seen by Netscape is not at all the same as the web seen by Internet Explorer. The ever-improving technical capability of the WWW has enabled the development of real-time web-based services such as webcasts, web radio and live web cams. Java and Javascript. Another significant advance in the technology was Sun Microsystems' Java programming language, which enabled web servers to embed small programs (called applets) directly into the information being served that would run on the user's computer, allowing faster and richer user interaction. The similarly named, but actually quite different, JavaScript is a scripting language developed for Web pages. In conjunction with the Document Object Model (DOM), JavaScript has become a much more powerful language than its creators originally envisaged. Sociological Implications. The exponential growth of the Internet was primarily attributed to the emergence of the web browser Mosaic, followed by another, Netscape Navigator during the mid-1990s. It brought unprecedented attention to the Internet from media, industries, policy makers, and the general public. Eventually, it led to several visions of how our society might change, although some point out that those visions are not unique to the Internet, but repeated with many new technologies (especially information and communications technologies) of various era. Because the web is global in scale, some suggested that it will nurture mutual understanding on a global scale. Publishing web pages. The web is available to individuals outside the mass media. To "publish" a web page, one does not have to go through a publisher or other media institution, and the potential reader is around the globe, some thought. This to some is an opportunity to enhance democracy by giving voices to alternative and minority views. Some others took it as a path to anarchy and unrestrained freedom of expression. Yet others took it as a sign that hierarchically organized society, mass media being a symptomatic part of it, will be replaced by the so-called network society. Also, the hyper-text seemed to promote a non-hierarchical and non-linear way of expression and thinking. Unlike books and documents, hypertext does not have a linear order from the beginning to the end. It is not broken down into the hierarchy of chapters, sections, subsections, etc. This reminded some of the ideas of Marshall McLuhan that new media change people's perception of the world, mentality, and way of thinking. While not unique issue to the web, hypertext in this sense is closely related to the notion of "death of author" and intertextuality in structuralist literary theory. These bold visions are at least not fully realized yet. We can find both supporting and countering aspects of web usage. First, regarding the increased global unity, indeed, many different kinds of information are now available on the web, and for those who wish to know other societies, their cultures, and people, it became easier. When one travels to a foreign country or a remote town, s/he might be able to find some information about the place on the web, especially if the place is in one of the developed countries. Local newspapers, government publications, and other materials are easier to access, and therefore the variety of information obtainable with the same effort may be said to have increased, for the users of the Internet. At the same time, there are some obvious limitations. The web is so far a very text-centered medium, and those who are illiterate cannot make much use of it. Even among the literate, usage of a computer may or may not be easy enough. It has been known during the late 1990s, though with ample exceptions, that web users are dominantly young males in college or with a college degree. Now the trend has been changing and female and elderly are also using the web, level of education and income are related to the web use, some think (See also the Wikipedia article Digital divide). Another significant obstacle is language. Currently, only a limited number of languages are useable on the web, due to software and standard issues, and none would understand all the available languages. These factors would challenge the notion that the World Wide Web will bring unity to the world. Second, the increased opportunity to individuals is certainly observable in the countless personal pages, as well as other groups such as families, small shops, which are not among those who publish materials. The emergence of free web hosting services is perhaps an important factor in bringing this possibility into reality. The activities of alternative media expanded into the web as well. Yet not a small part of those pages seem to be either prematurely abandoned or one-time practice. Very few of those pages, even when they are well-developed, are popular. When it comes to the expression of ideas and provision of information, it seems that the major media organizations and those companies who became major organizations through their online operations are still favored by the dominant majority. Besides, the Web is not necessarily a tool for political self-education and deliberation. The most popular uses of the Web include searching and downloading pornography, which perhaps has a very limited effect in improving democracy. The most intensively accessed web pages include the document detailing the former U.S. president Bill Clinton's sexual misconduct with Monica Lewinsky, as well as the lingerie fashion show by Victoria's Secret. In sum, both in terms of writers and readers, the Web is not popularly used for democracy. While this is not enough to categorically reject the possibility of the Web as a tool for democracy, the effect so far seems to be smaller than some of the expectations for a quite simple reason, lack of interest and popularity. Anarchistic freedom of expression may be enjoyed by some, but many web hosting companies have developed their acceptable use policy over time, sometimes prohibiting some sensitive and potentially illegal expressions. And again, those expressions may not reach great many. The web is still largely a hierarchical place, some may argue. Third, regarding the non-linear and non-hierarchical structure of the Web, the effect of those on people's perception and psychology are still largely unknown. Some argue that our culture is changing to that of postmodernity, which is closely related to a non-linear and non-hierarchical way of thinking, being, and even social organization. Yet the counter-evidence is available as well. Among the most notable would be the existence of web directories and search engines. Those sites often provide navigations to the most popular sites to visitors. Besides, it is quite obvious that many web sites are organized according to a simple hierarchy, having the "home page" at the top. At least the present state of the Web and web users seem to suggest the change has not been as great as envisioned by some.

