Solid cylinders.

The definitions and results in this section are taken from the 1913 text, "Plane and Solid Geometry" by George Wentworth and David Eugene Smith.  A "" is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Any line in this family of parallel lines is called an "element" of the cylindrical surface. From a kinematics point of view, given a plane curve, called the "directrix", a cylindrical surface is that surface traced out by a line, called the "generatrix", not in the plane of the directrix, moving parallel to itself and always passing through the directrix. Any particular position of the generatrix is an element of the cylindrical surface.  A solid bounded by a cylindrical surface and two parallel planes is called a (solid) '. The line segments determined by an element of the cylindrical surface between the two parallel planes is called an "element of the cylinder". All the elements of a cylinder have equal lengths. The region bounded by the cylindrical surface in either of the parallel planes is called a'of the cylinder. The two bases of a cylinder are congruent figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a ', otherwise it is called an '. If the bases are disks (regions whose boundary is a circle) the cylinder is called a ". In some elementary treatments, a cylinder always means a circular cylinder.  The " (or altitude) of a cylinder is the perpendicular distance between its bases.  The cylinder obtained by rotating a line segment about a fixed line that it is parallel to is a '. A cylinder of revolution is a right circular cylinder. The height of a cylinder of revolution is the length of the generating line segment. The line that the segment is revolved about is called the'of the cylinder and it passes through the centers of the two bases.

Right circular cylinders.

The bare term "cylinder" often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an "". The formulae for the surface area and the volume of a right circular cylinder have been known from early antiquity.  A right circular cylinder can also be thought of as the solid of revolution generated by rotating a rectangle about one of its sides. These cylinders are used in an integration technique (the "disk method") for obtaining volumes of solids of revolution.

Cylindric sections.

A cylindric section is the intersection of a cylinder's surface with a plane. They are, in general, curves and are special types of "plane sections". The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. Such a cylindric section of a right cylinder is a rectangle.  A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a "". If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic respectively.  For a right circular cylinder, there are several ways in which planes can meet a cylinder. First, planes that intersect a base in at most one point. A plane is tangent to the cylinder if it meets the cylinder in a single element. The right sections are circles and all other planes intersect the cylindrical surface in an ellipse. If a plane intersects a base of the cylinder in exactly two points then the line segment joining these points is part of the cylindric section. If such a plane contains two elements, it has a rectangle as a cylindric section, otherwise the sides of the cylindric section are portions of an ellipse. Finally, if a plane contains more than two points of a base, it contains the entire base and the cylindric section is a circle.  In the case of a right circular cylinder with a cylindric section that is an ellipse, the eccentricity of the cylindric section and semi-major axis of the cylindric section depend on the radius of the cylinder and the angle between the secant plane and cylinder axis, in the following way:

Volume.

If the base of a circular cylinder has a radius and the cylinder has height, then its volume is given by  This formula holds whether or not the cylinder is a right cylinder.  This formula may be established by using Cavalieri's principle.  In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the height. For example, an elliptic cylinder with a base having semi-major axis, semi-minor axis and height has a volume, where is the area of the base ellipse (= ). This result for right elliptic cylinders can also be obtained by integration, where the axis of the cylinder is taken as the positive -axis and the area of each elliptic cross-section, thus:  Using cylindrical coordinates, the volume of a right circular cylinder can be calculated by integration over

Surface area.

Having radius and altitude (height), the surface area of a right circular cylinder, oriented so that its axis is vertical, consists of three parts:  The area of the top and bottom bases is the same, and is called the "base area",. The area of the side is known as the "",.  An "open cylinder" does not include either top or bottom elements, and therefore has surface area (lateral area)  The surface area of the solid right circular cylinder is made up the sum of all three components: top, bottom and side. Its surface area is therefore, where is the diameter of the circular top or bottom.  For a given volume, the right circular cylinder with the smallest surface area has. Equivalently, for a given surface area, the right circular cylinder with the largest volume has, that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle).  The lateral area,, of a circular cylinder, which need not be a right cylinder, is more generally given by: where is the length of an element and is the perimeter of a right section of the cylinder. This produces the previous formula for lateral area when the cylinder is a right circular cylinder.

Right circular hollow cylinder (cylindrical shell).

A "right circular hollow cylinder" (or "") is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis, as in the diagram.  Let the height be, internal radius, and external radius. The volume is given by  Thus, the volume of a cylindrical shell equals 2(average radius)(altitude)(thickness).  The surface area, including the top and bottom, is given by  Cylindrical shells are used in a common integration technique for finding volumes of solids of revolution.

"On the Sphere and Cylinder".

In the treatise by this name, written c. 225 BCE, Archimedes obtained the result of which he was most proud, namely obtaining the formulas for the volume and surface area of a sphere by exploiting the relationship between a sphere and its circumscribed right circular cylinder of the same height and diameter. The sphere has a volume that of the circumscribed cylinder and a surface area that of the cylinder (including the bases). Since the values for the cylinder were already known, he obtained, for the first time, the corresponding values for the sphere. The volume of a sphere of radius is. The surface area of this sphere is. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.

Cylindrical surfaces.

In some areas of geometry and topology the term "cylinder" refers to what has been called a "cylindrical surface". A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Such cylinders have, at times, been referred to as "". Through each point of a generalized cylinder there passes a unique line that is contained in the cylinder. Thus, this definition may be rephrased to say that a cylinder is any ruled surface spanned by a one-parameter family of parallel lines.  A cylinder having a right section that is an ellipse, parabola, or hyperbola is called an "elliptic cylinder", "parabolic cylinder" and "hyperbolic cylinder", respectively. These are degenerate quadric surfaces.  When the principal axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the quadric in three dimensions is given by with the coefficients being real numbers and not all of, and being 0. If at least one variable does not appear in the equation, then the quadric is degenerate. If one variable is missing, we may assume by an appropriate rotation of axes that the variable does not appear and the general equation of this type of degenerate quadric can be written as where  If this is the equation of an "elliptic cylinder". Further simplification can be obtained by translation of axes and scalar multiplication. If formula_11 has the same sign as the coefficients and, then the equation of an elliptic cylinder may be rewritten in Cartesian coordinates as:  This equation of an elliptic cylinder is a generalization of the equation of the ordinary, "circular cylinder" (). Elliptic cylinders are also known as "cylindroids", but that name is ambiguous, as it can also refer to the Plücker conoid.  If formula_11 has a different sign than the coefficients, we obtain the "imaginary elliptic cylinders":  which have no real points on them. (formula_15 gives a single real point.)  If and have different signs and formula_16, we obtain the "hyperbolic cylinders", whose equations may be rewritten as:  Finally, if assume, without loss of generality, that and to obtain the "parabolic cylinders" with equations that can be written as:

Projective geometry.

In projective geometry, a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity. If the cone is a quadratic cone, the plane at infinity (which passes through the vertex) can intersect the cone at two real lines, a single real line (actually a coincident pair of lines), or only at the vertex. These cases give rise to the hyperbolic, parabolic or elliptic cylinders respectively.  This concept is useful when considering degenerate conics, which may include the cylindrical conics.

Prisms.

A "solid circular cylinder" can be seen as the limiting case of a -gonal prism where approaches infinity. The connection is very strong and many older texts treat prisms and cylinders simultaneously. Formulas for surface area and volume are derived from the corresponding formulas for prisms by using inscribed and circumscribed prisms and then letting the number of sides of the prism increase without bound. One reason for the early emphasis (and sometimes exclusive treatment) on circular cylinders is that a circular base is the only type of geometric figure for which this technique works with the use of only elementary considerations (no appeal to calculus or more advanced mathematics). Terminology about prisms and cylinders is identical. Thus, for example, since a "truncated prism" is a prism whose bases do not lie in parallel planes, a solid cylinder whose bases do not lie in parallel planes would be called a "truncated cylinder".  From a polyhedral viewpoint, a cylinder can also be seen as a dual of a bicone as an infinite-sided bipyramid.

A cylinder (from Greek κύλινδρος – "kulindros", "roller", "tumbler") has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.

Válec je v prostorové geometrii těleso, vymezené dvěma rovnoběžnými podstavami a pláštěm. Plášť je rozvinutelná plocha, všechny povrchové (tvořící) přímky pláště jsou rovnoběžné a pokud jsou k podstavám kolmé, hovoříme o kolmém válci. V opačném případě se jedná o válec kosý. Vzdálenost mezi podstavami se nazývá "výška válce". Vzdálenost mezi dvěma podstavami podél pláště (tj. podél povrchové přímky) se nazývá "strana válce".


History.

Early years.

At the close of 1893, a small group of young people based around three brothers – Václav, Bohumil and Rudolf Rudl – had the idea of setting up a sports club. On 16 November, the founders' meeting approved the club's articles of association and one month later, on 17 December, the first annual general meeting took place. Soon after that, the Athletic Club Sparta came up with its tricolour, in which blue symbolises Europe, red is the symbol of the royal city, though the reason for the yellow is not known any more.  At the very beginning of the club's football history, the players used to wear black jerseys with a big "S" on the front. They then played for two years in black-and-white striped jerseys, which they returned to, wearing them as a reserve strip, for two years in 1996. In 1906, club president Dr. Petřík was in England where he saw the famous Woolwich Arsenal play with their red jerseys and decided to bring one set to Prague. At that time, he did not realise he was setting up one of the club's greatest traditions. Together with the red jerseys, Sparta players wear white shorts and black socks.  Shortly after World War I, a team was put together that triggered off the famous period of the 1920s and '30s referred to as "Iron Sparta". A football league in Czechoslovakia was established in the mid-twenties and the club collected title after title. To this day, the fans still recall the names of the players of that period with admiration: Peyer, Hojer, Perner, Káďa, Kolenatý, Červený. A few years later, some no less famous names appeared, such as Hochman, Burgr, Hajný, Šíma, Silný, Čtyřoký, Košťálek and in particular Oldřich Nejedlý, the top scorer at the 1934 FIFA World Cup. Shortly before this most famous era kicked off, Vlasta Burian, the man who later became the king of Czech comedians, played in goal for the club.  The milestones of the first golden period of the club's history are two Central European Cup titles, which in the '20 and the '30s enjoyed the same recognition as that of today's Champions League. Sparta's three titles are important milestones in the cup's history. After two triumphs in 1927 and 1935, the third came in 1964, at a time when the cup's importance was gradually falling behind that of other European cups.  In 1946, AC Sparta toured Great Britain opening with a 2–2 draw against Arsenal on 2 October.

