title: Triangle content: are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.) Some individually necessary and sufficient conditions for a pair of triangles to be congruent are: Some individually sufficient conditions are: An important condition is: Using right triangles and the concept of similarity, the trigonometric functions sine and cosine can be defined. These are functions of an angle which are investigated in trigonometry. A central theorem is the Pythagorean theorem, which states in any right triangle, the square of the length of


title: Triangle content: the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length "c", and the legs have lengths "a" and "b", then the theorem states that The converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side "c". Some other facts about right triangles: For all triangles, angles and sides are related by the law of cosines and law of sines (also called the "cosine rule" and "sine rule"). The triangle inequality states that the sum


title: Triangle content: of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality. Three given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both


title: Triangle content: of these conditions hold: (a) each of the angles is positive, and (b) the angles sum to 180°. If degenerate triangles are permitted, angles of 0° are permitted. Three positive angles "α", "β", and "γ", each of them less than 180°, are the angles of a triangle if and only if any one of the following conditions holds: the last equality applying only if none of the angles is 90° (so the tangent function's value is always finite). There are thousands of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property:


title: Triangle content: see the article Encyclopedia of Triangle Centers for a catalogue of them. Often they are constructed by finding three lines associated in a symmetrical way with the three sides (or vertices) and then proving that the three lines meet in a single point: an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for determining when three such lines are concurrent. Similarly, lines associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear: here Menelaus' theorem gives a useful general criterion. In this section just a few of


title: Triangle content: the most commonly encountered constructions are explained. A perpendicular bisector of a side of a triangle is a straight line passing through the midpoint of the side and being perpendicular to it, i.e. forming a right angle with it. The three perpendicular bisectors meet in a single point, the triangle's circumcenter, usually denoted by O; this point is the center of the circumcircle, the circle passing through all three vertices. The diameter of this circle, called the "circumdiameter", can be found from the law of sines stated above. The circumcircle's radius is called the "circumradius". Thales' theorem implies that if


title: Triangle content: the circumcenter is located on a side of the triangle, then the opposite angle is a right one. If the circumcenter is located inside the triangle, then the triangle is acute; if the circumcenter is located outside the triangle, then the triangle is obtuse. An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. This opposite side is called the "base" of the altitude, and the point where the altitude intersects the base (or its extension) is called the "foot" of the altitude. The length of


title: Triangle content: the altitude is the distance between the base and the vertex. The three altitudes intersect in a single point, called the orthocenter of the triangle, usually denoted by H. The orthocenter lies inside the triangle if and only if the triangle is acute. An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a single point, the incenter, usually denoted by I, the center of the triangle's incircle. The incircle is the circle which lies inside the triangle and touches all three sides. Its


title: Triangle content: radius is called the "inradius". There are three other important circles, the excircles; they lie outside the triangle and touch one side as well as the extensions of the other two. The centers of the in- and excircles form an orthocentric system. A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter, usually denoted by G. The centroid of a rigid triangular object (cut out of a thin sheet


title: Triangle content: of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. The centroid cuts every median in the ratio 2:1, i.e. the distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side. The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle. The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter.


title: Triangle content: The radius of the nine-point circle is half that of the circumcircle. It touches the incircle (at the Feuerbach point) and the three excircles. The orthocenter (blue point), center of the nine-point circle (red), centroid (orange), and circumcenter (green) all lie on a single line, known as Euler's line (red line). The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter. The center of the incircle is not in general located on Euler's line. If one


title: Triangle content: reflects a median in the angle bisector that passes through the same vertex, one obtains a symmedian. The three symmedians intersect in a single point, the symmedian point of the triangle. There are various standard methods for calculating the length of a side or the measure of an angle. Certain methods are suited to calculating values in a right-angled triangle; more complex methods may be required in other situations. In right triangles, the trigonometric ratios of sine, cosine and tangent can be used to find unknown angles and the lengths of unknown sides. The sides of the triangle are known


title: Triangle content: as follows: The "sine" of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case This ratio does not depend on the particular right triangle chosen, as long as it contains the angle "A", since all those triangles are similar. The "cosine" of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In our case The "tangent" of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In our case


title: Triangle content: The acronym "SOH-CAH-TOA" is a useful mnemonic for these ratios. The inverse trigonometric functions can be used to calculate the internal angles for a right angled triangle with the length of any two sides. Arcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse. Arccos can be used to calculate an angle from the length of the adjacent side and the length of the hypotenuse. Arctan can be used to calculate an angle from the length of the opposite side and the length of the adjacent side. In introductory


title: Triangle content: geometry and trigonometry courses, the notation sin, cos, etc., are often used in place of arcsin, arccos, etc. However, the arcsin, arccos, etc., notation is standard in higher mathematics where trigonometric functions are commonly raised to powers, as this avoids confusion between multiplicative inverse and compositional inverse. The law of sines, or sine rule, states that the ratio of the length of a side to the sine of its corresponding opposite angle is constant, that is This ratio is equal to the diameter of the circumscribed circle of the given triangle. Another interpretation of this theorem is that every triangle


title: Triangle content: with angles α, β and γ is similar to a triangle with side lengths equal to sin α, sin β and sin γ. This triangle can be constructed by first constructing a circle of diameter 1, and inscribing in it two of the angles of the triangle. The length of the sides of that triangle will be sin α, sin β and sin γ. The side whose length is sin α is opposite to the angle whose measure is α, etc. The law of cosines, or cosine rule, connects the length of an unknown side of a triangle to the


title: Triangle content: length of the other sides and the angle opposite to the unknown side. As per the law: For a triangle with length of sides "a", "b", "c" and angles of α, β, γ respectively, given two known lengths of a triangle "a" and "b", and the angle between the two known sides γ (or the angle opposite to the unknown side "c"), to calculate the third side "c", the following formula can be used: If the lengths of all three sides of any triangle are known the three angles can be calculated: The law of tangents, or tangent rule, can


title: Triangle content: be used to find a side or an angle when two sides and an angle or two angles and a side are known. It states that: "Solution of triangles" is the main trigonometric problem: to find missing characteristics of a triangle (three angles, the lengths of the three sides etc.) when at least three of these characteristics are given. The triangle can be located on a plane or on a sphere. This problem often occurs in various trigonometric applications, such as geodesy, astronomy, construction, navigation etc. Calculating the area "T" of a triangle is an elementary problem encountered often in


title: Triangle content: many different situations. The best known and simplest formula is: where "b" is the length of the base of the triangle, and "h" is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. In 499 CE Aryabhata, used this illustrated method in the "Aryabhatiya" (section 2.6). Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the surveyor of a triangular field might find


title: Triangle content: it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, depending on what is known about the triangle. The following is a selection of frequently used formulae for the area of a triangle. The height of a triangle can be found through the application of trigonometry. "Knowing SAS": Using the labels in the image on the right, the altitude is . Substituting this in the formula formula_26 derived above, the area of the triangle can be expressed as: (where α is the interior angle at "A",


title: Triangle content: β is the interior angle at "B", formula_28 is the interior angle at "C" and "c" is the line AB). Furthermore, since sin α = sin ("π" − α) = sin (β + formula_28), and similarly for the other two angles: "Knowing AAS": and analogously if the known side is "a" or "c". "Knowing ASA": and analogously if the known side is "b" or "c". The shape of the triangle is determined by the lengths of the sides. Therefore, the area can also be derived from the lengths of the sides. By Heron's formula: where formula_34 is the semiperimeter, or


title: Triangle content: half of the triangle's perimeter. Three other equivalent ways of writing Heron's formula are The area of a parallelogram embedded in a three-dimensional Euclidean space can be calculated using vectors. Let vectors AB and AC point respectively from "A" to "B" and from "A" to "C". The area of parallelogram "ABDC" is then which is the magnitude of the cross product of vectors AB and AC. The area of triangle ABC is half of this, The area of triangle "ABC" can also be expressed in terms of dot products as follows: In two-dimensional Euclidean space, expressing vector AB as a


title: Triangle content: free vector in Cartesian space equal to ("x","y") and AC as ("x","y"), this can be rewritten as: If vertex "A" is located at the origin (0, 0) of a Cartesian coordinate system and the coordinates of the other two vertices are given by and , then the area can be computed as times the absolute value of the determinant For three general vertices, the equation is: which can be written as If the points are labeled sequentially in the counterclockwise direction, the above determinant expressions are positive and the absolute value signs can be omitted. The above formula is known


title: Triangle content: as the shoelace formula or the surveyor's formula. If we locate the vertices in the complex plane and denote them in counterclockwise sequence as , , and , and denote their complex conjugates as formula_45, formula_46, and formula_47, then the formula is equivalent to the shoelace formula. In three dimensions, the area of a general triangle , and ) is the Pythagorean sum of the areas of the respective projections on the three principal planes (i.e. "x" = 0, "y" = 0 and "z" = 0): The area within any closed curve, such as a triangle, is given by the


title: Triangle content: line integral around the curve of the algebraic or signed distance of a point on the curve from an arbitrary oriented straight line "L". Points to the right of "L" as oriented are taken to be at negative distance from "L", while the weight for the integral is taken to be the component of arc length parallel to "L" rather than arc length itself. This method is well suited to computation of the area of an arbitrary polygon. Taking "L" to be the "x"-axis, the line integral between consecutive vertices ("x","y") and ("x","y") is given by the base times the