Spanish/Exercises/Possessive Adjectives. ^Lesson 5^ Rellena los espacios en blanco "Fill in the blank". 1. Manuel tiene una bicicleta. _____ bicicleta es azul. "Manuel no has a bike. His bike is blue". 2. _____ clases son a las nueve de la mañana. "My classes are at 9:00 am". 3. Nosotros visitamos a _____ abuelos. "We visit our grandparents". 4. Los mexicanos tienen _____ día de independencia el 16 de septiembre. "The Mexicans have their independence day on September 16" 5. ¿Pueden mostrarme _____ casa? "Can you (plural) show me your house?" 6. La clase de Señor Ford es fantástica. _____ clase es fantástica. "Mr. Ford's (his) class is fantastic." Soluciones a los ejercicios ^Lesson 5^

GCSE Science/Electromagnetism. Electric currents produce magnetic fields and moving magnetic fields produce electric currents. This module looks that this property of electric and magnetic fields in detail. You will learn about the magnetic fields generated by a wire and a solenoid, then go on to look at motors generators and transformers. Review of Magnetism. From work in lower school you should already be familiar with the basic properties of magnets. They are: Notice the similarity between magnetism and electricity. Electricity attracts neutral materials (recall a rubbed balloon picking up small bits of paper). Electricity comes in two forms:positive and negative. Like charges repel, unlike charges attract. Physicists long ago realised that these similarities were important. It is now realised that electricity and magnetism are closely related forces. They are really two different aspects of the same force! We call that force electromagnetism. This next section of the electricity module is probably the hardest. But it is also the most interesting. Work the problems in the text as you go along and you "will" be able to cope.

GCSE Science. This General Science book is aimed at GCSE students rather than university students. Contents by Topic. /Introduction/ Contents by Modules. The GCSE exam can be modular or combined. It is sensible however to divide the subject into modules despite the exam system used. Although this page is set out using the English system, students from other nations will still find much of the material relevant. Coursework. Common coursework experiments. __NOEDITSECTION__