Golden years.

Golden periods alternated with years when Sparta fans only nostalgically remembered the "good old times". After substantial changes driven by the socialist regime, bringing frequent changes of the club's name rather than achievements to be proud of, the title in 1954 was the last one before a long period of misery. Only the great era of the team around Andrej Kvašňák in the 1960s brought back memories of the club's golden years.  There are still many people who recollect the era of Andrej Kvašňák, Jiří Tichý and Václav Mašek. Those were the days when Sparta hosted the biggest number of fans in its history, with the stadium at that time accommodating almost 40,000. All three of the above-mentioned heroes were part of the national team that finished second at the 1962 World Cup in Chile. Other important players in these "golden years" were Josef Vojta, Vladimír Táborský and Ivan Mráz.

Relegation and comeback.

Up until 1975, Sparta was the only Czech club that had never been relegated to the second division. In this year, however, due to a number of circumstances, the team dropped to division two. The club only spent one year in this division, with the crucial matches for the club's comeback to the elite being sold out.  Nevertheless, the club did not win another league title until the early 1980s. Built around Chovanec, Berger, Hašek, Skuhravý and Griga, the team regained its former status and won five league titles in a row between 1986 and 1991. In 1983–84, the team got as far as the UEFA Cup quarter-finals, falling to Hajduk Split. In the early 1990s, this successful era was continued by the next generation of players, such as Siegl, Horňák, Němeček, Frýdek, Němec and Kouba.

1990s to present.

Sparta has achieved a number of international successes, including two Central European Cup titles in the period of "Iron Sparta". More recent high points include Sparta's performance in the first year of the UEFA Champions League, in 1991–92. Sparta defeated Rangers, then Marseille and reached the semi-final group. Playing Barcelona, Dynamo Kyiv and Benfica, Sparta finished second. Unlike today's system, only the group winner reached the final. Being second in the group, Sparta was unofficially Europe's third or fourth best team.  Sparta participated in the group stage of Champions League between 1997 and 2006. The club enjoyed their best Champions League performances in the 1999–2000 and 2001–02 seasons, reaching the now-defunct second group stage on both occasions. In 1999–2000, it won its initial group under the management of Ivan Hašek, and was then third in the quarter-final group. In that group, Sparta came up against a Barcelona squad which went on to reach the semi-finals.  In the 2001–02 season, Sparta was drawn against the eventual winners of both the European competitions during the course of its run. Feyenoord lost twice to Sparta in the champions league group stage and managed to qualify for the UEFA Cup, which it went on to win. Sparta went on to meet Real Madrid in the quarter-final that year. Sparta did not qualify for the group stage in 2002–03, when it was beaten by the Belgian club Genk in the third round of qualifying. 2003–04 saw Sparta take on two Italian giants; initially, the club beat Lazio in the group stage, but after an initial draw Sparta failed to get into the quarter-finals past Milan. The group stage in 2004–05 did not work out at all well for Sparta. After drawing with Manchester United at the sold-out Toyota Arena, the other matches were lost and the club finished last in the group with the club achieving their worst-ever return of just one point from the six matches.  Sparta, usually along with Slavia, has always been a base for the national team; Sparta players contributed to the biggest achievements of the Czechoslovak and Czech national teams. It all started in 1934, when Oldřich Nejedlý was the top scorer at the World Cup in Rome; four years later, seven Sparta players were part of the national team at the World Cup in France. In 1962, Kvašňák and Tichý played for the "silver" team in Chile. In 1990 in Italy, where the national team got as far as the quarterfinal, the team's play was mainly created by Chovanec, Bílek, Hašek and other Sparta players, such as Skuhravý, who went on to become a star of the Italian league. Sparta players also contributed to the last big achievement of the already independent Czech Republic team in 1996. Kouba, Frýdek and Horňák returned to Letná from England with silver medals. On top of that, the team was coached by Dušan Uhrin, who had spent his best years at Sparta, and Pavel Novotný came to Sparta two years later. Sparta players also featured in more recent qualification and tournament games of the Czech national team. Miroslav Baranek, Tomáš Votava, Vratislav Lokvenc, Milan Fukal, Martin Hašek, Libor Sionko, Jiří Novotný, Jaromír Blažek and the outstanding talent of Tomáš Rosický helped the team in its UEFA Euro 2000 campaign in Belgium and the Netherlands.  The next era culminating in the bronze medal in the Euro 2004 in Portugal saw Sparta players leaving their unmistakable mark in the national team successes. Zdeněk Grygera, Tomáš Hübschman, Jaromír Blažek, Karel Poborský and academy products Petr Čech and Tomáš Rosický helped Czech football to become recognised as being amongst the elite in Europe and most have played for elite European clubs. Currently, Sparta is one of only two teams in the domestic league which supplies players to the national side. It goes without saying that the club also supplies players to the country's various youth teams.  Historical names:

Club symbols.

The name "Sparta" was inspired by the fighting spirit and courage of the people from the ancient city of Sparta. From the very beginning, the colours of Sparta were blue (symbolizing speed, athletics and sport in general), red and yellow (the official colours of Royal City of Prague). In 1906, one of the members of the committee brought (from his trip to England) jerseys of the London club Arsenal. From that time, Sparta has typically played in their red (or, to be more precise, dark red or maroon) colours.  Another symbol of Sparta is the big "S"; thus, Sparta and Slavia Prague are usually collectively called the "Prague "S"" and contest the Prague derby. Sparta Prague has three stars above its crest to signify winning 30–39 national league championships, adding a new star for every ten league titles.  The Czech films "Proč?" ("Why?"), "Horem pádem" ("Up and Down") and "Non Plus Ultras" take the culture of Sparta fandom as one of their subjects.

Supporters.

The supporters of Sparta Prague are called "Letenští", meaning "From Letná". They sit in the sectors H37-H40 in the southeast corner of the stadium, although some reports suggest that by July 2020 the supporters section will be moved behind the goal in the south stand, around sectors D33-D36. The fans have good relations with those of FC Nitra and the now defunct FC VSS Košice in Slovakia. They also have historical ties to the Premier League club Arsenal F.C..

Stadium.

Sparta play their home matches at Generali Česká pojišťovna Arena in the Letná district of Prague. For training Sparta use a football centre at Strahov Stadium (formerly the second largest stadium in the world) whose space was rebuilt to eight football pitches (six fields of standard sizes and two futsal-sized). These are currently used as a training facility by both youth academy and reserve squad.

Players.

Reserve squad.

"To see Sparta Prague's reserve squad, go to AC Sparta Prague B"

European cups all-time statistics.

The following is a list of the all-time statistics from Sparta's games in the three UEFA tournaments it has participated in, as well as the overall total. The list contains the tournament, the number of seasons (S), games played (P), won (W), drawn (D) and lost (L). The statistics include qualification matches.

UEFA club coefficient ranking.

"As of 14 May 2019, Source: "

Honours.

Domestic.

Czechoslovak First League / Czech First League:  Czechoslovak Cup/Czech Cup:  Czech Supercup:

Athletic Club Sparta Praha (), commonly known as Sparta Prague, is a Czech football club based in Prague. It is the most successful club in the Czech Republic and one of the most successful in central Europe, winning the central European Cup (also known as the Mitropa Cup) three times as well as having reached the semi-finals of the European Cup (now the UEFA Champions League) in 1992 and the UEFA Cup Winners' Cup in 1973.

AC Sparta Praha fotbal (celým názvem: Athletic Club Sparta Praha fotbal, akciová společnost) je český profesionální fotbalový klub, který sídlí v pražském Bubenči. Oddíl je členem asociace Association Club Sparta Praha. Sparta je nejúspěšnějším českým fotbalovým týmem, získala 36 titulů z československé a české ligy, několikrát účinkovala v Lize mistrů UEFA a během více než 120leté historie klubu v jeho dresu působila řada reprezentantů. Současným vlastníkem klubu je J&T Credit Investments, a. s., jejímiž akcionáři jsou Daniel Křetínský (10 %) a kyperská společnost ACSP Holding Limited (90 %), která je vlastněna neprůhlednou sítí společností z daňových rájů; podle vyjádření firmy však probíhají transakce, po kterých má Daniel Křetínský získat až 55% vlastnický podíl.


Life.

Early life.

Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819), who lived in Dublin at 29 Dominick Street, later renumbered to 36. Hamilton's father, who was from Dublin, worked as a solicitor. By the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim, Co. Meath.  Hamilton is said to have shown immense talent at a very early age. Hamilton's predecessor as Royal Astronomer of Ireland and later Bishop of Cloyne Dr. John Brinkley remarked of the 18-year-old Hamilton, 'This young man, I do not say "will be", but "is", the first mathematician of his age.'  His uncle observed that Hamilton had a remarkable ability to learn languages, and from a young age, had displayed an uncanny ability to acquire them (although this is disputed by some historians, who claim he had only a very basic understanding of them). At the age of seven, he had already made very considerable progress in Hebrew, and before he was thirteen he had acquired, under the care of his uncle (a linguist), almost as many languages as he had years of age. These included the classical and modern European languages, and Persian, Arabic, Hindustani, Sanskrit, and even Marathi and Malay. He retained much of his knowledge of languages to the end of his life, often reading Persian and Arabic in his spare time, although he had long since stopped studying languages, and used them just for relaxation.  In September 1813, the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other in a mental arithmetic contest with Colburn emerging the clear victor. In reaction to his defeat, Hamilton dedicated less time to studying languages and more time to studying mathematics.

Education.

Hamilton was part of a small but well-regarded school of mathematicians associated with Trinity College in Dublin, which he entered at age 18. The college awarded him two Optimes, or off-the-chart grades. He studied both classics and mathematics (BA in 1827, MA in 1837). While still an undergraduate he was appointed Andrews professor of Astronomy and Royal Astronomer of Ireland. He then took up residence at Dunsink Observatory where he spent the rest of his life.

Personal life.

While attending Trinity College, Hamilton proposed to his friend's sister, who rejected him. Hamilton, being a sensitive young man, became sick and depressed, and almost committed suicide. He was rejected again in 1831 by Ellen de Vere, a sister of the poet Aubrey Thomas de Vere (1814-1902). His proposal to Helen Marie Bayly, a country preacher's daughter, was accepted, and they married in 1833. Hamilton had three children with Bayly: William Edwin Hamilton (born 1834), Archibald Henry (born 1835), and Helen Elizabeth (born 1840). Bayly proved to be pious, shy, timid, and chronically ill, and Hamilton's married life was reportedly difficult.

Death and legacy.

Hamilton retained his faculties unimpaired to the very last, and steadily continued the task of finishing the "Elements of Quaternions" which had occupied the last six years of his life. He died on 2 September 1865, following a severe attack of gout. He is buried in Mount Jerome Cemetery in Dublin.  Hamilton is recognised as one of Ireland's leading scientists and, as Ireland becomes more aware of its scientific heritage, he is increasingly celebrated. The Hamilton Institute is an applied mathematics research institute at Maynooth University and the Royal Irish Academy holds an annual public Hamilton lecture at which Murray Gell-Mann, Frank Wilczek, Andrew Wiles, and Timothy Gowers have all spoken. The year 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the "Hamilton Year, celebrating Irish science". Trinity College Dublin marked the year by launching the Hamilton Mathematics Institute.  Two commemorative stamps were issued by Ireland in 1943 to mark the centenary of the announcement of quaternions. A 10 Euros commemorative silver Proof coin was issued by the Central Bank of Ireland in 2005 to commemorate 200 years since his birth.  The newest maintenance depot for the Dublin LUAS tram system has been named after him. It is located adjacent to the Broombridge stop on the Green Line.

Astronomy.

In his youth Hamilton owned a telescope, and became an expert at calculating celestial phenomena, for instance the locations of the visibility of eclipses of the moon. Also having received extremely high grades for both the Classics and Science, it was not too unusual that, on 16 June 1827, only 21 years old and still an undergraduate, he was elected Royal Astronomer of Ireland and came to live at Dunsink Observatory where he remained until his death in 1865.  In his early years at Dunsink, Hamilton observed the heavens quite regularly. Observational astronomy in those days mostly consisted of measuring star positions, which was not too interesting for a mathematical mind. But the main reason for ultimately leaving the regular observing completely to his astronomy assistant Charles Thompson was that Hamilton frequently suffered from illnesses after having observed.  Nowadays Hamilton is not seen as one of the great astronomers but in his lifetime he was. His Introductory lectures in astronomy were famous; in addition to his students, they attracted many scholars and poets, and even ladies–in those days a remarkable feat. The poet Felicia Hemans wrote her poem "The Prayer of the Lonely Student" after hearing one of his lectures.

Physics.

Hamilton made important contributions to optics and to classical mechanics. His first discovery was in an early paper that he communicated in 1823 to Dr. Brinkley, who presented it under the title of ""Caustics"" in 1824 to the Royal Irish Academy. It was referred as usual to a committee. While their report acknowledged its novelty and value, they recommended further development and simplification before publication. Between 1825 and 1828 the paper grew to an immense size, mostly by the additional details that the committee had suggested. But it also became more intelligible, and the features of the new method were now easily seen. Until this period Hamilton himself seems not to have fully understood either the nature or importance of optics, as later he intended to apply his method to dynamics.  In 1827, Hamilton presented a theory of a single function, now known as Hamilton's principal function, that brings together mechanics, optics, and mathematics, and which helped to establish the wave theory of light. He proposed it when he first predicted its existence in the third supplement to his ""Systems of Rays"", read in 1832. The Royal Irish Academy paper was finally entitled ""Theory of Systems of Rays"" (23 April 1827), and the first part was printed in 1828 in the "Transactions of the Royal Irish Academy". The more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers ""On a General Method in Dynamics"", which appeared in the Philosophical Transactions in 1834 and 1835. In these papers, Hamilton developed his great principle of ""Varying Action"". The most remarkable result of this work is the prediction that a single ray of light entering a biaxial crystal at a certain angle would emerge as a hollow cone of rays. This discovery is still known by its original name, ""conical refraction"".  The step from optics to dynamics in the application of the method of ""Varying Action"" was made in 1827, and communicated to the Royal Society, in whose "Philosophical Transactions" for 1834 and 1835 there are two papers on the subject, which, like the ""Systems of Rays"", display a mastery over symbols and a flow of mathematical language almost unequaled. The common thread running through all this work is Hamilton's principle of ""Varying Action"". Although it is based on the calculus of variations and may be said to belong to the general class of problems included under the principle of least action which had been studied earlier by Pierre Louis Maupertuis, Euler, Joseph Louis Lagrange, and others, Hamilton's analysis revealed much deeper mathematical structure than had been previously understood, in particular the symmetry between momentum and position. Paradoxically, the credit for discovering the quantity now called the Lagrangian and Lagrange's equations belongs to Hamilton. Hamilton's advances enlarged greatly the class of mechanical problems that could be solved, and they represent perhaps the greatest addition which dynamics had received since the work of Isaac Newton and Lagrange. Many scientists, including Liouville, Jacobi, Darboux, Poincaré, Kolmogorov, and Arnold, have extended Hamilton's work, thereby expanding our knowledge of mechanics and differential equations.  While Hamiltonian mechanics is based on the same physical principles as the mechanics of Newton and Lagrange, it provides a powerful new technique for working with the equations of motion. More importantly, both the Lagrangian and Hamiltonian approaches, which were initially developed to describe the motion of discrete systems, have proven critical to the study of continuous classical systems in physics, and even quantum mechanical systems. Indeed, the techniques find use in electromagnetism, quantum mechanics, quantum relativity theory, and quantum field theory. In the Dictionary of Irish Biography David Spearman writes:

Mathematics.

Hamilton's mathematical studies seem to have been undertaken and carried to their full development without any assistance whatsoever, and the result is that his writings do not belong to any particular ""school"". Not only was Hamilton an expert as an arithmetic calculator, but he seems to have occasionally had fun in working out the result of some calculation to an enormous number of decimal places. At the age of eight Hamilton engaged Zerah Colburn, the American ""calculating boy"", who was then being exhibited as a curiosity in Dublin. Two years later, aged ten, Hamilton stumbled across a Latin copy of Euclid, which he eagerly devoured; and at twelve he studied Newton's "Arithmetica Universalis". This was his introduction to modern analysis. Hamilton soon began to read the "Principia", and by age sixteen he had mastered a great part of it, as well as some more modern works on analytical geometry and the differential calculus.  Around this time Hamilton was also preparing to enter Trinity College, Dublin, and therefore had to devote some time to classics. In mid-1822 he began a systematic study of Laplace's "Mécanique Céleste".  From that time Hamilton appears to have devoted himself almost wholly to mathematics, though he always kept himself well acquainted with the progress of science both in Britain and abroad. Hamilton found an important defect in one of Laplace's demonstrations, and he was induced by a friend to write out his remarks, so that they could be shown to Dr. John Brinkley, then the first Royal Astronomer of Ireland, and an accomplished mathematician. Brinkley seems to have immediately perceived Hamilton's talents, and to have encouraged him in the kindest way.  Hamilton's career at College was perhaps unexampled. Amongst a number of extraordinary competitors, he was first in every subject and at every examination. He achieved the rare distinction of obtaining an optime both for Greek and for physics. Hamilton might have attained many more such honours (he was expected to win both the gold medals at the degree examination), if his career as a student had not been cut short by an unprecedented event. This was Hamilton's appointment to the Andrews Professor of Astronomy in the University of Dublin, vacated by Dr. Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorised Hamilton's personal friend (also an elector) to urge Hamilton to become a candidate, a step which Hamilton's modesty had prevented him from taking. Thus, when barely 22, Hamilton was established at the Dunsink Observatory, near Dublin.  Hamilton was not especially suited for the post, because although he had a profound acquaintance with theoretical astronomy, he had paid little attention to the regular work of the practical astronomer. Hamilton's time was better employed in original investigations than it would have been spent in observations made even with the best of instruments. Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as he best could for the advancement of science, without being tied down to any particular branch. If Hamilton had devoted himself to practical astronomy, the University of Dublin would assuredly have furnished him with instruments and an adequate staff of assistants.  He was twice awarded the Cunningham Medal of the Royal Irish Academy. The first award, in 1834, was for his work on conical refraction, for which he also received the Royal Medal of the Royal Society the following year. He was to win it again in 1848.  In 1835, being secretary to the meeting of the British Association which was held that year in Dublin, he was knighted by the lord-lieutenant. Other honours rapidly succeeded, among which his election in 1837 to the president's chair in the Royal Irish Academy, and the rare distinction of being made a corresponding member of the Saint Petersburg Academy of Sciences. Later, in 1864, the newly established United States National Academy of Sciences elected its first Foreign Associates, and decided to put Hamilton's name on top of their list.