title: Triangle content: mean height, namely . The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal. The area of a triangle then falls out as the case of a polygon with three sides. While the line integral method has in common with other coordinate-based methods the arbitrary choice of a coordinate system, unlike the others it makes no arbitrary choice of vertex of the triangle as origin or of side as base. Furthermore, the choice of coordinate system defined by "L" commits to only two degrees of freedom rather than the usual


title: Triangle content: three, since the weight is a local distance (e.g. in the above) whence the method does not require choosing an axis normal to "L". When working in polar coordinates it is not necessary to convert to Cartesian coordinates to use line integration, since the line integral between consecutive vertices ("r",θ) and ("r",θ) of a polygon is given directly by . This is valid for all values of θ, with some decrease in numerical accuracy when |θ| is many orders of magnitude greater than π. With this formulation negative area indicates clockwise traversal, which should be kept in mind when mixing


title: Triangle content: polar and cartesian coordinates. Just as the choice of "y"-axis () is immaterial for line integration in cartesian coordinates, so is the choice of zero heading () immaterial here. Three formulas have the same structure as Heron's formula but are expressed in terms of different variables. First, denoting the medians from sides "a", "b", and "c" respectively as "m", "m", and "m" and their semi-sum as σ, we have Next, denoting the altitudes from sides "a", "b", and "c" respectively as "h", "h", and "h", and denoting the semi-sum of the reciprocals of the altitudes as formula_51 we have And


title: Triangle content: denoting the semi-sum of the angles' sines as , we have where "D" is the diameter of the circumcircle: formula_54 See Pick's theorem for a technique for finding the area of any arbitrary lattice polygon (one drawn on a grid with vertically and horizontally adjacent lattice points at equal distances, and with vertices on lattice points). The theorem states: where "formula_56" is the number of internal lattice points and "B" is the number of lattice points lying on the border of the polygon. Numerous other area formulas exist, such as where "r" is the inradius, and "s" is the semiperimeter


title: Triangle content: (in fact, this formula holds for "all" tangential polygons), and where formula_59 are the radii of the excircles tangent to sides "a, b, c" respectively. We also have and for circumdiameter "D"; and for angle α ≠ 90°. The area can also be expressed as In 1885, Baker gave a collection of over a hundred distinct area formulas for the triangle. These include: for circumradius (radius of the circumcircle) "R", and The area "T" of any triangle with perimeter "p" satisfies with equality holding if and only if the triangle is equilateral. Other upper bounds on the area "T" are


title: Triangle content: given by and both again holding if and only if the triangle is equilateral. There are infinitely many lines that bisect the area of a triangle. Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given triangle. The formulas in this section are true for all Euclidean triangles. The medians


title: Triangle content: and the sides are related by and and equivalently for "m" and "m". For angle A opposite side "a", the length of the internal angle bisector is given by for semiperimeter "s", where the bisector length is measured from the vertex to where it meets the opposite side. The interior perpendicular bisectors are given by where the sides are formula_78 and the area is formula_79 The altitude from, for example, the side of length "a" is The following formulas involve the circumradius "R" and the inradius "r": where "h" etc. are the altitudes to the subscripted sides; and The product


title: Triangle content: of two sides of a triangle equals the altitude to the third side times the diameter "D" of the circumcircle: Suppose two adjacent but non-overlapping triangles share the same side of length "f" and share the same circumcircle, so that the side of length "f" is a chord of the circumcircle and the triangles have side lengths ("a", "b", "f") and ("c", "d", "f"), with the two triangles together forming a cyclic quadrilateral with side lengths in sequence ("a", "b", "c", "d"). Then Let "G" be the centroid of a triangle with vertices "A", "B", and "C", and let "P"


title: Triangle content: be any interior point. Then the distances between the points are related by The sum of the squares of the triangle's sides equals three times the sum of the squared distances of the centroid from the vertices: Let "q", "q", and "q" be the distances from the centroid to the sides of lengths "a", "b", and "c". Then and for area "T". Carnot's Theorem states that the sum of the distances from the circumcenter to the three sides equals the sum of the circumradius and the inradius. Here a segment's length is considered to be negative if and only if


title: Triangle content: the segment lies entirely outside the triangle. This method is especially useful for deducing the properties of more abstract forms of triangles, such as the ones induced by Lie algebras, that otherwise have the same properties as usual triangles. Euler's theorem states that the distance "d" between the circumcenter and the incenter is given by or equivalently where "R" is the circumradius and "r" is the inradius. Thus for all triangles "R" ≥ 2"r", with equality holding for equilateral triangles. If we denote that the orthocenter divides one altitude into segments of lengths "u" and "v", another altitude into segment


title: Triangle content: lengths "w" and "x", and the third altitude into segment lengths "y" and "z", then "uv" = "wx" = "yz". The distance from a side to the circumcenter equals half the distance from the opposite vertex to the orthocenter. The sum of the squares of the distances from the vertices to the orthocenter "H" plus the sum of the squares of the sides equals twelve times the square of the circumradius: In addition to the law of sines, the law of cosines, the law of tangents, and the trigonometric existence conditions given earlier, for any triangle Morley's trisector theorem states


title: Triangle content: that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle. As discussed above, every triangle has a unique inscribed circle (incircle) that is interior to the triangle and tangent to all three sides. Every triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the sides. Marden's theorem shows how to find the foci of this ellipse. This ellipse has the greatest area of any ellipse tangent to all three sides of the triangle. The Mandart inellipse of a triangle


title: Triangle content: is the ellipse inscribed within the triangle tangent to its sides at the contact points of its excircles. For any ellipse inscribed in a triangle "ABC", let the foci be "P" and "Q". Then Every convex polygon with area "T" can be inscribed in a triangle of area at most equal to 2"T". Equality holds (exclusively) for a parallelogram. The Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the sides of a triangle with the three lines that are parallel to the sides and that pass through its symmedian point. In either its simple


title: Triangle content: form or its self-intersecting form, the Lemoine hexagon is interior to the triangle with two vertices on each side of the triangle. Every acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two of them lie on the same side and hence one side of the square coincides with part of a side of the triangle). In a right triangle two of the squares coincide and have a vertex at the triangle's right angle, so a right triangle has only two "distinct" inscribed


title: Triangle content: squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side. Within a given triangle, a longer common side is associated with a smaller inscribed square. If an inscribed square has side of length "q" and the triangle has a side of length "a", part of which side coincides with a side of the square, then "q", "a", the altitude "h" from the side "a", and the triangle's area "T" are related according to The largest possible ratio of the area of the inscribed square to the area of the triangle


title: Triangle content: is 1/2, which occurs when , , and the altitude of the triangle from the base of length "a" is equal to "a". The smallest possible ratio of the side of one inscribed square to the side of another in the same non-obtuse triangle is formula_98 Both of these extreme cases occur for the isosceles right triangle. From an interior point in a reference triangle, the nearest points on the three sides serve as the vertices of the pedal triangle of that point. If the interior point is the circumcenter of the reference triangle, the vertices of the pedal triangle


title: Triangle content: are the midpoints of the reference triangle's sides, and so the pedal triangle is called the midpoint triangle or medial triangle. The midpoint triangle subdivides the reference triangle into four congruent triangles which are similar to the reference triangle. The Gergonne triangle or intouch triangle of a reference triangle has its vertices at the three points of tangency of the reference triangle's sides with its incircle. The extouch triangle of a reference triangle has its vertices at the points of tangency of the reference triangle's excircles with its sides (not extended). The tangential triangle of a reference triangle (other than


title: Triangle content: a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices. As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides. Further, every triangle has a unique Steiner circumellipse, which passes through the triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area. The Kiepert hyperbola is the unique conic which passes through the triangle's three vertices, its


title: Triangle content: centroid, and its circumcenter. Of all triangles contained in a given convex polygon, there exists a triangle with maximal area whose vertices are all vertices of the given polygon. One way to identify locations of points in (or outside) a triangle is to place the triangle in an arbitrary location and orientation in the Cartesian plane, and to use Cartesian coordinates. While convenient for many purposes, this approach has the disadvantage of all points' coordinate values being dependent on the arbitrary placement in the plane. Two systems avoid that feature, so that the coordinates of a point are not affected


title: Triangle content: by moving the triangle, rotating it, or reflecting it as in a mirror, any of which give a congruent triangle, or even by rescaling it to give a similar triangle: A non-planar triangle is a triangle which is not contained in a (flat) plane. Some examples of non-planar triangles in non-Euclidean geometries are spherical triangles in spherical geometry and hyperbolic triangles in hyperbolic geometry. While the measures of the internal angles in planar triangles always sum to 180°, a hyperbolic triangle has measures of angles that sum to less than 180°, and a spherical triangle has measures of angles that


title: Triangle content: sum to more than 180°. A hyperbolic triangle can be obtained by drawing on a negatively curved surface, such as a saddle surface, and a spherical triangle can be obtained by drawing on a positively curved surface such as a sphere. Thus, if one draws a giant triangle on the surface of the Earth, one will find that the sum of the measures of its angles is greater than 180°; in fact it will be between 180° and 540°. In particular it is possible to draw a triangle on a sphere such that the measure of each of its internal


title: Triangle content: angles is equal to 90°, adding up to a total of 270°. Specifically, on a sphere the sum of the angles of a triangle is where "f" is the fraction of the sphere's area which is enclosed by the triangle. For example, suppose that we draw a triangle on the Earth's surface with vertices at the North Pole, at a point on the equator at 0° longitude, and a point on the equator at 90° West longitude. The great circle line between the latter two points is the equator, and the great circle line between either of those points and