GCSE Science/Electricity multiple choice. Question 5. A student rubs a polythene strip with fur and suspends it from a clamp stand. She then rubs another polythene strip with fur and brings it up to the first strip. The two strips repel each other. Look at the following four statements: Which two of the above statements are false? Question 6. A student decided to silver plate his/her mother's forks. S/he set up the apparatus above. S/he set the power pack and variable resistor so that the ammeter read 0.1 A. S/he allowed the fork to remain in the electrolysis apparatus for 10 min. Once s/he removed the fork s/he tested it by trying to scratch the silver off. S/he found that the layer of silver was too thin and decided that s/he would have to take steps to make the layer a lot thicker. Which one of the following steps would not produce a thicker layer of silver ? Question 7. What is the maximum power that an appliance should have if it is connect to a 230V supply by a 5A cable ? Question 8. The graph above shows how the potential difference across a conductor varied with the current flowing through it. Which of the following statements is true ? Question 9. Two students, Jane and John are working together to make an electromagnet. John coils some plastic coated wire around a pencil and attaches the two ends to a 1.5V cell. He finds the electromagnet that he has made will deflect a compass placed near it but will not pick up a paperclip. Jane suggest that using an iron nail rather than a pencil will make the magnet stronger. Is she correct, and why? Question 10. Jane and John have made an electromagnet using a soft iron core with 10 windings of insulated copper wire and a voltage of 1.5V. They found that they could pick up 3 paper clips with this magnet if they were careful. Which of the following changes would "not" result in more paper clips being picked up? Question 11. A photocopying machine creates a picture by making use of static electricity. Put the following statements about how the process works in the correct order. (Don't see your order in among the options? Check again because the correct order is certainly in there). Question 12. A wire is connected to a power pack and placed in the magnetic field of two bar magnets. When the power pack is switched on the wire jumps upwards. What effect will increasing the current in the wire have ? Question 13. This is the same setup as in question 12. What can be done to make the wire move downwards ?

GCSE Science/Electricity multiple choice practice question 1. A kettle is fitted with a 13A fuse. Which one of the following statements is "correct"?

Spanish/Exercises/Comparisons. ^Lesson 5^ Llena los blancos. "Fill in the blank". 1. Mario es __________ alto como Luigi. 2. El Sr. Perez tiene __________ perros como Sr. Gonzales. 3. Serena es __________ fuerte que Venus. 4. Mi carro cuesta __________ dinero como tu carro. 5. Los niños juegan __________ horas que los mayores. 6. México es __________ hermoso como España. 7. El abuelo tiene __________ pelo como su hijo. 8. Los gatos son __________ atrevidos como los tigres. 9. Argentina tiene __________ personas como Colombia. Soluciones a los ejercicios "Solutions to exercices" ^Lesson 5^

GCSE Science/Electricity multiple choice practice question 1 answer 2. Sorry this is the wrong answer The current is determined by the voltage and the resistance of the kettle element. The fuse can't control the current.

GCSE Science/Electricity multiple choice practice question 1 answer 3. Sorry this is the wrong answer. Although the circuit symbol for a fuse looks a bit like a resistor, inside a fuse is just a piece of wire. It can't keep the current down to below 13A in this way.

GCSE Science/Electricity multiple choice practice question 1 answer 4. Well done! This is the correct answer! Next question

GCSE Science/Magnetic effects of a current. When a current flows down a wire it creates a magnetic field. To see this, place a small plotting compass near the wire and turn the current on. The compass needle will deflect. The shape of the magnetic field around a wire is circular. Look at the diagram on the right. The wire is coming straight out of the screen so you only see it's cross section (the red circle) The plotting compasses show how the field wraps around the wire. Creating an electromagnet. Solenoids are made by coiling wire. The magnetic field of a solenoid looks like the field of an ordinary bar magnet. A solenoid makes a pretty weak bar magnet on its own, but if a piece of iron is put inside the solenoid, the field becomes much much stronger. Try the following experiment: You will find that the solenoid with the iron core is much much stronger than the one with the air core. Q1) Why is it important to use plastic-coated wire? Making the field stronger. To make the field stronger we can: Reversing the field. To make the north pole and south pole swap positions we can: Speaking of north and south poles, there is a little trick to help find out which end is the north pole and which is the south. Look down the solenoid and work out which way the current is flowing. Remember, current flows from the positive to the negative terminal on the power pack. If the current is flowing clockwise, the end will be a south pole. If it is going counterclockwise, the end will be a north pole. The easy way to remember this is to put arrows on the end of a capital N and S like this: If you do not understand how to determine the pole using the clockwise and anti-clockwise way you can use the right hand grip rule

United States Government. __NOEDITSECTION__ The Constitution and Government of the United States of America. Part IV- American Government: Theory and Analysis. Part V- Appendices