Quaternions.

The other great contribution Hamilton made to mathematical science was his discovery of quaternions in 1843. However, in 1840, Benjamin Olinde Rodrigues had already reached a result that amounted to their discovery in all but name.  Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional plane) to higher spatial dimensions. He failed to find a useful 3-dimensional system (in modern terminology, he failed to find a real, three-dimensional skew-field), but in working with four dimensions he created quaternions. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation  suddenly occurred to him; Hamilton then promptly carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge). This event marks the discovery of the quaternion group.  A plaque under the bridge was unveiled by the Taoiseach Éamon de Valera, himself a mathematician and student of quaternions, on 13 November 1958. Since 1989, the National University of Ireland, Maynooth has organised a pilgrimage called the "Hamilton Walk", in which mathematicians take a walk from Dunsink Observatory to the bridge, where no trace of the carving remains, though a stone plaque does commemorate the discovery.  The quaternion involved abandoning commutativity, a radical step for the time. Not only this, but Hamilton also invented the cross and dot products of vector algebra, the quaternion product being the cross product minus the dot product. Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the'scalar' part, and the remaining three as the'vector' part. Hamilton coined the words tensor and scalar, and was the first to use the word vector in the modern sense.  Hamilton introduced, as a method of analysis, both quaternions and biquaternions, the extension to eight dimensions by introduction of complex number coefficients. When his work was assembled in 1853, the book "Lectures on Quaternions" had "formed the subject of successive courses of lectures, delivered in 1848 and subsequent years, in the Halls of Trinity College, Dublin". Hamilton confidently declared that quaternions would be found to have a powerful influence as an instrument of research. When he died, Hamilton was working on a definitive statement of quaternion science. His son William Edwin Hamilton brought the "Elements of Quaternions", a hefty volume of 762 pages, to publication in 1866. As copies ran short, a second edition was prepared by Charles Jasper Joly, when the book was split into two volumes, the first appearing 1899 and the second in 1901. The subject index and footnotes in this second edition improved the "Elements" accessibility.  One of the features of Hamilton's quaternion system was the differential operator del which could be used to express the gradient of a vector field or to express the curl. These operations were applied by Clerk Maxwell to the electrical and magnetic studies of Michael Faraday in Maxwell's Treatise on Electricity and Magnetism (1873). Though the del operator continues to be used, the real quaternions fall short as a representation of spacetime. On the other hand, the biquaternion algebra, in the hands of Arthur W. Conway and Ludwik Silberstein, provided representational tools for Minkowski space and the Lorentz group early in the twentieth century.  Today, the quaternions are used in computer graphics, control theory, signal processing, and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. The rationale is that combining quaternion transformations is more numerically stable than combining many matrix transformations. In control and modelling applications, quaternions do not have a computational singularity (undefined division by zero) that can occur for quarter-turn rotations (90 degrees) that are achievable by many Air, Sea and Space vehicles. In pure mathematics, quaternions show up significantly as one of the four finite-dimensional normed division algebras over the real numbers, with applications throughout algebra and geometry.  It is believed by some modern mathematicians that Hamilton's work on quaternions was satirized by Charles Lutwidge Dodgson in Alice in Wonderland. In particular, the Mad Hatter's tea party was meant to represent the folly of quaternions and the need to revert to Euclidean geometry.

Other original work.

Hamilton originally matured his ideas before putting pen to paper. The discoveries, papers, and treatises previously mentioned might well have formed the whole work of a long and laborious life. But not to speak of his enormous collection of books, full to overflowing with new and original matter, which have been handed over to Trinity College, Dublin, the previous mentioned works barely form the greater portion of what Hamilton has published. Hamilton developed the variational principle, which was reformulated later by Carl Gustav Jacob Jacobi. He also introduced the icosian game or "Hamilton's puzzle" which can be solved using the concept of a Hamiltonian path.  Hamilton's extraordinary investigations connected with the solution of algebraic equations of the fifth degree, and his examination of the results arrived at by N. H. Abel, G. B. Jerrard, and others in their researches on this subject, form another contribution to science. There is next Hamilton's paper on fluctuating functions, a subject which, since the time of Joseph Fourier, has been of immense and ever increasing value in physical applications of mathematics. There is also the extremely ingenious invention of the hodograph. Of his extensive investigations into the solutions (especially by numerical approximation) of certain classes of physical differential equations, only a few items have been published, at intervals, in the "Philosophical Magazine".  Besides all this, Hamilton was a voluminous correspondent. Often a single letter of Hamilton's occupied from fifty to a hundred or more closely written pages, all devoted to the minute consideration of every feature of some particular problem; for it was one of the peculiar characteristics of Hamilton's mind never to be satisfied with a general understanding of a question; Hamilton pursued the problem until he knew it in all its details. Hamilton was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician, Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland. He worked in both pure mathematics and mathematics for physics. He made important contributions to optics, classical mechanics and algebra. Although Hamilton was not a physicist–he regarded himself as a pure mathematician–his work was of major importance to physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Sir William Rowan Hamilton (4. srpna 1805, Dublin – 2. září 1865, Dublin) byl irský matematik, fyzik a astronom. Je znám především tím, že jako první popsal kvaterniony, ale přispěl i k rozvoji optiky, dynamiky, a algebry.


General officer ranks.

The various grades of general officer are at the top of the military rank structure. Lower-ranking officers in land-centric military forces are typically known as field officers or field-grade officers, and below them are company-grade officers.

Common systems.

There are two common systems of general ranks used worldwide. In addition, there is a third system, the Arab system of ranks, which is used throughout the Middle East and North Africa but is not used elsewhere in the world.  Variations of one form, the old European system, were once used throughout Europe. It is used in the United Kingdom (although it did not originate there), from which it eventually spread to the Commonwealth and the United States of America. The general officer ranks are named by prefixing "general", as an adjective, with field officer ranks, although in some countries the highest general officers are titled field marshal, marshal, or captain general.  The other is derived from the French Revolution, where generals' ranks are named according to the unit they (theoretically) command.

Old European system.

The system used either a "brigadier general" or a "colonel general" rank (i.e. exclude one of the italicised ranks).  The rank of field marshal was used by some countries as the highest rank, while in other countries it was used as a divisional or brigade rank. Many countries (notably pre-revolutionary France and eventually much of Latin America) actually used two brigade command ranks, which is why some countries now use two stars as their brigade general insignia. Mexico and Argentina still use two brigade command ranks.  In some nations (particularly in the Commonwealth since the 1920s), the equivalent to brigadier general is brigadier, which is not always considered by these armies to be a general officer rank, although it is always treated as equivalent to the rank of brigadier general for comparative purposes.  As a lieutenant outranks a sergeant major; confusion often arises because a lieutenant is outranked by a major. Originally the serjeant major was, exclusively, the commander of the infantry, junior only to the captain general and lieutenant general. The distinction of serjeant major general only applied after serjeant majors were introduced as a rank of field officer. Serjeant was eventually dropped from both rank titles, creating the modern rank titles. Serjeant major (later spelled sergeant major) as a senior rank of non-commissioned officer was a later creation.

Arab system.

The armies of Arab countries use traditional Arabic titles. These were formalized in their current system to replace the Turkish system that was formerly in use in the Arab world and the Turco-Egyptian ranks in Egypt.

Other variations.

Other nomenclatures for general officers include the titles and ranks:  In addition to militarily educated generals, there are also generals in medicine and engineering. The rank of the most senior chaplain, (chaplain general), is also usually considered to be a general officer rank.

Specific rank of general.

In the old European system, a general, without prefix or suffix (and sometimes referred to informally as a "full general"), is usually the most senior type of general, above lieutenant general and directly below field marshal as a four-star rank (NATO OF-9).  Usually it is the most senior peacetime rank, with more senior ranks (for example, field marshal, marshal of the air force, fleet admiral) being used only in wartime or as honorary titles.  In some armies, however, the rank of captain general, general of the army, army general or colonel general occupied or occupies this position. Depending on circumstances and the army in question, these ranks may be considered to be equivalent to a "full" general or to a field marshal five-star rank (NATO OF-10).  The rank of general came about as a "captain-general", the captain of an army in general (i.e., the whole army). The rank of captain-general began appearing around the time of the organisation of professional armies in the 17th century. In most countries "captain-general" contracted to just "general".

General ranks by country.

The following articles deal with the rank of general, or its equivalent, as it is or was employed in the militaries of those countries:

Air force and naval equivalents.

Some countries (such as the United States) use the general officer ranks for both the army and the air force, as well as their marine corps; other nations only use the general officer ranks for the army, while in the air force they use air officers as the equivalent of general officers. They use the air force rank of air chief marshal as the equivalent of the specific army rank of general. This latter group includes the British Royal Air Force and many current and former Commonwealth air forces—e.g. Royal Australian Air Force, Indian Air Force, Royal New Zealand Air Force, Nigerian Air Force, Pakistan Air Force, etc.  In most navies, flag officers are the equivalent of general officers, and the naval rank of admiral is equivalent to the specific army rank of general. A noteworthy historical exception was the Cromwellian naval rank "general at sea". In recent years in the American service there is a tendency to use "flag officer" and "flag rank" to refer to generals and admirals of the services collectively.