title: Triangle content: the North Pole is a line of longitude; so there are right angles at the two points on the equator. Moreover, the angle at the North Pole is also 90° because the other two vertices differ by 90° of longitude. So the sum of the angles in this triangle is . The triangle encloses 1/4 of the northern hemisphere (90°/360° as viewed from the North Pole) and therefore 1/8 of the Earth's surface, so in the formula ; thus the formula correctly gives the sum of the triangle's angles as 270°. From the above angle sum formula we can also


title: Triangle content: see that the Earth's surface is locally flat: If we draw an arbitrarily small triangle in the neighborhood of one point on the Earth's surface, the fraction "f" of the Earth's surface which is enclosed by the triangle will be arbitrarily close to zero. In this case the angle sum formula simplifies to 180°, which we know is what Euclidean geometry tells us for triangles on a flat surface. Rectangles have been the most popular and common geometric form for buildings since the shape is easy to stack and organize; as a standard, it is easy to design furniture and


title: Triangle content: fixtures to fit inside rectangularly shaped buildings. But triangles, while more difficult to use conceptually, provide a great deal of strength. As computer technology helps architects design creative new buildings, triangular shapes are becoming increasingly prevalent as parts of buildings and as the primary shape for some types of skyscrapers as well as building materials. In Tokyo in 1989, architects had wondered whether it was possible to build a 500-story tower to provide affordable office space for this densely packed city, but with the danger to buildings from earthquakes, architects considered that a triangular shape would be necessary if such


title: Triangle content: a building were to be built. In New York City, as Broadway crisscrosses major avenues, the resulting blocks are cut like triangles, and buildings have been built on these shapes; one such building is the triangularly shaped Flatiron Building which real estate people admit has a "warren of awkward spaces that do not easily accommodate modern office furniture" but that has not prevented the structure from becoming a landmark icon. Designers have made houses in Norway using triangular themes. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs.


title: Triangle content: Triangles are sturdy; while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures. A triangle will not change shape unless its sides are bent or extended or broken or if its joints break; in essence, each of the three sides supports the other two. A rectangle, in contrast, is more dependent on the strength of its joints in a structural sense. Some innovative designers have proposed making bricks not out of rectangles, but with triangular shapes which can be combined in three dimensions. It


title: Triangle content: is likely that triangles will be used increasingly in new ways as architecture increases in complexity. It is important to remember that triangles are strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss. Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A


title: Tuba content: rotary-valved tubas pitched in the same octave as euphoniums. The "Small Swiss Tuba in C" is a tenor tuba pitched in C, and provided with 6 valves to make the lower notes in the orchestral repertoire possible. The French C tuba was the standard instrument in French orchestras until overtaken by F and C tubas since the Second World War. One popular example of the use of the French C tuba is the "Bydło" movement in Ravel's orchestration of Mussorgsky's "Pictures at an Exhibition", though the rest of the work is scored for this instrument as well. Larger BBB subcontrabass


title: Thermometer content: Thermometer A thermometer is a device that measures temperature or a temperature gradient. A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass thermometer or the digital sensor in an infrared thermometer) in which some change occurs with a change in temperature; and (2) some means of converting this change into a numerical value (e.g. the visible scale that is marked on a mercury-in-glass thermometer or the digital readout on an infrared model). Thermometers are widely used in technology and industry to monitor processes, in meteorology, in medicine, and in scientific research. Some of


title: Thermometer content: the principles of the thermometer were known to Greek philosophers of two thousand years ago. The modern thermometer gradually evolved from the thermoscope with the addition of a scale in the early 17th century and standardisation through the 17th and 18th centuries. While an individual thermometer is able to measure degrees of hotness, the readings on two thermometers cannot be compared unless they conform to an agreed scale. Today there is an absolute thermodynamic temperature scale. Internationally agreed temperature scales are designed to approximate this closely, based on fixed points and interpolating thermometers. The most recent official temperature scale is


title: Thermometer content: the International Temperature Scale of 1990. It extends from to approximately . Various authors have credited the invention of the thermometer to Hero of Alexandria. The thermometer was not a single invention, however, but a development. Hero of Alexandria (10–70 AD) knew of the principle that certain substances, notably air, expand and contract and described a demonstration in which a closed tube partially filled with air had its end in a container of water. The expansion and contraction of the air caused the position of the water/air interface to move along the tube. Such a mechanism was later used to


title: Thermometer content: show the hotness and coldness of the air with a tube in which the water level is controlled by the expansion and contraction of the gas. These devices were developed by several European scientists in the 16th and 17th centuries, notably Galileo Galilei. As a result, devices were shown to produce this effect reliably, and the term "thermoscope" was adopted because it reflected the changes in sensible heat (the concept of temperature was yet to arise). The difference between a thermoscope and a thermometer is that the latter has a scale. Though Galileo is often said to be the inventor


title: Thermometer content: of the thermometer, what he produced were thermoscopes. The first clear diagram of a thermoscope was published in 1617 by Giuseppe Biancani (1566 – 1624): the first showing a scale and thus constituting a thermometer was by Robert Fludd in 1638. This was a vertical tube, closed by a bulb of air at the top, with the lower end opening into a vessel of water. The water level in the tube is controlled by the expansion and contraction of the air, so it is what we would now call an air thermometer. The first person to put a scale on


title: Thermometer content: a thermoscope is variously said to be Francesco Sagredo (1571–1620) or Santorio Santorio in about 1611 to 1613. The word thermometer (in its French form) first appeared in 1624 in "La Récréation Mathématique" by J. Leurechon, who describes one with a scale of 8 degrees. The word comes from the Greek words θερμός, "thermos", meaning "hot" and μέτρον, "metron", meaning "measure". The above instruments suffered from the disadvantage that they were also barometers, i.e. sensitive to air pressure. In 1629, Joseph Solomon Delmedigo, a student of Galileo, published what is apparently the first description and illustration of a sealed liquid-in-glass


title: Thermometer content: thermometer. It is described as having a bulb at the bottom of a sealed tube partially filled with brandy. The tube has a numbered scale. Delmedigo does not claim to have invented this instrument, nor does he name anyone else as its inventor. In about 1654 Ferdinando II de' Medici, Grand Duke of Tuscany (1610–1670), actually produced such an instrument, the first modern-style thermometer, dependent on the expansion of a liquid, and independent of air pressure. Many other scientists experimented with various liquids and designs of thermometer. However, each inventor and each thermometer was unique—there was no standard scale. In


title: Thermometer content: 1665 Christiaan Huygens (1629–1695) suggested using the melting and boiling points of water as standards, and in 1694 Carlo Renaldini (1615–1698) proposed using them as fixed points on a universal scale. In 1701, Isaac Newton (1642–1726/27) proposed a scale of 12 degrees between the melting point of ice and body temperature. In 1714 Dutch scientist and inventor Daniel Gabriel Fahrenheit invented the first reliable thermometer, using mercury instead of alcohol and water mixtures. In 1724 he proposed a temperature scale which now (slightly adjusted) bears his name. He could do this because he manufactured thermometers, using mercury (which has a


title: Thermometer content: high coefficient of expansion) for the first time and the quality of his production could provide a finer scale and greater reproducibility, leading to its general adoption. In 1742, Anders Celsius (1701–1744) proposed a scale with zero at the boiling point and 100 degrees at the freezing point of water, though the scale which now bears his name has them the other way around. French entomologist René Antoine Ferchault de Réaumur invented an alcohol thermometer and temperature scale in 1730 that ultimately proved to be less reliable than Fahrenheit's mercury thermometer. The first physician that put thermometer measurements to clinical


title: Thermometer content: practice was Herman Boerhaave (1668–1738). In 1866, Sir Thomas Clifford Allbutt (1836–1925) invented a clinical thermometer that produced a body temperature reading in five minutes as opposed to twenty. In 1999, Dr. Francesco Pompei of the Exergen Corporation introduced the world's first temporal artery thermometer, a non-invasive temperature sensor which scans the forehead in about two seconds and provides a medically accurate body temperature. Old thermometers were all non-registering thermometers. That is, the thermometer did not hold the temperature reading after it was moved to a place with a different temperature. Determining the temperature of a pot of hot liquid


title: Thermometer content: required the user to leave the thermometer in the hot liquid until after reading it. If the non-registering thermometer was removed from the hot liquid, then the temperature indicated on the thermometer would immediately begin changing to reflect the temperature of its new conditions (in this case, the air temperature). Registering thermometers are designed to hold the temperature indefinitely, so that the thermometer can be removed and read at a later time or in a more convenient place. Mechanical registering thermometers hold either the highest or lowest temperature recorded, until manually re-set, e.g., by shaking down a mercury-in-glass thermometer, or


title: Thermometer content: until an even more extreme temperature is experienced. Electronic registering thermometers may be designed to remember the highest or lowest temperature, or to remember whatever temperature was present at a specified point in time. Thermometers increasingly use electronic means to provide a digital display or input to a computer. Thermometers may be described as empirical or absolute. Absolute thermometers are calibrated numerically by the thermodynamic absolute temperature scale. Empirical thermometers are not in general necessarily in exact agreement with absolute thermometers as to their numerical scale readings, but to qualify as thermometers at all they must agree with absolute thermometers


title: Thermometer content: and with each other in the following way: given any two bodies isolated in their separate respective thermodynamic equilibrium states, all thermometers agree as to which of the two has the higher temperature, or that the two have equal temperatures. For any two empirical thermometers, this does not require that the relation between their numerical scale readings be linear, but it does require that relation to be strictly monotonic. This is a fundamental character of temperature and thermometers. As it is customarily stated in textbooks, taken alone, the so-called "zeroth law of thermodynamics" fails to deliver this information, but the