United States Government/The Three Branches. Introduction. The United States Constitution divides government into three separate and distinct branches: the Executive, Legislative and Judicial branches. The concept of separate branches with distinct powers is known as "separation of powers." That doctrine arose from the writings of several European philosophers. The Englishman John Locke first pioneered the idea, but he only suggested a separation between the executive and legislative. The Frenchman Charles-Louis de Secondat, Baron de Montesquieu, added the judicial branch. Each branch is theoretically equal to each of the others. The branches check each others powers and use a system known as checks and balances. Thus, no branch can gain too much power and influence, thus reducing the opportunity for tyrannical government. The Preamble to the American Constitution sets out these aims in the general statement: "We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this constitution for the United States of America". The Legislative. The Congress is the Legislative Branch. Its main function is to make laws. It also oversees the execution of these laws, and checks various executive and judicial powers. The Congress is "bicameral" - it is composed of two houses. One house is the House of Representatives and the other is the Senate. The House of Representatives is currently composed of four hundred and thirty-five members. Each of the fifty states is allocated one or more representatives based on its population which is calculated on a decennial basis (once in ten years) . Each state is guaranteed at least one representative. A state that is allocated more than one representative divides itself, as state procedures dictate, into a number of districts equal to the number of representatives to which it is entitled. The people of each district vote to elect one representative to Congress (States that have only one representative allocated choose "at-large" representatives - the state votes as one entire district). The District of Columbia and a number of U.S. territories have been permitted to elect delegates to the House of Representatives. These delegates may participate in debates, and sit and vote in committee, but are not allowed to vote in the full House. Every House member faces re-election in an even-numbered year and is elected to a two-year term. The House is presided over by a Speaker, who is directly elected by the members of the House. The Senate is the upper house of the legislative branch of the United States and possesses one hundred members which is considerably less than the four hundred and thirty-five members of the House of Representatives. Each state chooses two senators, regardless of that state's population. The Constitution originally dictated that a state's senators were to be chosen by the state's legislature; after the Seventeenth Amendment was ratified in 1913, senators were elected directly by the state's population. In contrast to the House's two-year terms, Senators are elected to a six-year stint in office. In addition, only one-third of the Senate stands for election during an even year. These differences between the two houses were deliberately put into place by the Founding Fathers; the Senate was intended to be a more stable, austere body, whereas the House would be more responsive to the people's will. The Vice-President is President of the Senate, but he/she only votes if there is a tie. The Senate also chooses a President Pro Tempore to preside in the Vice-President's absence (though, in practice, most of the time, senators from the majority take turns presiding for short periods). The Senate and the House are both required to approve legislation before it becomes a law. The two houses are equal in legislative power, but revenue bills (bills relating to taxation) may only originate in the House. However, as with any other bill, the Senate's approval is still required, and the Senate may amend such bills. The Senate holds additional powers relating to treaties and the appointments of executive and judicial officials. This power is known as "advice and consent." The Senate's advice and consent is required for the President to appoint judges and many executive officers, and also to ratify treaties. To grant advice and consent on treaties, two-thirds of the Senators must concur (agree). While most votes require a simple majority to pass, it sometimes takes three-fifths of senators to bring a bill to a vote. This is because Senate rules hold that a bill cannot be voted on as long as it is being debated--and there is no limit on how long a senator may debate a bill. Senators sometimes use this rule to filibuster a bill--that is, continue debating a bill endlessly so that it cannot be voted on. The only way to end a filibuster is for three-fifths of all Senators to vote for a cloture resolution, which ends all debate and brings the bill up for voting. Use of the filibuster tends to be controversial. Whichever party is in the majority tends to call its use "obstructionism," while the other side sees it as an important check on the majority. The House has the sole power to impeach federal executive and judicial officers. According to the Constitution, officers may be impeached for "treason, bribery, or other high crimes and misdemeanors.” The Senate has the sole power to try all such impeachments, a two-thirds vote being required for conviction. The Constitution requires that any individual convicted by the Senate to be removed from office. The Senate also has the power to bar that individual from further federal office. The Senate may not impose any further punishment, although the parties are still subject to trial in the courts. As the Vice-President (being next-in-line to the Presidency) would have an obvious conflict of interest in presiding at a trial of the President, in such cases, the Chief Justice presides. Interestingly, no similar provision prevents the Vice-President from presiding at his or her own trial. The Executive. The President, Vice President, and other executive officials make up the Executive Branch. The main function of this branch is to execute the laws created by Congress. The President and the Vice-President are chosen by the Electoral College, a body of people elected for the purpose of electing the President. One may wait to consider the Electoral College in further detail. The President appoints several "Secretaries" to head executive departments. An executive department is a body covering a broad topic of law- examples include the Department of Agriculture and the Department of Justice. The several secretaries (in the case of the Justice Department, the Attorney General) serve as advisors to the President and also as the chief officers of their own departments. This group of advisors is collectively known as the President's "cabinet". The President nominates these Secretaries, as well as other important federal officials, and the Senate "advise and consents" to them . The Judicial. The Supreme Court and the lower courts compose the Judicial Branch. The judiciary must interpret the laws of the United States. In the course of such interpretations, the courts may find that a law violates the constitution. If so, the court declares the law unconstitutional. Thus, the judiciary also has a role in determining the law of the land. The judges of federal courts are nominated by the President and advised and consented to by the Senate. The number of judges and the exact structure of the courts is set by law, and not by the Constitution. The Legislative Process: How A Bill Becomes A Law. After both houses of Congress pass a bill, perhaps observing the different rules and procedures in each house, but with the exact same final text, the bill is submitted to the President. Immediately, a ten-day clock for the president to act in starts to tick. Sundays are excluded in this calculation. Once he receives the bill, the President has many options. The outcome of the process depends on the route taken by him. Checks and Balances. In order to prevent any branch of government from becoming too powerful, the Framers of the Constitution created a system of checks and balances. Each branch of government has checks on the others, while it is itself also checked. The complex system can be outlined as follows: Checks of the Legislative "Checks on the Executive" "Checks on the Judicial" "Internal Checks" Checks of the Executive "Checks on the Legislative" "Checks on the Judicial" Checks of the Judicial "Checks on the Legislative" "Checks on the Executive"