A general officer is an officer of high rank in the army, and in some nations' air forces, space forces, or marines.

Generál je vojenská hodnost, která je v mnoha státech v hierarchii armády hodností nejvyšší. U některých dalších národů existuje (existovala) ještě vyšší hodnost maršál, někdy je však spíše čestná, bez nějakých dalších pravomocí. Hodnost generál je používána pozemními a některými vzdušnými ozbrojenými silami, v některých státech se objevuje i u policejních a dalších státních hierarchizovaných složek. V námořních ozbrojených silách je obvykle jejím ekvivalentem hodnost admirála. Ve většině armád slovo generál neoznačuje jednu konkrétní hodnost, ale soubor tzv. generálských hodností. Výjimečně však může označovat něco jiného, např. funkci vrchního velitele. Generál také může znamenat pouze obecně významného vojenského velitele, zejména pokud působil samostatně a jde o starověkou nebo středověkou osobnost.


Etymology.

The word "poison" was first used in 1200 to mean "a deadly potion or substance"; the English term comes from the "...Old French poison, puison (12c., Modern French poison) "a drink", especially a medical drink, later "a (magic) potion, poisonous drink" (14c.), from Latin potionem (nominative potio) "a drinking, a drink", also "poisonous drink" (Cicero), from potare "to drink". The use of "poison" as an adjective ("poisonous") dates from the 1520s. Using the word "poison" with plant names dates from the 18th century. The term "poison ivy", for example, was first used in 1784 and the term "poison oak" was first used in 1743. The term "poison gas" was first used in 1915.

Terminology.

The term "poison" is often used colloquially to describe any harmful substance—particularly corrosive substances, carcinogens, mutagens, teratogens and harmful pollutants, and to exaggerate the dangers of chemicals. Paracelsus (1493–1541), the father of toxicology, once wrote: "Everything is poison, there is poison in everything. Only the dose makes a thing not a poison" (see median lethal dose). The term "poison" is also used in a figurative sense: "His brother's presence poisoned the atmosphere at the party". The law defines "poison" more strictly. Substances not legally required to carry the label "poison" can also cause a medical condition of poisoning.  Some poisons are also toxins, which is any poison produced by animals, vegetables or bacteria, such as the bacterial proteins that cause tetanus and botulism. A distinction between the two terms is not always observed, even among scientists. The derivative forms "toxic" and "poisonous" are synonymous. Animal poisons delivered subcutaneously (e.g., by sting or bite) are also called "venom". In normal usage, a poisonous organism is one that is harmful to consume, but a venomous organism uses venom to kill its prey or defend itself while still alive. A single organism can be both poisonous and venomous, but that is rare.  All living things produce substances to protect them from getting eaten, so the term "poison" is usually only used for substances which are poisonous to humans, while substances that mainly are poisonous to a common pathogen to the organism and humans are considered antibiotics. Bacteria are for example a common adversary for "Penicillium chrysogenum" mold and humans, and since the mold's poison only targets bacteria humans may use it for getting rid of bacteria in their bodies. Human antimicrobial peptides which are toxic to viruses, fungi, bacteria and cancerous cells are considered a part of the immune system.  In nuclear physics, a poison is a substance that obstructs or inhibits a nuclear reaction. For an example, see nuclear poison.  Environmentally hazardous substances are not necessarily poisons, and vice versa. For example, food-industry wastewater—which may contain potato juice or milk—can be hazardous to the ecosystems of streams and rivers by consuming oxygen and causing eutrophication, but is nonhazardous to humans and not classified as a poison.  Biologically speaking, any substance, if given in large enough amounts, is poisonous and can cause death. For instance, several kilograms worth of water would constitute a lethal dose. Many substances used as medications—such as fentanyl—have an only one order of magnitude greater than the ED50. An alternative classification distinguishes between lethal substances that provide a therapeutic value and those that do not.

Poisoning.

Poisoning can be either acute or chronic, and caused by a variety of natural or synthetic substances. Substances that destroy tissue but do not absorb, such as lye, are classified as corrosives rather than poisons.

Acute.

Acute poisoning is exposure to a poison on one occasion or during a short period of time. Symptoms develop in close relation to the exposure. Absorption of a poison is necessary for systemic poisoning. Furthermore, many common household medications are not labeled with skull and crossbones, although they can cause severe illness or even death. Poisoning can be caused by excessive consumption of generally safe substances, as in the case of water intoxication.  Agents that act on the nervous system can paralyze in seconds or less, and include both biologically derived neurotoxins and so-called nerve gases, which may be synthesized for warfare or industry.  Inhaled or ingested cyanide, used as a method of execution in gas chambers, almost instantly starves the body of energy by inhibiting the enzymes in mitochondria that make ATP. Intravenous injection of an unnaturally high concentration of potassium chloride, such as in the execution of prisoners in parts of the United States, quickly stops the heart by eliminating the cell potential necessary for muscle contraction.  Most biocides, including pesticides, are created to act as acute poisons to target organisms, although acute or less observable chronic poisoning can also occur in non-target organisms (secondary poisoning), including the humans who apply the biocides and other beneficial organisms. For example, the herbicide 2,4-D imitates the action of a plant hormone, which makes its lethal toxicity specific to plants. Indeed, 2,4-D is not a poison, but classified as "harmful" (EU).  Many substances regarded as poisons are toxic only indirectly, by toxication. An example is "wood alcohol" or methanol, which is not poisonous itself, but is chemically converted to toxic formaldehyde and formic acid in the liver. Many drug molecules are made toxic in the liver, and the genetic variability of certain liver enzymes makes the toxicity of many compounds differ between individuals.  Exposure to radioactive substances can produce radiation poisoning, an unrelated phenomenon.  Two common cases of acute natural poisoning are theobromine poisoning of dogs and cats, and mushroom poisoning in humans. Dogs and cats are not natural herbivores, but a chemical defense developed by "Theobroma cacao" can be incidentally fatal nevertheless. Many omnivores, including humans, readily consume edible fungi, and thus many fungi have evolved to become decisively inedible, in this case as a direct defense.

Chronic.

Chronic poisoning is long-term repeated or continuous exposure to a poison where symptoms do not occur immediately or after each exposure. The patient gradually becomes ill, or becomes ill after a long latent period. Chronic poisoning most commonly occurs following exposure to poisons that bioaccumulate, or are biomagnified, such as mercury, gadolinium, and lead.

Epidemiology.

In 2010, poisoning resulted in about 180,000 deaths down from 200,000 in 1990. There were approximately 727,500 emergency department visits in the United States involving poisonings—3.3% of all injury-related encounters.

Applications.

Poisonous compounds may be useful either for their toxicity, or, more often, because of another chemical property, such as specific chemical reactivity. Poisons are widely used in industry and agriculture, as chemical reagents, solvents or complexing reagents, e.g. carbon monoxide, methanol and sodium cyanide, respectively. They are less common in household use, with occasional exceptions such as ammonia and methanol. For instance, phosgene is a highly reactive nucleophile acceptor, which makes it an excellent reagent for polymerizing diols and diamines to produce polycarbonate and polyurethane plastics. For this use, millions of tons are produced annually. However, the same reactivity makes it also highly reactive towards proteins in human tissue and thus highly toxic. In fact, phosgene has been used as a chemical weapon. It can be contrasted with mustard gas, which has only been produced for chemical weapons uses, as it has no particular industrial use.  Biocides need not be poisonous to humans, because they can target metabolic pathways absent in humans, leaving only incidental toxicity. For instance, the herbicide 2,4-dichlorophenoxyacetic acid is a mimic of a plant growth hormone, which causes uncontrollable growth leading to the death of the plant. Humans and animals, lacking this hormone and its receptor, are unaffected by this, and need to ingest relatively large doses before any toxicity appears. Human toxicity is, however, hard to avoid with pesticides targeting mammals, such as rodenticides.  The risk from toxicity is also distinct from toxicity itself. For instance, the preservative thiomersal used in vaccines is toxic, but the quantity administered in a single shot is negligible.

History.

Throughout human history, intentional application of poison has been used as a method of murder, pest-control, suicide, and execution. As a method of execution, poison has been ingested, as the ancient Athenians did (see Socrates), inhaled, as with carbon monoxide or hydrogen cyanide (see gas chamber), or injected (see lethal injection). Poison's lethal effect can be combined with its allegedly magical powers; an example is the Chinese "gu" poison. Poison was also employed in gunpowder warfare. For example, the 14th-century Chinese text of the "Huolongjing" written by Jiao Yu outlined the use of a poisonous gunpowder mixture to fill cast iron grenade bombs.  While arsenic is a naturally occurring environmental poison, its artificial concentrate was once nicknamed inheritance powder. In Medieval Europe, it was common for monarchs to employ personal food tasters to thwart royal assassination, in the dawning age of the Apothecary.

Figurative use.

The term "poison" is also used in a figurative sense. The "[s]lang sense of "alcoholic drink" [is] first attested 1805, American English." (e.g., a bartender might ask a customer "what's your poison?") Figurative use of the term dates from the late 15th century. Figuratively referring to persons as poison dates from 1910. The figurative term "poison-pen letter" became well known in "...1913 by a notorious criminal case in Pennsylvania, U.S.; the phrase dates to 1898."