title: Thermometer content: statement of the zeroth law of thermodynamics by James Serrin in 1977, though rather mathematically abstract, is more informative for thermometry: "Zeroth Law – There exists a topological line formula_1 which serves as a coordinate manifold of material behaviour. The points formula_2 of the manifold formula_1 are called 'hotness levels', and formula_1 is called the 'universal hotness manifold'." To this information there needs to be added a sense of greater hotness; this sense can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of


title: Thermometer content: thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum; this frequency is always positive, but can have values that tend to zero. Another way of identifying hotter as opposed to colder conditions is supplied by Planck's principle, that when a process of isochoric adiabatic work is the sole means of change of internal energy of a closed system, the final state of the system is never colder than the initial state; except for phase changes with latent heat, it is hotter than the initial state. There are several principles on which


title: Thermometer content: empirical thermometers are built, as listed in the section of this article entitled "Primary and secondary thermometers". Several such principles are essentially based on the constitutive relation between the state of a suitably selected particular material and its temperature. Only some materials are suitable for this purpose, and they may be considered as "thermometric materials". Radiometric thermometry, in contrast, can be only slightly dependent on the constitutive relations of materials. In a sense then, radiometric thermometry might be thought of as "universal". This is because it rests mainly on a universality character of thermodynamic equilibrium, that it has the universal


title: Thermometer content: property of producing blackbody radiation. There are various kinds of empirical thermometer based on material properties. Many empirical thermometers rely on the constitutive relation between pressure, volume and temperature of their thermometric material. For example, mercury expands when heated. If it is used for its relation between pressure and volume and temperature, a thermometric material must have three properties: (1) Its heating and cooling must be rapid. That is to say, when a quantity of heat enters or leaves a body of the material, the material must expand or contract to its final volume or reach its final pressure and


title: Thermometer content: must reach its final temperature with practically no delay; some of the heat that enters can be considered to change the volume of the body at constant temperature, and is called the latent heat of expansion at constant temperature; and the rest of it can be considered to change the temperature of the body at constant volume, and is called the specific heat at constant volume. Some materials do not have this property, and take some time to distribute the heat between temperature and volume change. (2) Its heating and cooling must be reversible. That is to say, the material


title: Thermometer content: must be able to be heated and cooled indefinitely often by the same increment and decrement of heat, and still return to its original pressure, volume and temperature every time. Some plastics do not have this property; (3) Its heating and cooling must be monotonic. That is to say, throughout the range of temperatures for which it is intended to work, At temperatures around about 4 °C, water does not have the property (3), and is said to behave anomalously in this respect; thus water cannot be used as a material for this kind of thermometry for temperature ranges near


title: Thermometer content: 4 °C. Gases, on the other hand, all have the properties (1), (2), and (3)(a)(α) and (3)(b)(α). Consequently, they are suitable thermometric materials, and that is why they were important in the development of thermometry. According to Preston (1894/1904), Regnault found constant pressure air thermometers unsatisfactory, because they needed troublesome corrections. He therefore built a constant volume air thermometer. Constant volume thermometers do not provide a way to avoid the problem of anomalous behaviour like that of water at approximately 4 °C. Planck's law very accurately quantitatively describes the power spectral density of electromagnetic radiation, inside a rigid walled cavity


title: Thermometer content: in a body made of material that is completely opaque and poorly reflective, when it has reached thermodynamic equilibrium, as a function of absolute thermodynamic temperature alone. A small enough hole in the wall of the cavity emits near enough blackbody radiation of which the spectral radiance can be precisely measured. The walls of the cavity, provided they are completely opaque and poorly reflective, can be of any material indifferently. This provides a well-reproducible absolute thermometer over a very wide range of temperatures, able to measure the absolute temperature of a body inside the cavity. A thermometer is called primary


title: Thermometer content: or secondary based on how the raw physical quantity it measures is mapped to a temperature. As summarized by Kauppinen et al., "For primary thermometers the measured property of matter is known so well that temperature can be calculated without any unknown quantities. Examples of these are thermometers based on the equation of state of a gas, on the velocity of sound in a gas, on the thermal noise voltage or current of an electrical resistor, and on the angular anisotropy of gamma ray emission of certain radioactive nuclei in a magnetic field." In contrast, "Secondary thermometers are most widely


title: Thermometer content: used because of their convenience. Also, they are often much more sensitive than primary ones. For secondary thermometers knowledge of the measured property is not sufficient to allow direct calculation of temperature. They have to be calibrated against a primary thermometer at least at one temperature or at a number of fixed temperatures. Such fixed points, for example, triple points and superconducting transitions, occur reproducibly at the same temperature." Thermometers can be calibrated either by comparing them with other calibrated thermometers or by checking them against known fixed points on the temperature scale. The best known of these fixed points


title: Thermometer content: are the melting and boiling points of pure water. (Note that the boiling point of water varies with pressure, so this must be controlled.) The traditional way of putting a scale on a liquid-in-glass or liquid-in-metal thermometer was in three stages: Other fixed points used in the past are the body temperature (of a healthy adult male) which was originally used by Fahrenheit as his upper fixed point ( to be a number divisible by 12) and the lowest temperature given by a mixture of salt and ice, which was originally the definition of . (This is an example of


title: Thermometer content: a Frigorific mixture). As body temperature varies, the Fahrenheit scale was later changed to use an upper fixed point of boiling water at . These have now been replaced by the defining points in the International Temperature Scale of 1990, though in practice the melting point of water is more commonly used than its triple point, the latter being more difficult to manage and thus restricted to critical standard measurement. Nowadays manufacturers will often use a thermostat bath or solid block where the temperature is held constant relative to a calibrated thermometer. Other thermometers to be calibrated are put into


title: Thermometer content: the same bath or block and allowed to come to equilibrium, then the scale marked, or any deviation from the instrument scale recorded. For many modern devices calibration will be stating some value to be used in processing an electronic signal to convert it to a temperature. The precision or resolution of a thermometer is simply to what fraction of a degree it is possible to make a reading. For high temperature work it may only be possible to measure to the nearest 10 °C or more. Clinical thermometers and many electronic thermometers are usually readable to 0.1 °C. Special


title: Thermometer content: instruments can give readings to one thousandth of a degree. However, this precision does not mean the reading is true or accurate, it only means that very small changes can be observed. A thermometer calibrated to a known fixed point is accurate (i.e. gives a true reading) at that point. Most thermometers are originally calibrated to a constant-volume gas thermometer. In between fixed calibration points, interpolation is used, usually linear. This may give significant differences between different types of thermometer at points far away from the fixed points. For example, the expansion of mercury in a glass thermometer is slightly


title: Thermometer content: different from the change in resistance of a platinum resistance thermometer, so these two will disagree slightly at around 50 °C. There may be other causes due to imperfections in the instrument, e.g. in a liquid-in-glass thermometer if the capillary tube varies in diameter. For many purposes reproducibility is important. That is, does the same thermometer give the same reading for the same temperature (or do replacement or multiple thermometers give the same reading)? Reproducible temperature measurement means that comparisons are valid in scientific experiments and industrial processes are consistent. Thus if the same type of thermometer is calibrated in


title: Thermometer content: the same way its readings will be valid even if it is slightly inaccurate compared to the absolute scale. An example of a reference thermometer used to check others to industrial standards would be a platinum resistance thermometer with a digital display to 0.1 °C (its precision) which has been calibrated at 5 points against national standards (−18, 0, 40, 70, 100 °C) and which is certified to an accuracy of ±0.2 °C. According to British Standards, correctly calibrated, used and maintained liquid-in-glass thermometers can achieve a measurement uncertainty of ±0.01 °C in the range 0 to 100 °C, and


title: Thermometer content: a larger uncertainty outside this range: ±0.05 °C up to 200 or down to −40 °C, ±0.2 °C up to 450 or down to −80 °C. In theory any physical phenomenon exhibiting a temperature dependence could be used as a thermometer, measuring temperature indirectly. Some of these properties have been exploited. For example, blackbody radiation allows one to measure the temperature in a blast furnace or kiln, or the temperature of a distant star Thermometers utilize a range of physical effects to measure temperature. Temperature sensors are used in a wide variety of scientific and engineering applications, especially measurement systems.


title: Thermometer content: Temperature systems are primarily either electrical or mechanical, occasionally inseparable from the system which they control (as in the case of a mercury-in-glass thermometer). Thermometers are used in roadways in cold weather climates to help determine if icing conditions exist. Indoors, thermistors are used in climate control systems such as air conditioners, freezers, heaters, refrigerators, and water heaters. Galileo thermometers are used to measure indoor air temperature, due to their limited measurement range. Such liquid crystal thermometers (which use thermochromic liquid crystals) are also used in mood rings and used to measure the temperature of water in fish tanks. Fiber


title: Thermometer content: Bragg grating temperature sensors are used in nuclear power facilities to monitor reactor core temperatures and avoid the possibility of nuclear meltdowns. Nanothermometry is an emergent research field dealing with the knowledge of temperature in the sub-micrometric scale. Conventional thermometers cannot measure the temperature of an object which is smaller than a micrometre, and new methods and materials have to be used. Nanothermometry is used in such cases. Nanothermometers are classified as luminescent thermometers (if they use light to measure temperature) and non-luminescent thermometers (systems where thermometric properties are not directly related to luminescence). Thermometers used specifically for low temperatures.