Algebra. Preface. Chapter 0: An Introduction to Mathematics<br> Unit 1: Numbers, Variables and Relationships. How can we use numbers and variables to find out unknown information? Chapter 1: Elementary Arithmetic<br>Chapter 2: An Introduction to Algebra<br>Chapter 3: Solving Equations<br>Chapter 4: Inequalities<br> Unit 2: An Introduction To Graphing. Math is a method of solving problems. You take information you know, and by manipulating it using mathematical principles, you can find information you don't know. Functions are the mathematical framework for solving problems. They have parameters, rules, and ways of being solved. This section will introduce you to functions and how to use them. Chapter 5: The Cartesian Plane<br>Chapter 6: Graphing Linear Functions<br>Chapter 7: Systems and Matrices<br>Chapter 8: Piecewise Functions<br> Unit 3: Polynomials. Chapter 9: Quadratic Functions<br>Chapter 10: Higher-Degree Polynomials<br> Unit 4: Other Functions. Chapter 11: Properties of Functions<br> Chapter 12: Exponents and Logarithms<br> Chapter 13: Rational and Radical Functions<br> Chapter 14: Trigonometry<br> Unit 5: Algebra in Discrete Mathematics. Chapter 15: Sequences and Series<br>Chapter 16: Probability and Statistics<br> Unit 6: Analytic Geometry. Chapter 17: Conic Sections<br> Chapter 18: Parametric Equations and Polar Coordinates<br> Chapter 19: Vectors<br> Unit 7: Advanced Algebra. Now that you have completed your mathematical journey, you may be wondering where to head over next. This unit provides six optional chapters that can be done in any order you please. The six chapters are meant to be independent from one another, and any of the chapters can be skipped entirely to put more focus on the topics that are of greater interest to you. Chapter 20: Complex Numbers<br> Chapter 21: Advanced Polynomials<br> Chapter 22: Continued Fractions<br> Chapter 23: Theory of Equations and Inequalities<br> Chapter 24: Limits of Functions<br> Chapter 25: Group Theory<br>