In biology, poisons are substances that cause death, injury or harm to organs, usually by chemical reactions or other activity on the molecular scales, when an organism absorbs a sufficient quantity.

V biologii se jako jed označuje látka, která může způsobit poruchy funkce organismů, obvykle chemickou reakcí nebo jinou aktivitou na molekulární úrovni, dostane-li se tato látka do organismu v dostatečném množství.


Design.

The BT tanks were "convertible tanks". This was a feature designed by J. Walter Christie to reduce wear of the unreliable tank tracks of the 1930s. In about thirty minutes, the crew could remove the tracks and engage a chain drive to the rearmost road wheel on each side, allowing the tank to travel at very high speeds on roads. In wheeled mode, the tank was steered by pivoting the front road wheels. Soviet tank forces soon found the convertible option of little practical use; in a country with few paved roads, it consumed space and added needless complexity and weight. The feature was dropped from later Soviet designs.  Christie, a race car mechanic and driver from New Jersey, had failed to convince the U.S. Army Ordnance Bureau to adopt his Christie tank design. In 1930, Soviet agents at Amtorg, ostensibly a Soviet trade organization, used their New York political contacts to persuade U.S. military and civilian officials to provide plans and specifications of the Christie tank to the Soviet Union. At least two of Christie's M1931 tanks (without turrets) were later purchased in the United States and sent to the Soviet Union under false documentation, in which they were described as "agricultural tractors". Both tanks were delivered to the Kharkov Komintern Locomotive Plant (KhPZ). The original Christie tanks were designated "fast tanks" by the Soviets, abbreviated to BT (later referred to as BT-1). Based both on them and on other plans obtained earlier, three unarmed BT-2 prototypes were completed in October 1931 and mass production began in 1932. Most BT-2s were equipped with a 37 mm gun and a machine gun, but a shortage of 37 mm guns led to some early examples being fitted with three machine guns. The sloping front hull (glacis plate) armor design of the Christie M1931 prototype was retained in later Soviet tank hull designs, later adopted for side armor as well. The BT-5 and later models were equipped with 45 mm guns.

Variants.

Soviet Union variants:  Foreign variants:

Combat history.

BT tanks saw service in the Second Sino-Japanese War, Spanish Civil War, Battles of Khalkhin Gol (also known as the Nomohan Incident), the Winter War in Finland, and in World War II.

Spanish Civil War.

In the Spanish Civil War (1936–1939), a regiment of 50 BT-5s fought on the Republican side. They were manned by the members International Brigades trained in USSR and by some Soviet tankists. Their first combat on 13 October 1937 during the Zaragoza Offensive was disastrous: 13 tanks were lost due to bad tactics. Later, 12 more were lost from December 1937 to February 1938 during the Battle of Teruel. A few captured BT-5s were also used by the Nationalist side.

Chinese service.

The Chinese Nationalist Army had four BT-5s which fought against the Imperial Japanese Army during the Second Sino-Japanese War (1937–1945).

Battles of Khalkin Gol.

During the Battles of Khalkhin Gol (also known as the Nomonhan Incident), which lasted from May to September in 1939, BT tanks were easily attacked by Japanese "close quarter" teams (tank killer squads) which were – in lieu of anti-tank weapons – armed with petrol (gasoline) bottles (later called "Molotov cocktails"). The BT-5s and BT-7s, operating in temperatures greater than on the Mongolian plains, easily caught fire when a Molotov cocktail ignited their gasoline engines. General Georgy Zhukov made it one of his "points" when briefing Joseph Stalin, that his "...BT tanks were a bit fireprone..." Conversely, many Japanese tank crews held the Soviet 45mm gun of the BT-5 and BT-7 in high esteem, noting, "...no sooner did they see the flash from a Russian gun, than they'd notice a hole in their tank, adding that the Soviet gunners were accurate too!"  After the Battles of Khalkhin Gol, the Soviet military broke into two camps; one side was represented by Spanish Civil War veterans General Pavel Rychagov of the Soviet Air Force, Soviet armour expert General Dimitry Pavlov, and Stalin's favorite, Marshal Grigory Kulik, Chief of Artillery Administration. The other side consisted of the Khalkhin Gol veterans led by Generals Zhukov and Grigory Kravchenko of the Soviet Air Force. The lessons of Russia's "first real war on a massive scale using tanks, artillery, and airplanes" at Khalkhin Gol went unheeded.

Winter War.

During the Winter War against Finland in 1939–1940, BT-2 and BT-5 tanks had less success against Finnish Army forces than they had against the Japanese at Khalkin Gol.

World War II.

During the Second World War in Europe, BT-5 and BT-7 tanks were used in the 1939 Soviet invasion of Poland. The Red Army planned to replace the BT tank series with the T-34 and had just begun doing so when Operation Barbarossa, the German invasion of the Soviet Union, began on 22 June 1941. BT-series tanks took part in large numbers in the battles that followed during 1941, during which thousands were abandoned or destroyed. A few remained in use in 1942, but rarely saw combat against German forces after that time.  During the final weeks of World War II, a significant number of BT-7 tanks took part in the Soviet invasion of Manchuria in August 1945, seeing combat against Japanese occupation forces in Northeast China. This was the last combat action for the BT tanks.

Technical legacy.

The BT tank series was numerous, forming the cavalry tank arm of the Red Army in the 1930s and had much better mobility than other contemporary tank designs. For these reasons, there were many experiments and derivatives of the design, mostly conducted at the KhPZ factory in Kharkov.  The most important legacy of the BT tank was the T-34 medium tank. In 1937, a new design team was formed at the KhPZ to create the next generation of BT tanks. Initially, the chief designer was Mikhail Koshkin and after his death, Morozov. The team built two prototypes. The light one was called the "A-20". The more heavily armed and armoured BT derivative, the "A-32", was a "universal tank" to replace all the T-26 infantry tanks, BT cavalry tanks and T-28 medium tanks. Such a plan was controversial, but concerns about tank performance under the threat of the German blitzkrieg led to the approval for production of a still more heavily armoured version, the T-34 medium tank.  Along the way, an important technical development was the "BT-IS" and "BT-SW-2" testbed vehicles, concentrating on sloped armour. This proof-of-concept led directly to the armour layout of the T-34. BT tank chassis were also used as the basis for engineering support vehicles and mobility testing vehicles. A bridgelayer variant had a T-38 turret and launched a bridge across small gaps. Standard tanks were fitted as fascine carriers. The RBT-5 hosted a pair of large artillery rocket launchers, one on each side of the turret. Several designs for extremely wide tracks, including, oddly, wooden'snowshoes' were tried on BT tanks.  The "KBT-7" was a thoroughly modern armoured command vehicle that was in the prototype stage when World War II broke out. The design was not pursued during the war.  In the Kiev manoeuvres of 1936, foreign military observers were shown hundreds of BT tanks roll by a reviewing stand. In the audience were British Army representatives, who returned home to advocate for use of Christie suspension on British cruiser tanks, which they incorporated from the Cruiser Mk III onwards. The pointed shape of the hull front armor on the BT tank also influenced the design of the British Matilda tank.

The BT tanks (, lit. "fast moving tank" or "high-speed tank") were a series of Soviet light tanks produced in large numbers between 1932 and 1941. They were lightly armoured, but reasonably well-armed for their time, and had the best mobility of all contemporary tanks. The BT tanks were known by the nickname "Betka" from the acronym, or its diminutive "Betushka". The successor of the BT tanks was the famous T-34 medium tank, introduced in 1940, which would replace all of the Soviet fast tanks, infantry tanks, and medium tanks in service.

Zkratkou BT (z ruského "Быстроходный танк" – rychle jedoucí tank) se označuje řada lehkých rychlých tanků Rudé armády používaných ve 30. a 40. letech 20. století.


Formation.

Living organisms are composed of organic compounds. In life they secrete or excrete organic materials into their environment, shed body parts such as leaves and roots and after organisms die, their bodies are broken down by bacterial and fungal action. Larger molecules of organic matter can be formed from the polymerization of different parts of already broken down matter. The composition of natural organic matter depends on its origin, transformation mode, age, and existing environment, thus its bio-physico-chemical functions vary with different environments.

Natural ecosystem functions.

Organic matter is common throughout the ecosystem and is cycled through decomposition processes by soil microbial communities that are crucial for nutrient availability. After degrading and reacting, it can move into soil and mainstream water via waterflow. Organic matter provides nutrition to living organisms. Organic matter acts as a buffer in aqueous solution to maintain a neutral pH in the environment. The buffer acting component has been proposed to be relevant for neutralizing acid rain.

Source cycle.

A majority of organic matter not already in the soil comes from groundwater. When the groundwater saturates the soil or sediment around it, organic matter can freely move between the phases. Groundwater has its own sources of natural organic matter also:  One source of groundwater organic matter is soil organic matter and sedimentary organic matter. The major method of movement into soil is from groundwater, but organic matter from soil moves into groundwater as well. Most of the matter in lakes, rivers, and surface water areas comes from deteriorated material in the water and surrounding shores, and some from groundwater.  This movement enables a cycle to form. Organisms decompose into organic matter, which is then transported and recycled. Not all biomass migrates, some is rather stationary, turning only over the course of millions of years.

Soil organic matter.