title: Thermometer content: Various thermometric techniques have been used throughout history such as the Galileo thermometer to thermal imaging. Medical thermometers such as mercury-in-glass thermometers, infrared thermometers, pill thermometers, and liquid crystal thermometers are used in health care settings to determine if individuals have a fever or are hypothermic. Thermometers are important in food safety, where food at temperatures within can be prone to potentially harmful levels of bacterial growth after several hours which could lead to foodborne illness. This includes monitoring refrigeration temperatures and maintaining temperatures in foods being served under heat lamps or hot water baths. Cooking thermometers are important for


title: Thermometer content: determining if a food is properly cooked. In particular meat thermometers are used to aid in cooking meat to a safe internal temperature while preventing over cooking. They are commonly found using either a bimetallic coil, or a thermocouple or thermistor with a digital readout. Candy thermometers are used to aid in achieving a specific water content in a sugar solution based on its boiling temperature. Alcohol thermometers, infrared thermometers, mercury-in-glass thermometers, recording thermometers, thermistors, and Six's thermometers are used in meteorology and climatology in various levels of the atmosphere and oceans. Aircraft use thermometers and hygrometers to determine if


title: Thermometer content: atmospheric icing conditions exist along their flight path. These measurements are used to initialize weather forecast models. Thermometers are used in roadways in cold weather climates to help determine if icing conditions exist and indoors in climate control systems. Thermometer A thermometer is a device that measures temperature or a temperature gradient. A thermometer has two important elements: (1) a temperature sensor (e.g. the bulb of a mercury-in-glass thermometer or the digital sensor in an infrared thermometer) in which some change occurs with a change in temperature; and (2) some means of converting this change into a numerical value (e.g.


title: Triode content: Triode A triode is an electronic amplifying vacuum tube (or "thermionic valve" in British English) consisting of three electrodes inside an evacuated glass envelope: a heated filament or cathode, a grid, and a plate (anode). Developed from Lee De Forest's 1906 Audion, a partial vacuum tube that added a grid electrode to the thermionic diode (Fleming valve), the triode was the first practical electronic amplifier and the ancestor of other types of vacuum tubes such as the tetrode and pentode. Its invention founded the electronics age, making possible amplified radio technology and long-distance telephony. Triodes were widely used in consumer


title: Triode content: electronics devices such as radios and televisions until the 1970s, when transistors replaced them. Today, their main remaining use is in high-power RF amplifiers in radio transmitters and industrial RF heating devices. In recent years there has been a resurgence in demand for low power triodes due to renewed interest in tube-type audio systems by audiophiles who prefer the sound of tube-based electronics. The name "triode" was coined by British physicist William Eccles sometime around 1920, derived from the Greek τρίοδος, "tríodos", from "tri-" (three) and "hodós" (road, way), originally meaning the place where three roads meet. Before thermionic valves


title: Triode content: were invented, Philipp Lenard used the principle of grid control while conducting photoelectric experiments in 1902. The first vacuum tube used in radio was the thermionic diode or Fleming valve, invented by John Ambrose Fleming in 1904 as a detector for radio receivers. It was an evacuated glass bulb containing two electrodes, a heated filament and a plate (anode). Triodes came about in 1906 when American engineer Lee De Forest and Austrian physicist Robert von Lieben independently patented tubes that added a third electrode, a grid, between the filament and plate to control current. Von Lieben's partially-evacuated three-element tube, patented


title: Triode content: in March 1906, contained a trace of mercury vapor and was intended to amplify weak telephone signals. Starting in October 1906 De Forest patented a number of three-element tube designs by adding an electrode to the diode, which he called Audions, intended to be used as radio detectors. The one which became the design of the triode, in which the grid was located between the filament and plate, was patented January 29, 1907. Like the von Lieben vacuum tube, De Forest's Audions were incompletely evacuated and contained some gas at low pressure. Von Lieben's tube did not see much development


title: Triode content: due to his death at the outbreak World War I, 7 years after he invented it. De Forest's Audion did not see much use until its ability to amplify was recognized around 1912 by several researchers, who used it to build the first successful amplifying radio receivers and electronic oscillators. The many uses for amplification motivated its rapid development. By 1913 improved versions with higher vacuum were developed by Harold Arnold at American Telephone and Telegraph Company, which had purchased the rights to the Audion from De Forest, and Irving Langmuir at General Electric, who named his tube the "Pliotron",


title: Triode content: These were the first vacuum tube triodes. The name "triode" appeared later, when it became necessary to distinguish it from other kinds of vacuum tubes with more or fewer elements (e.g. diodes, tetrodes, pentodes, etc.). There were lengthy lawsuits between De Forest and von Lieben, and De Forest and the Marconi Company, who represented John Ambrose Fleming, the inventor of the diode. The discovery of the triode's amplifying ability in 1912 revolutionized electrical technology, creating the new field of "electronics", the technology of active (amplifying) electrical devices. The triode was immediately applied to many areas of communication. Triode "continuous wave"


title: Triode content: radio transmitters replaced the cumbersome inefficient "damped wave" spark gap transmitters, allowing the transmission of sound by amplitude modulation (AM). Amplifying triode radio receivers, which had the power to drive loudspeakers, replaced weak crystal radios, which had to be listened to with earphones, allowing families to listen together. This resulted in the evolution of radio from a commercial message service to the first mass communication medium, with the beginning of radio broadcasting around 1920. Triodes made transcontinental telephone service possible. Vacuum tube triode repeaters, invented at Bell Telephone after its purchase of the Audion rights, allowed telephone calls to travel


title: Triode content: beyond the unamplified limit of about 800 miles. The opening by Bell of the first transcontinental telephone line was celebrated 3 years later, on January 25, 1915. Other inventions made possible by the triode were television, public address systems, electric phonographs, and talking motion pictures. The triode served as the technological base from which later vacuum tubes developed, such as the tetrode (Walter Schottky, 1916) and pentode (Gilles Holst and Bernardus Dominicus Hubertus Tellegen, 1926), which remedied some of the shortcomings of the triode detailed below. The triode was very widely used in consumer electronics such as radios, televisions, and


title: Triode content: audio systems until it was replaced in the 1960s by the transistor, invented in 1947, which brought the "vacuum tube era" introduced by the triode to a close. Today triodes are mostly used in high-power applications for which solid state semiconductor devices are unsuitable, such as radio transmitters and industrial heating equipment. However, more recently the triode and other vacuum tube devices have been experiencing a resurgence and comeback in high fidelity audio and musical equipment. They also remain in use as vacuum fluorescent displays (VFDs), which come in a variety of implementations but all are essentially triode devices. All


title: Triode content: triodes have a hot cathode electrode heated by a filament, which releases electrons, and a flat metal plate electrode to which the electrons are attracted, with a grid consisting of a screen of wires between them to control the current. These are sealed inside a glass container from which the air has been removed to a high vacuum, about 10 atm. Since the filament eventually burns out, the tube has a limited lifetime and is made as a replaceable unit; the electrodes are attached to terminal pins which plug into a socket. The operating lifetime of a triode is about


title: Triode content: 2000 hours for small tubes and 10,000 hours for power tubes. Low power triodes have a concentric construction "(see drawing right)", with the grid and anode as circular or oval cylinders surrounding the cathode. The cathode is a narrow metal tube down the center. Inside the cathode is a filament called the "heater" consisting of a narrow strip of high resistance tungsten wire, which heats the cathode red-hot (800 - 1000 °C). This type is called an "indirectly heated cathode" The cathode is coated with a mixture of alkaline earth oxides such as calcium and thorium oxide which reduces its


title: Triode content: work function so it produces more electrons. The grid is constructed of a helix or screen of thin wires surrounding the cathode. The anode is a cylinder or rectangular box of sheet metal surrounding the grid. It is blackened to radiate heat and is often equipped with heat-radiating fins. The electrons travel in a radial direction, from cathode through the grid to the anode. The elements are held in position by mica or ceramic insulators and are supported by stiff wires attached to the base, where the electrodes are brought out to connecting pins. A "getter", a small amount of


title: Triode content: shiny barium metal evaporated onto the inside of the glass, helps maintain the vacuum by absorbing gas released in the tube over time. High-power triodes generally use a filament which serves as the cathode (a directly heated cathode) because the emission coating on indirectly heated cathodes is destroyed by the higher ion bombardment in power tubes. A thoriated tungsten filament is most often used, in which thorium in the tungsten forms a monolayer on the surface which increases electron emission. These generally run at higher temperatures than indirectly heated cathodes. The envelope of the tube is often made of more


title: Triode content: durable ceramic rather than glass, and all the materials have higher melting points to withstand higher heat levels produced. Tubes with anode power dissipation over several hundred watts are usually actively cooled; the anode, made of heavy copper, projects through the wall of the tube and is attached to a large external finned metal heat sink which is cooled by forced air or water. A type of low power triode for use at ultrahigh frequencies (UHF), the "lighthouse" tube, has a planar construction to reduce interelectrode capacitance and lead inductance, which gives it the appearance of a "lighthouse". The disk-shaped


title: Triode content: cathode, grid and plate form planes up the center of the tube - a little like a sandwich with spaces between the layers. The cathode at the bottom is attached to the tube's pins, but the grid and plate are brought out to low inductance terminals on the upper level of the tube: the grid to a metal ring halfway up, and the plate to a metal button at the top. These are one example of "disk seal" design. Smaller examples dispense with the octal pin base shown in the illustration and rely on contact rings for all connections, including