Algebra/Solving equations. Quadratic equations. Up to now you have only dealt with equations and expressions involving just x; in this section we'll move onto solving things which have formula_1 in them. All quadratic equations can be arranged in the form formula_2, and "a","b","c" are all constants. Now let's look at some examples: Examples: Rearrange the following equations in the form formula_3: Solution for (1): Solution for (2): Factorization. Factorization is the most common way to solve quadratic equations. Let us consider again the first example above: formula_11 We have already simplified the equation into Now, we want to factorize the equation - that is to say, get it into a form such as: Look at the number term c. In this example, it is -3. Now, if we are lucky, the numbers "something" and "something else" will turn out to be nice whole numbers, so let's think of two numbers that will multiply together to give -3. Either 3 and -1, or -3 and 1. But we also need to get the x term correct (here, b=2). In fact, we need our two factors of c to add together to make b. And (3)+(-1)=2. So, we have found our 'somethings': they are 3 and -1. Let's fill them in. Just to check, we can multiply out the brackets to check we have what we started with: Now, we know that in an equation the left side is always equal to the right side. And in this case the right side of the equation is 0, so from that we can conclude the term formula_16 must equal to zero as well. And that means that either formula_17 or formula_18 must equal zero. (Not convinced? Remember (x+3) and (x-1) are just numbers. Can you find two non-zero numbers which multiply to make zero?) Let's write that algebraically: Thus, there are two different solutions to the same equation! This is the case for all quadratic equations. We say that this quadratic equation has "two distinct and real roots". With practice, you will often be able to write down the equation in factorised form almost immediately. Here is another example, in this case the x easily factorises out: Completing the square. Sometimes the roots (solutions) of a quadratic equation cannot be easily obtained by factorisation. In such cases, we have to solve the equation by completing the square, or using the quadratic formula (see below). In order to complete the square, we need to rewrite the given equation in the form formula_21. Now here is an example: In general, we get Note that when we reach the stage of taking the square root of both sides of the equation, we might have a negative left-hand side. In this case, the roots will be complex. If you have not yet learned about complex numbers, it is possible to simply state that the equation "has no real roots". Quadratic Formula. The quadratic formula is a special generalization of completing the square that allows the two roots of a quadratic equation to be obtained by simple substitution. It can be used to solve any quadratic equation and is very quick to work out on a calculator. Complete the square: Simplify: Which equals 4y to the 19th power. which is the desired form of the quadratic formula. Hence, given that a quadratic is in the form formula_32, the two roots are: The quantity formula_34 in the equation, known as the discriminant, is an indication of the solubility and nature of the roots: Weda's Theorem. If the quadratic equation formula_35 has two real roots formula_36 and formula_37, then formula_38 This is because formula_39 and formula_40. By simply adding or multiplying the two roots we will get the above two equations. This is called Weda's Theorem. Using Weda's Theorem we can find the second root of a given quadratic equation without solving the equation. Example: Given that one of the real roots of the equation formula_41 is 2, find the other root without solving the equation. Solution: formula_42 We can also determine the signs of two roots by applying the following rules: Another problem involving Weda's Theorem: Example: For the equation formula_47, given that the sum of squares of roots is formula_48, find the value of formula_49. Solution: formula_50 Pythagorean Theorem ____________________ a^+b^=c^ Solving simultaneous linear and nonlinear equations. In previous chapters you have already learned how to solve simultaneous linear equations. Now we will learn how to solve a system of simultaneous linear and non-linear equations with two unknowns. It is usually done by substitution method. Example: Solve the following simultaneous equations: formula_51 Solution: formula_52 ∴ x=-1 and y=1, or x=-2 and y=0.