The organic matter in soil derives from plants, animals and microorganisms. In a forest, for example, leaf litter and woody material falls to the forest floor. This is sometimes referred to as organic material. When it decays to the point in which it is no longer recognizable, it is called soil organic matter. When the organic matter has broken down into a stable substance that resist further decomposition it is called humus. Thus soil organic matter comprises all of the organic matter in the soil exclusive of the material that has not decayed.  An important property of soil organic matter is that it improves the capacity of a soil to hold water and nutrients, and allows their slow release, thereby improving the conditions for plant growth. Another advantage of humus is that it helps the soil to stick together which allows nematodes, or microscopic bacteria, to easily decay the nutrients in the soil.  There are several ways to quickly increase the amount of humus. Combining compost, plant or animal materials/waste, or green manure with soil will increase the amount of humus in the soil.  These three materials supply nematodes and bacteria with nutrients for them to thrive and produce more humus, which will give plants enough nutrients to survive and grow.

Priming effect.

The "priming effect" is characterized by intense changes in the natural process of soil organic matter (SOM) turnover, resulting from relatively moderate intervention with the soil. The phenomenon is generally caused by either pulsed or continuous changes to inputs of fresh organic matter (FOM). Priming effects usually result in an acceleration of mineralization due to a "trigger" such as the FOM inputs. The cause of this increase in decomposition has often been attributed to an increase in microbial activity resulting from higher energy and nutrient availability released from the FOM. After the input of FOM, specialized microorganisms are believed to grow quickly and only decompose this newly added organic matter. The turnover rate of SOM in these areas is at least one order of magnitude higher than the bulk soil.  Other soil treatments, besides organic matter inputs, which lead to this short-term change in turnover rates, include "input of mineral fertilizer, exudation of organic substances by roots, mere mechanical treatment of soil or its drying and rewetting."  Priming effects can be either "positive" or "negative" depending on the reaction of the soil with the added substance. A positive priming effect results in the acceleration of mineralization while a negative priming effect results in immobilization, leading to N unavailability. Although most changes have been documented in C and N pools, the priming effect can also be found in phosphorus and sulfur, as well as other nutrients.  Löhnis was the first to discover the priming effect phenomenon in 1926 through his studies of green manure decomposition and its effects on legume plants in soil. He noticed that when adding fresh organic residues to the soil, it resulted in intensified mineralization by the humus N. It was not until 1953, though, that the term "priming effect" was given by Bingeman in his paper titled, "The effect of the addition of organic materials on the decomposition of an organic soil". Several other terms had been used before "priming effect" was coined, including priming action, added nitrogen interaction (ANI), extra N and additional N. Despite these early contributions, the concept of the priming effect was widely disregarded until about the 1980s-1990s.  The priming effect has been found in many different studies and is regarded as a common occurrence, appearing in most plant soil systems. However, the mechanisms which lead to the priming effect are more complex then originally thought, and still remain generally misunderstood.  Although there is a lot of uncertainty surrounding the reason for the priming effect, a few "undisputed facts" have emerged from the collection of recent research:  Recent findings suggest that the same priming effect mechanisms acting in soil systems may also be present in aquatic environments, which suggests a need for broader considerations of this phenomenon in the future.

Decomposition.

One suitable definition of organic matter is biological material in the process of decaying or decomposing, such as humus. A closer look at the biological material in the process of decaying reveals so-called organic compounds (biological molecules) in the process of breaking up (disintegrating).  The main processes by which soil molecules disintegrates are by bacterial or fungal enzymatic catalysis. If bacteria or fungi were not present on Earth, the process of decomposition would have proceeded much slower.

Organic chemistry.

Measurements of organic matter generally measure only organic compounds or carbon, and so are only an approximation of the level of once-living or decomposed matter. Some definitions of organic matter likewise only consider "organic matter" to refer to only the carbon content, or organic compounds, and do not consider the origins or decomposition of the matter. In this sense, not all organic compounds are created by living organisms, and living organisms do not only leave behind organic material. A clam's shell, for example, while biotic, does not contain much organic carbon, so may not be considered organic matter in this sense. Conversely, urea is one of many organic compounds that can be synthesized without any biological activity.  Organic matter is heterogeneous and very complex. Generally, organic matter, in terms of weight, is:  The molecular weights of these compounds can vary drastically, depending on if they repolymerize or not, from 200 to 20,000 amu. Up to one third of the carbon present is in aromatic compounds in which the carbon atoms form usually six-membered rings. These rings are very stable due to resonance stabilization, so they are difficult to break down. The aromatic rings are also susceptible to electrophilic and nucleophilic attack from other electron-donating or electron-accepting material, which explains the possible polymerization to create larger molecules of organic matter.  There are also reactions that occur with organic matter and other material in the soil to create compounds never seen before. Unfortunately, it is very difficult to characterize these because so little is known about natural organic matter in the first place. Research is currently being done to figure out more about these new compounds and how many of them are being formed.

Aquatic.

Aquatic organic matter can be further divided into two components: (1) dissolved organic matter (DOM), measured as colored dissolved organic matter (CDOM) or dissolved organic carbon (DOC), and (2) particulate organic matter (POM). They are typically differentiated by that which can pass through a 0.45 micrometre filter (DOM), and that which cannot (POM).

Detection.

Organic matter plays an important role in drinking water and wastewater treatment and recycling, natural aquatic ecosystems, aquaculture, and environmental rehabilitation. It is therefore important to have reliable methods of detection and characterisation, for both short- and long-term monitoring. A variety of analytical detection methods for organic matter have existed for up to decades, to describe and characterise organic matter. These include, but are not limited to: total and dissolved organic carbon, mass spectrometry, nuclear magnetic resonance (NMR) spectroscopy, infrared (IR) spectroscopy, UV-Visible spectroscopy, and fluorescence spectroscopy. Each of these methods has its own advantages and limitations.

Water purification.

The same capability of natural organic matter that helps with water retention in soil creates problems for current water purification methods. In water, organic matter can still bind to metal ions and minerals. These bound molecules are not necessarily stopped by the purification process, but do not cause harm to any humans, animals, or plants. However, because of the high level of reactivity of organic matter, by-products that do not contain nutrients can be made. These by-products can induce biofouling, which essentially clogs water filtration systems in water purification facilities, as the by-products are larger than membrane pore sizes. This clogging problem can be treated by chlorine disinfection (chlorination), which can break down residual material that clogs systems. However, chlorination can form disinfection by-products.  Water with organic matter can be disinfected with ozone-initiated radical reactions. The ozone (three oxygens) has very strong oxidation characteristics. It can form hydroxyl radicals (OH) when it decomposes, which will react with the organic matter to shut down the problem of biofouling.

Vitalism.

The equation of "organic" with living organisms comes from the now-abandoned idea of vitalism that attributed a special force to life that alone could create organic substances. This idea was first questioned after the artificial synthesis of urea by Friedrich Wöhler in 1828.

See also.

Compare with:

Organic matter, organic material, or natural organic matter refers to the large source of carbon-based compounds found within natural and engineered, terrestrial and aquatic environments. It is matter composed of organic compounds that have come from the remains of organisms such as plants and animals and their waste products in the environment. Organic molecules can also be made by chemical reactions that don't involve life. Basic structures are created from cellulose, tannin, cutin, and lignin, along with other various proteins, lipids, and carbohydrates. Organic matter is very important in the movement of nutrients in the environment and plays a role in water retention on the surface of the planet.

Organická látka (česky méně často ústrojná látka) je obecný název pro materiál, tvořený převážně organickými sloučeninami, který však obvykle obsahuje i příměsi anorganických sloučenin. Obvykle se jedná o velice různorodou směs, kde sice některé látky převažují, ale která může mít prakticky libovolné složení. Z hlediska své struktury může být heterogenní nebo homogenní.


Nature.

Mountains.

The landscape relief of the Jeseník region is characteristic with the impressive mountain ridges of Hrubý Jeseník, towering as high as above the line of forests, with that flat ridges of Zlatohorská vrchovina (Highland) in the southeast, with the border range of Golden Mountains and its foothills Žulovská pahorkatina (Hilly Country) protruding from the lowlands at the Czech-Poland frontier in the northeast. All these mountain ridges are considered a part of the extensive unit of the Eastern Sudeten, now commonly called Jeseníky Mountains.  The uncovered top of Keprník (Mt., 1426 m) with its top rocks upon the Hrubý Jeseník, reaches the highest point in the region and on the contrary, the river Vidnavka leaves the country in the lowest point (230 m) at Vidnava. Most of the area is covered by forest. In higher locations there are mountain green-fields and varied flora. Originally broadleaved and fir forests have been recently substituted by the spruce monoculture. Bare spots above the line of forests (about 1330 m) are overgrown with grass and locally with man-planted dwarf pines. There are only few places where remnants of the original growth have been conserved. The deep forests of Golden Mountains and Žulovská pahorkatina passes into green-fields, pastures with scattered villages and lonely houses.

Rivers.

Most of the rivers and streams belong to the area which feeds the Baltic sea with water: the biggest Bělá river with its tributary Staříč, the gold-bearing Černá Opava fed by Rejvíz highmoor bog water and river Vidnávka and its tributaries flowing down Golden Mountains. Mountain torrents from many waterfalls and cascades, in shallow depressions with impermeable underlying bed highmoor bogs originated. The springs on the hill-sides around the town of Jeseník, with favourable climate, are the critical agents for the rise of the spa resort.  The educational path Rejvíz with the Great Moss Pond and the Nýznerov Waterfalls at the Stříbrný Creek, Vidnavka grass-fields, Ztracené Údolí (Lost Valley) at Vápenná and many other places of interest are worth seeing. There are karst formations in the limestone areas. The caves "Na Pomezí", rich in dropstone decoration and historically valuable caves "Na Špičáku" are also opened for tourists.

Fauna.