title: Triode content: heater and D.C. cathode. As well, high-frequency performance is limited by transit time: the time required for electrons to travel from cathode to anode. Transit time effects are complicated, but one simple effect is input conductance, also known as grid loading. At extreme high frequencies, electrons arriving at the grid may become out of phase with those departing towards the anode. This imbalance of charge causes the grid to exhibit a reactance that is much less than its low-frequency "open circuit" characteristic. Transit time effects are reduced by reduced spacings in the tube. Tubes such as the 416B (a Lighthouse


title: Triode content: design) and the 7768 (an all-ceramic miniaturised design) are specified for operation to 4 GHz. They feature greatly reduced grid-cathode spacings in the order of 0.1 mm. These greatly reduced grid spacings also give a much higher amplification factor than conventional axial designs. The 7768 has an amplification factor of 225, compared with 100 for the 6AV6 used in domestic radios and about the maximum possible for an axial design. Anode-grid capacitance is not especially low in these designs. The 6AV6 anode-grid capacitance is 2 picofarads (pF), the 7768 has a value of 1.7 pF. The close electrode spacing used


title: Triode content: in microwave tubes "increases" capacitances, but this increase is offset by their overall reduced dimensions compared to lower-frequency tubes. In the triode, electrons are released into the tube from the metal cathode by heating it, a process called thermionic emission. The cathode is heated red hot by a separate current flowing through a thin metal filament. In a few triodes, the filament itself is the cathode, while in most the filament heats a separate cathode electrode. Virtually all the air is removed from the tube, so the electrons can move freely. The negative electrons are attracted to the positively charged


title: Triode content: anode, and flow through the spaces between the grid wires to it, creating a current through the tube from cathode to anode. The magnitude of this current can be controlled by a voltage applied between the cathode and the grid. The grid acts like a gate for the electrons. A more negative voltage on the grid will repel some of the electrons, so fewer get through to the anode, reducing the anode current. A positive voltage on the grid will attract more electrons from the cathode, so more reach the anode, increasing the anode current. Therefore, a low power varying


title: Triode content: (AC) signal applied to the grid can control a much more powerful anode current, resulting in amplification. Variation in the grid voltage will cause identical proportional variations in the anode current. By placing a suitable load resistance in the anode circuit, the varying current will cause a varying voltage across the resistance which can be much larger than the input voltage variations, resulting in voltage gain. The triode is a normally "on" device; and current flows to the anode with zero voltage on the grid. The anode current is progressively reduced as the grid is made more negative with respect


title: Triode content: to the cathode. Usually a constant DC voltage ("bias") is applied to the grid to set the DC current through the tube, and the varying signal voltage is superimposed on it. A sufficiently negative voltage on the grid, usually around 3-5 volts in small tubes such as the 6AV6, but as much as –130 volts in early audio power devices such as the '45, will prevent any electrons from getting through to the anode, turning off the anode current. This is called the "cutoff voltage". Since below cutoff the anode current ceases to respond to the grid voltage, the voltage


title: Triode content: on the grid must remain above the cutoff voltage for faithful (linear) amplification. The triode is very similar in operation to the n-channel JFET; it is normally on, and progressively switched off as the grid/gate is pulled increasingly negative of the source/cathode. Cutoff voltage is equivalent to the JFET's pinch-off voltage (V)or VGS(off); the point at which current stops flowing entirely. Although S.G. Brown's Type G Telephone Relay (using a magnetic "earphone" mechanism driving a carbon microphone element) was able to give power amplification and had been in use as early as 1914, it was a purely mechanical device with


title: Triode content: limited frequency range and fidelity. It was suited only to a limited range of audio frequencies - essentially voice frequencies. The triode was the first non-mechanical device to provide power gain at audio and radio frequencies, and made radio practical. Triodes are used for amplifiers and oscillators. Many types are used only at low to moderate frequency and power levels. Large water-cooled triodes may be used as the final amplifier in radio transmitters, with ratings of thousands of watts. Specialized types of triode ("lighthouse" tubes, with low capacitance between elements) provide useful gain at microwave frequencies. Vacuum tubes are obsolete


title: Triode content: in mass-marketed consumer electronics, having been overtaken by less expensive transistor-based solid-state devices. However, more recently, vacuum tubes have been making somewhat of a comeback. Triodes continue to be used in certain high-power RF amplifiers and transmitters. While proponents of vacuum tubes claim their superiority in areas such as high-end and professional audio applications, empirical evidence shows that the solid-state MOSFET is virtually identical in performance. In triode datasheets, characteristics linking the anode current (I) to anode voltage (V) and grid voltage (V) are usually given. From here, a circuit designer can choose the operating point of the particular triode.


title: Triode content: In the example characteristic shown on the image, if an anode voltage V of 200V and a grid voltage bias of −1 volt are selected, a plate (anode) current of 2.25mA will be present (using the yellow curve on the graph). Changing the grid voltage will change the plate current; by suitable choice of a plate load resistor, amplification is obtained. In the class-A triode amplifier, an anode resistor would be connected between the anode and the positive voltage source. For example, with R = 10000 ohms, the voltage drop on it would be V = I × R =


title: Triode content: 22.5V if an anode current of I = 2.25mA is chosen. If the input voltage amplitude (at the grid) changes from −1.5V to −0.5V (difference of 1V), the anode current will change from 1.2 to 3.3mA (see image). This will change the resistor voltage drop from 12 to 33V (a difference of 21V). Since the grid voltage changes from −1.5V to −0.5V, and the anode resistor voltage drops from 12 to 33 V, an amplification of the signal resulted. The amplification factor is 21: output voltage amplitude divided by input voltage amplitude. Triode A triode is an electronic amplifying vacuum


title: "The History of the Decline and Fall of the Roman Empire" content: Gibbon challenged Church history by estimating far smaller numbers of Christian martyrs than had been traditionally accepted. The Church's version of its early history had rarely been questioned before. Gibbon, however, knew that modern Church writings were secondary sources, and he shunned them in favor of primary sources. Historian S.P. Foster says that Gibbon: Volume I was originally published in sections, as was common for large works at the time. The first two were well received and widely praised. The last quarto in Volume I, especially Chapters XV and XVI, was highly controversial, and Gibbon was attacked as a "paganist".


title: TRS-80 content: was provided with the Level II ROMS. Disk BASIC added the ability to perform disk I/O, and in some cases (NewDos/80, MultiDOS, DosPlus, LDOS) added powerful sorting, searching, full screen editing, and other features. Level II BASIC reserved some of these keywords and issued a "codice_11", suggesting a behind-the-scenes change of direction intervened between the creation of the Level II ROMs and the introduction of Disk BASIC. Microsoft also marketed an enhanced BASIC called Level III BASIC written by Bill Gates, that was supplied on a cassette tape. The cassette contains a "Cassette File" version on one side and a


title: "Age of Enlightenment" content: Grand Architect, the masonic terminology for the deistic divine being who created a scientifically ordered universe. German historian Reinhart Koselleck claimed: "On the Continent there were two social structures that left a decisive imprint on the Age of Enlightenment: the Republic of Letters and the Masonic lodges". Scottish professor Thomas Munck argues that "although the Masons did promote international and cross-social contacts which were essentially non-religious and broadly in agreement with enlightened values, they can hardly be described as a major radical or reformist network in their own right". Many of the Masons values seemed to greatly appeal to Enlightenment


title: "Tabasco sauce" content: Tabasco sauce Tabasco sauce is a brand of hot sauce made exclusively from tabasco peppers ("Capsicum frutescens" var. "tabasco"), vinegar, and salt. It is produced by McIlhenny Company of Avery Island, Louisiana. Although the name comes from the Mexican state of Tabasco, the sauce is a U.S. product produced by McIlhenny Company. According to company legend, Tabasco sauce was first produced in 1868 by Edmund McIlhenny, a Maryland-born former banker who moved to Louisiana around 1840. However, as Jeffrey Rothfeder's book "McIlhenny's Gold" points out, at least some of the self-promotional McIlhenny Company official history is fictitious. An October 10,


title: "Tabasco sauce" content: 2007 book review by Mark Robichaux in The Wall Street Journal, Oct. 10, 2007, quotes that book: "The story actually begins in the pre-Civil War era with a New Orleans plantation owner named Maunsel White, who was famous for the food served at his sumptuous dinner parties. Mr. White's table no doubt groaned with the region's varied fare — drawing inspiration from European, Caribbean and Cajun sources — but one of his favorite sauces was of his own devising, made from a pepper named for its origins in the Mexican state of Tabasco. White added the sauce to various dishes


title: "Tabasco sauce" content: and bottled it for his guests. Although the McIlhennys have tried to dismiss the possibility, it seems clear now that in 1849, a full two decades before Edmund McIlhenny professed to discover the Tabasco pepper, White was already growing Tabasco chilies on his plantation." Rothfeder cited a January 26, 1850 letter to the "New Orleans Daily Delta" newspaper crediting the slave-owning banker-politician Maunsel White as having introduced "Tobasco red pepper" (sic) to the southern United States and asserting that the McIlhenny sauce was at least inspired by White's recipe. Jean Andrews, in her book "Peppers: the Domesticated Capsicums," goes further


title: "Tabasco sauce" content: to declare — citing United States Circuit Court testimony from 1922 — that prior to his death in 1862, “White gave some [pepper] pods, along with his sauce recipe, to his friend Edmund McIlhenny, during a visit to White’s Deer Range Plantation.” To distribute his sauce, Edmund McIlhenny initially used discarded cologne bottles sourced from a New Orleans glass supplier. On his death in 1890, McIlhenny was succeeded by his eldest son, John Avery McIlhenny, who expanded and modernized the business, but resigned after only a few years in order to join Theodore Roosevelt's 1st US Volunteer Cavalry Regiment, the


title: "Tabasco sauce" content: Rough Riders. On John's departure, brother Edward Avery McIlhenny, a self-taught naturalist fresh from an Arctic adventure, assumed control of the company and also focused on expansion and modernization, running the business from 1898 until his death in 1949. Walter S. McIlhenny in turn succeeded his uncle Edward Avery McIlhenny, serving as president of McIlhenny Company from 1949 until his death in 1985. Edward McIlhenny Simmons then ran the company as president and CEO for several years,remaining as board chairman until his death in 2012. Paul McIlhenny became company president in 1998 and was chairman until his death in 2013.


title: "Tabasco sauce" content: In 2012, McIlhenny cousin Tony Simmons assumed the company's presidency and runs the company today. McIlhenny is one of just a few U.S. companies to have received a royal warrant of appointment that certifies the company as a supplier to Queen Elizabeth II. McIlhenny is one of the 850 companies around the world that have been officially designated as suppliers to the queen by such warrants. The warrant held is "Supplier of Tabasco Sauce HM The Queen – Master of the Household – Granted in 2009". Originally all peppers used in Tabasco sauce were grown on Avery Island. Today peppers


title: "Tabasco sauce" content: grown on the Island are used to produce seed stock, which is then shipped to foreign growers, primarily in Central and South America. More predictable weather and readily available farmland in these locales allow a constant year-round supply. This ensures the availability of peppers should severe weather or other problems occur at a particular growing location. Following company tradition, peppers are picked by hand. To ensure ripeness, pickers compare peppers to a little red stick ("le petit bâton rouge"); peppers that match the color of the stick are then introduced into the sauce production process. Peppers are ground into a


title: "Tabasco sauce" content: mash on the day of harvest and placed along with salt in white oak barrels (aging barrels previously used for Jack Daniel's Tennessee whiskey). To prepare the barrel, the inside of the barrel is de-charred (top layer of wood is removed), torched, and cleaned, to minimize the presence of any residual whiskey. The barrels are then used in warehouses on Avery Island for aging the mash. After aging for up to three years, the mash is strained to remove skins and seeds. The resulting liquid is then mixed with vinegar, stirred occasionally for a month, and then bottled as finished


title: "Tabasco sauce" content: sauce. Tabasco has released a Tabasco reserve edition with peppers aged for up to eight years, mixed with wine vinegar . Tabasco diamond reserve edition has been released as of 2018. This sauce consists of peppers that have been aged for up to fifteen years, then mixed with sparkling white wine vinegar. It becomes black instead of red. Much of the salt used in Tabasco production comes from an Avery Island salt mine, one of the largest in the U.S. In 2005, Avery Island was hit hard by Hurricane Rita. As a result, the family constructed a -high levee around


title: "Tabasco sauce" content: the low side of the factory and invested in back-up generators. Several sauces are produced under the "Tabasco" brand name, including jalapeño-based green, chipotle-based smoked, habanero, garlic, "sweet and spicy", and "Buffalo style" sauces. The habanero, chipotle, and garlic sauces include the tabasco peppers blended with other peppers, whereas the jalapeño variety does not include tabasco peppers. None of these sauces, however, has the three-year aging process the flagship product uses. The brand also produces a selection of Tabasco Chocolate. The flagship red variety of Tabasco pepper sauce measures 2,500–5,000 SHU on the Scoville scale. The habanero sauce is considerably


title: "Tabasco sauce" content: hotter, rating above 7,000+ Scoville units. The chipotle sauce adds chipotle pepper to the original sauce, measuring 1,500–2,500. The garlic variety, which blends milder peppers in with the tabasco peppers, rates 1,200–1,400 Scovilles, and the green pepper (jalapeño) sauce is even milder at 600–1,200 Scovilles. The Sweet and Spicy sauce is the mildest of all the sauces at only 100–600 Scoville units. In 2017, Tabasco released a limited edition sauce made with the Trinidad Moruga Scorpion pepper, which can reach up to 2,000,000 scoville units. Tabasco brand pepper sauce is sold in more than 185 countries and territories and is


title: "Tabasco sauce" content: packaged in 22 languages and dialects. The Tabasco bottle is still modeled after the cologne-style bottles used for the first batch of sauce in 1868. As many as 720,000 two-ounce (57 ml) bottles of Tabasco sauce are produced daily at the Tabasco factory on Avery Island. Bottles range from the common two-ounce and five-ounce (59 ml and 148 ml) bottles, up to a one US gallon-(3.8 liter) jug for food service businesses, and down to a 1/8-ounce (3.7 ml) miniature bottle. There are also 0.11-ounce portion control (PC) packets of Tabasco sauce. One-eighth-ounce bottles of Tabasco, bearing the presidential seal,


title: "Tabasco sauce" content: are served on Air Force One. The US military has included Tabasco sauce in Meals, Ready-to-Eat (MREs) since the 1980s. The Australian, British and Canadian armies also issue small bottles of Tabasco sauce in their rations. McIlhenny Company produces Tabasco brand products that contain pepper seasoning, including popcorn, nuts, olives, mayonnaise, mustard, steak sauce, Worcestershire sauce, soy sauce, teriyaki sauce, marinating sauce, barbecue sauce, chili sauce, pepper jelly, and Bloody Mary mix. McIlhenny Company also permits other brands to use and advertise Tabasco sauce as an ingredient in their products (a common marketing practice called "co-branding"), including Spam, Hormel chili,


title: "Tabasco sauce" content: Slim Jim beef sticks, Heinz ketchup, A1 steak sauce, Plochman's mustard, Cheez-It crackers, Lawry's salt, Zapp's potato chips, Heluva Good dip, and Vlasic pickles. The original red Tabasco sauce has a shelf life of five years when stored in a cool and dry place; other Tabasco flavors have shorter shelf lives. Tabasco appeared on the menu of NASA's space shuttle program and went into orbit on the shuttles. It was on Skylab and on the International Space Station and is popular with astronauts as a means of countering the bland food they frequently are provided in space. During the Vietnam


title: "Tabasco sauce" content: War, Brigadier General Walter S. McIlhenny issued "The Charlie Ration Cookbook". (Charlie ration was the name for the field meal then given to troops.) This cookbook came wrapped around a two-ounce bottle of Tabasco sauce in a camouflaged, water-resistant container. It instructed troops how to mix C-rations to make such meals as "Combat Canapés" or "Breast of Chicken under Bullets." Soldiers also requested their families to send them Tabasco sauce in "care packages" from home. During the 1980s, the U.S. military began to include miniature bottles of Tabasco sauce in its MREs. Eventually, miniature bottles of Tabasco sauce were included


title: "Tabasco sauce" content: in two-thirds of all MRE menus. During the same period, McIlhenny Company issued a new military-oriented cookbook using characters from the comic strip "Beetle Bailey". Titled "The Unofficial MRE Cookbook", it was offered free of charge to U.S. troops. The Tabasco bottle is an original design and has remained almost unchanged up to the present. In 1894 composer George W. Chadwick composed the Burlesque Opera of Tabasco, a musical comedy that conductor Paul Mauffray revived in 2018 with support from McIlhenny Company. Tabasco has appeared in many movies and cartoons, as well as on television. Some appearances date as far


title: "Tabasco sauce" content: back as the Our Gang short "Birthday Blues" in 1932 and Charlie Chaplin's "Modern Times" in 1936. The bottle also graced the side of Darrell Waltrip's race car for a brief period. In "", the saloon bartender uses Tabasco as an ingredient for an instant hangover cure he calls "wake-up juice". Tabasco sauce Tabasco sauce is a brand of hot sauce made exclusively from tabasco peppers ("Capsicum frutescens" var. "tabasco"), vinegar, and salt. It is produced by McIlhenny Company of Avery Island, Louisiana. Although the name comes from the Mexican state of Tabasco, the sauce is a U.S. product produced


title: Talc content: Talc Talc or talcum is a clay mineral composed of hydrated magnesium silicate with the chemical formula HMg(SiO) or MgSiO(OH). In loose form, it is (in ratio with or without corn starch) one of the most widely used substances known as baby powder. It occurs as foliated to fibrous masses, and in an exceptionally rare crystal form. It has a perfect basal cleavage, and the folia are not elastic, although slightly flexible. The Mohs scale of mineral hardness, based on scratch hardness comparison, defines value 1 as the hardness of talc. Talc can easily be scratched by a fingernail. Talc


title: Talc content: has a specific gravity of 2.5–2.8, a clear or dusty luster, and is translucent to opaque. Talc is not soluble in water, but is slightly soluble in dilute mineral acids. Its colour ranges from white to grey or green and it has a distinctly greasy feel. Its streak is white. Soapstone is a metamorphic rock composed predominantly of talc. The word "talc" derives from Medieval Latin "talcum", which in turn originates from "ṭalq" which in turn was derived from "tālk". In ancient times, the word was used for various related minerals, including talc, mica, and selenite. Talc is a metamorphic


title: Talc content: mineral that results from the metamorphism of magnesian minerals such as serpentine, pyroxene, amphibole, and olivine, in the presence of carbon dioxide and water. This is known as "talc carbonation" or "steatization" and produces a suite of rocks known as talc carbonates. Talc is primarily formed by hydration and carbonation by this reaction: Talc can also be formed via a reaction between dolomite and silica, which is typical of skarnification of dolomites by silica-flooding in contact metamorphic aureoles: Talc can also be formed from magnesian chlorite and quartz in blueschist and eclogite metamorphism by the following metamorphic reaction: In this


title: Talc content: reaction, the ratio of talc and kyanite depends on aluminium content, with more aluminous rocks favoring production of kyanite. This is typically associated with high-pressure, low-temperature minerals such as phengite, garnet, and glaucophane within the lower blueschist facies. Such rocks are typically white, friable, and fibrous, and are known as whiteschist. Talc is a trioctahedral layered mineral; its structure is similar to pyrophyllite, but with magnesium in the octahedral sites of the composite layers. Talc is a common metamorphic mineral in metamorphic belts that contain ultramafic rocks, such as soapstone (a high-talc rock), and within whiteschist and blueschist metamorphic terranes.