Many kinds of wild animals live in the forests here: deer, roebuck, wild boar, hare; in the Šerák and Keprník area chamois, imported here from Austria Alpen in the beginning of the century. In the Jeseníky the grouse, hazel hen, black grouse, from birds of prey hawk, buzzard and rare falcon still nest in the region.

Nature protection.

In 1969 the Protected Landscape Area (CHKO) Jeseník was founded, comprising the mountain ridge of Hrubý Jeseník and a part of the Zlatohorská vrchovina (Highlands). Specifically valuable areas are protected in national reserves: Šerák-Keprník with conserved virgin forest and distinguished flora and Rejvíz with the highmoor bog and rich fauna and flora. Similar importance has the National Reserve Rašeliniště Skřitek ("the peat bog") and the largest and most valuable nature reservation Praděd with famous Velký and Malý Kotel (Big and Little Kettle) called the "Botanic Garden of the Middle Europe". The National Nature Monument Špičák is known with its karst formation and ingenuous growths of yew.

Clima.

Geomorphological diversity is incidental to climatic diversity as well. The rough climate of Hrubý Jeseník penetrates the moderate climate of Silesian Lowlands and causes frequent turns at weather. This specifically moderate climate with low precipitations is in Vidnavka area situated in the precipitation shadow of the Jeseník (Mts.).

History.

This mountain region has been already settled in the 12th century by Slavonic populations, which is documented by preserved place-names and fieldnames. The process of colonization was accomplished in the next century by the arrival of the German population. The Jeseník region was a part of the Nysa-Otmuchow principality and by Church in hands of the Wrocław bishops. German colonization was the work of Wrocław bishops Thomas I. and above all Thomas II. Since the 13th century the Czech, German and Polish influences have been mixed here, in addition to other nationalities such as Slovaks, Greeks, Romanians and Ukrainians.  Prospectors of noble metals and miners formed the important part of new settlers. The gold mining in the eras of the top and late Middle Ages was connected with personalities as were for example German businessmen kin of Fuggers from Augsburg. In the next centuries periods of economic prosperity and stability alternated with periods of the spirit and material breakdown. Especially the years of religious wars belonged to the darkest periods of the history. They brought the population much suffering and affliction.  An economic decline arrived with The Hussite Wars, when troops of warriors of God passed the country in their crusade against Wrocław. In 1424 the castles and bishop's towns of the region were captured. Much more disasters were brought by passes of armies during the Thirty Years Wars, which involved especially to country population the period of horrific, slaughter, and firing of farm-houses. Certainly it is not a hazard that just in that time of deep economic and moral declination the Jeseník region was affected by the wave of spiritual cancer in inquisition trials with alleged wise women. The trials framed in Jeseník and Nysa regions in the years 1622–1684, cost hundreds of human victims. Wars of Austria Heritage also unfavourably affected the region in the fortieth years of the 18th century.  The Wrocław Piece in 1742 split Silesia into two parts: Prussian and Austrian shares. The Jeseník region has devoted to Austrian Silesia since that year. After the separation of original economic centre in Nysa, it created a new administrative area called the Czech part of the Nysa principality. This status existed to the year 1848, when it died out with the feudal system.  Among glorious periods of the country below the Praděd there are for example beginnings of industrial enterprising in the last centuries (ferrous metallurgy, textile industry, stone industry). Origin and development of a spa resort forms the particularly important chapter in the regional history.

Economy.

The nature conditions, mineral resources and separation from centres inside the country determine the way of life of its inhabitants. The whole region is of agricultural and industrial character. Beside the quarrying and treatment of granite, limestone and marble, also the woodwork, textile and other branches of industries have arisen here. The mining of base metals and gold, having been kept at Zlaté Hory is declining now. Agriculture is prosperous particularly in undulated and fertile plain between Vidnava, Bernartice and Javorník called "Silesian Hanakia" due to its fairly sunny climate.

Complete list of municipalities.

Bělá pod Pradědem – Bernartice – Bílá Voda – Černá Voda – Česká Ves – Hradec-Nová Ves – Javorník – Jeseník – Kobylá nad Vidnavkou – Lipová-lázně – Mikulovice – Ostružná – Písečná – Skorošice – Stará Červená Voda – Supíkovice – Uhelná – Vápenná – Velká Kraš – Velké Kunětice – Vidnava – Vlčice – Zlaté Hory – Žulová

Jeseník District () is a district ("okres") in the Olomouc Region of the Czech Republic. Its seat is the town of Jeseník. With approximately 38,000 inhabitants it is the least populated district of the Czech Republic.

Okres Jeseník spadá do samosprávného Olomouckého kraje a do územního Severomoravského kraje, který však nemá správní orgány ani samosprávu. Zřízen byl oproti ostatním okresům z roku 1960 dodatečně, a to od 1. ledna 1996 vyčleněním z okresu Šumperk (pouze město Zlaté Hory přešlo z okresu Bruntál). Sídlem okresního úřadu okresu Jeseník bylo město Jeseník, které je od roku 2003 obcí s rozšířenou působností a jehož správní obvod je totožný s okresem.


Terminology.

Toxins are often distinguished from other chemical agents by their method of production—the word toxin does not specify method of delivery (compare with venom and the broader meaning of poison—all substances that can also cause disturbances to organisms). It simply means it is a biologically produced poison.  According to an International Committee of the Red Cross review of the Biological Weapons Convention, "Toxins are poisonous products of organisms; unlike biological agents, they are inanimate and not capable of reproducing themselves", and "Since the signing of the Constitution, there have been no disputes among the parties regarding the definition of biological agents or toxins".  According to Title 18 of the United States Code, "... the term "toxin" means the toxic material or product of plants, animals, microorganisms (including, but not limited to, bacteria, viruses, fungi, rickettsiae or protozoa), or infectious substances, or a recombinant or synthesized molecule, whatever their origin and method of production..."  A rather informal terminology of individual toxins relates them to the anatomical location where their effects are most notable:  On a broader scale, toxins may be classified as either exotoxins, being excreted by an organism, or endotoxins, that are released mainly when bacteria are lysed.

Biotoxins.

The term "biotoxin" is sometimes used to explicitly confirm the biological origin. Biotoxins can be further classified, for example, as fungal biotoxins, microbial toxins, plant biotoxins, or animal biotoxins.  Toxins produced by microorganisms are important virulence determinants responsible for microbial pathogenicity and/or evasion of the host immune response.  Biotoxins vary greatly in purpose and mechanism, and can be highly complex (the venom of the cone snail contains dozens of small proteins, each targeting a specific nerve channel or receptor), or relatively small protein.  Biotoxins in nature have two primary functions:  Some of the more well known types of biotoxins include:

Environmental toxins.

The term "environmental toxin" can sometimes explicitly include synthetic contaminants such as industrial pollutants and other artificially made toxic substances. As this contradicts most formal definitions of the term "toxin", it is important to confirm what the researcher means when encountering the term outside of microbiological contexts.  Environmental toxins from food chains that may be dangerous to human health include:

Finding information about toxins.

In general, when scientists determine the amount of a substance that may be hazardous for humans, animals and/or the environment they determine the amount of the substance likely to trigger effects and if possible establish a safe level. In Europe, the European Food Safety Authority produced risk assessments for more than 4,000 substances in over 1,600 scientific opinions and they provide open access summaries of human health, animal health and ecological hazard assessments in their: OpenFoodTox database. The OpenFoodTox database can be used to screen potential new foods for toxicity.  The Toxicology and Environmental Health Information Program (TEHIP) at the United States National Library of Medicine (NLM) maintains a comprehensive toxicology and environmental health web site that includes access to toxins-related resources produced by TEHIP and by other government agencies and organizations. This web site includes links to databases, bibliographies, tutorials, and other scientific and consumer-oriented resources. TEHIP also is responsible for the Toxicology Data Network (TOXNET), an integrated system of toxicology and environmental health databases that are available free of charge on the web.  TOXMAP is a Geographic Information System (GIS) that is part of TOXNET. TOXMAP uses maps of the United States to help users visually explore data from the United States Environmental Protection Agency's (EPA) Toxics Release Inventory and Superfund Basic Research Programs.

Computational resources for prediction of toxic peptides and proteins.

One of the bottlenecks in peptide/protein-based therapy is their toxicity. Recently, "in silico" models for predicting toxicity of peptides and proteins, developed by Gajendra Pal Singh Raghava's group, predict toxicity with reasonably good accuracy. The prediction models are based on machine learning technique and quantitative matrix using various properties of peptides. The prediction tool is freely accessible to public in the form of web server.

Misuse of the term.

When used non-technically, the term "toxin" is often applied to any toxic substance, even though the term toxicant would be more appropriate. Toxic substances not directly of biological origin are also termed poisons and many non-technical and lifestyle journalists follow this usage to refer to toxic substances in general.  In the context of quackery and alternative medicine, the term "toxin" is used to refer to any substance alleged to cause ill health. This could range from trace amounts of potentially dangerous pesticides, to supposedly harmful substances produced in the body by intestinal fermentation (auto-intoxication), to food ingredients such as table sugar, monosodium glutamate (MSG), and aspartame.

A toxin is a poisonous substance produced within living cells or organisms; synthetic toxicants created by artificial processes are thus excluded. The term was first used by organic chemist Ludwig Brieger (1849–1919), derived from the word toxic.

Toxin (z řeckého "toxikon") je jedovatá látka produkovaná živými buňkami nebo organismy (člověk je sice technicky také živý organismus, látky vyrobené člověkem v umělých procesech se však v této definici obvykle nepovažují za toxiny).