title: Talc content: Prime examples of whiteschists include the Franciscan Metamorphic Belt of the western United States, the western European Alps especially in Italy, certain areas of the Musgrave Block, and some collisional orogens such as the Himalayas, which stretch along Pakistan, India, Nepal, and Bhutan. Talc carbonate ultramafics are typical of many areas of the Archaean cratons, notably the komatiite belts of the Yilgarn Craton in Western Australia. Talc-carbonate ultramafics are also known from the Lachlan Fold Belt, eastern Australia, from Brazil, the Guiana Shield, and from the ophiolite belts of Turkey, Oman, and the Middle East. China is the key world


title: Talc content: talc and steatite producing country with an output of about 2.2M tonnes(2016), which accounts for 30% of total global output. The other major producers are Brazil (12%), India (11%), the U.S. (9%), France (6%), Finland (4%), Italy, Russia, Canada, and Austria (2%, each). Notable economic talc occurrences include the Mount Seabrook talc mine, Western Australia, formed upon a polydeformed, layered ultramafic intrusion. The France-based Luzenac Group is the world's largest supplier of mined talc. Its largest talc mine at Trimouns near Luzenac in southern France produces 400,000 tonnes of talc per year. Extraction in disputed areas of Nangarhar province, Afghanistan,


title: Talc content: has led the international monitoring group Global Witness to declare talc to be a conflict mineral, as the profits are used to fund the armed confrontation between the Taliban and Islamic State. Talc is used in many industries, including paper making, plastic, paint and coatings, rubber, food, electric cable, pharmaceuticals, cosmetics, and ceramics. A coarse grayish-green high-talc rock is soapstone or steatite, used for stoves, sinks, electrical switchboards, crayons, soap, etc. It is often used for surfaces of laboratory table tops and electrical switchboards because of its resistance to heat, electricity and acids. Talc finds use as a cosmetic (talcum


title: Talc content: powder), as a lubricant, and as a filler in paper manufacture. It is used to coat the insides of inner tubes and rubber gloves during manufacture to keep the surfaces from sticking. Talc, with heavy refinement, has been used in baby powder, an astringent powder used to prevent diaper rash. The American Academy of Pediatrics recommends that parents not use baby powder because it poses a risk of respiratory problems, including breathing trouble and serious lung damage if the baby inhales it. The small size of the particles makes it difficult to keep them out of the air while applying


title: Talc content: the powder. Zinc oxide-based ointments are a much safer alternative. It is also often used in basketball to keep a player's hands dry. Most tailor's chalk, or French chalk, is talc, as is the chalk often used for welding or metalworking. Talc is also used as food additive or in pharmaceutical products as a glidant. In medicine, talc is used as a pleurodesis agent to prevent recurrent pleural effusion or pneumothorax. In the European Union, the additive number is E553b. Due to its low shear strength, talc is one of the oldest known solid lubricants. Also a limited use of


title: Talc content: talc as friction-reducing additive in lubricating oils is made. Talc is widely used in the ceramics industry in both bodies and glazes. In low-fire art-ware bodies, it imparts whiteness and increases thermal expansion to resist crazing. In stonewares, small percentages of talc are used to flux the body and therefore improve strength and vitrification. It is a source of MgO flux in high-temperature glazes (to control melting temperature). It is also employed as a matting agent in earthenware glazes and can be used to produce magnesia mattes at high temperatures. ISO standard for quality (ISO 3262) Patents are pending on


title: Talc content: the use of magnesium silicate as a cement substitute. Its production requirements are less energy-intensive than ordinary Portland cement (at a heating requirement of around 650 °C for talc compared to 1500 °C for limestone to produce Portland cement), while it absorbs far more carbon dioxide as it hardens. This results in a negative carbon footprint overall, as the cement substitute removes 0.6 tonnes of CO per tonne used. This contrasts with a positive carbon footprint of 0.4 tonne per tonne of conventional cement. Talc is used in the production of the materials that are widely used in the building


title: Talc content: interiors such as base content paints in wall coatings. Other areas that use talc to a great extent are organic agriculture, food industry, cosmetics, and hygiene products such as baby powder and detergent powder. Talc is sometimes used as an adulterant to illegal heroin, to expand volume and weight and thereby increase its street value. With intravenous use, it may lead to pulmonary talcosis, a granulomatous inflammation in the lungs. Sterile talc powder (NDC 63256-200-05) is a sclerosing agent used in the procedure of pleurodesis. This can be helpful as a cancer treatment to prevent pleural effusions (an abnormal collection


title: Talc content: of fluid in the space between the lungs and the thoracic wall). It is inserted into the space via a chest tube, causing it to close up, so fluid cannot collect there. The finished product has been sterilized by gamma irradiation. Talc powder is a household item, sold globally for use in personal hygiene and cosmetics. Suspicions have been raised that its use contributes to certain types of disease, mainly cancers of the ovaries and lungs. It is classified as a group 3 agent in the IARC listing. Reviews by Cancer Research UK and the American Cancer Society conclude that


title: Talc content: some studies have found a link, but other studies have not. The studies discuss pulmonary issues, lung cancer, and ovarian cancer. One of these, published in 1993, was a US National Toxicology Program report, which found that cosmetic grade talc containing no asbestos-like fibres was correlated with tumor formation in rats forced to inhale talc for 6 hours a day, five days a week over at least 113 weeks. A 1971 paper found particles of talc embedded in 75% of the ovarian tumors studied. Research published in 1995 and 2000 concluded that it was plausible that talc could cause ovarian


title: Talc content: cancer, but no conclusive evidence was shown. In the United States, the Occupational Safety and Health Administration and National Institute for Occupational Safety and Health have set occupational exposure limits to respirable talc dusts at 2 mg/m over an eight-hour workday. At levels of 1000 mg/m, inhalation of talc is considered immediately dangerous to life and health. The United States Food and Drug Administration considers talc (magnesium silicate) to be generally recognized as safe (GRAS) for use as an anticaking agent in table salt in concentrations smaller than 2%. One particular issue with commercial use of talc is its frequent


title: Talc content: co-location in underground deposits with asbestos ore. Stringent quality control since 1976, including separating cosmetic- and food-grade talc from "industrial" grade talc, has eliminated this issue, but it remains a potential hazard requiring mitigation in the mining and processing of talc. A 2010 US FDA survey failed to find asbestos in a variety of talc-containing products. A 2018 Reuters investigation has asserted that pharmaceuticals company Johnson & Johnson knew for decades that there was asbestos in its baby powder. In 2006 the International Agency for Research on Cancer classified talcum powder as a possible human carcinogen if used in the


title: Talc content: female genital area. Yet no federal agency in the US acted to remove talcum powder from the market or add warnings. In February 2016, as the result of a lawsuit against Johnson & Johnson (J&J), a St. Louis jury awarded $72 million to the family of an Alabama woman who died from ovarian cancer. The family claimed that the use of talcum powder was responsible for her cancer. In May 2016, a South Dakota woman was awarded $55 million as the result of another lawsuit against J&J. The woman had used Johnson & Johnson's Baby Powder for more than 35


title: Talc content: years before being diagnosed with ovarian cancer in 2011. In October 2016, a St. Louis jury awarded $70.1 million to a Californian woman with ovarian cancer who had used Johnson's Baby Powder for 45 years. In August 2017, a Los Angeles jury awarded $417 million to a Californian woman, Eva Echeverria, who developed ovarian cancer as a "proximate result of the unreasonably dangerous and defective nature of talcum powder", her lawsuit against Johnson & Johnson stated. At least 1,200 to 2,000 other talcum powder-related lawsuits are pending. On 20 October 2017, Los Angeles Superior Court judge Maren Nelson, dismissed the


title: Talc content: verdict of Eva Echeverria against Johnson & Johnson and its talc-containing consumer products for causing cancer. The judge stated that Eva Echeverria proved there is "an ongoing debate in the scientific and medical community about whether talc more probably than not causes ovarian cancer and thus (gives) rise to a duty to warn", but not enough to sustain the jury's imposition of liability against Johnson & Johnson stated, and concluded that Echeverria did not adequately establish that talc causes ovarian cancer. In July 2018, a court in St. Louis awarded a $4.7bn claim ($4.14bn in punitive damages and $550m in


title: Talc content: compensatory damages) against J&J, concluding that the company had suppressed evidence of asbestos in its products for more than four decades. Talc Talc or talcum is a clay mineral composed of hydrated magnesium silicate with the chemical formula HMg(SiO) or MgSiO(OH). In loose form, it is (in ratio with or without corn starch) one of the most widely used substances known as baby powder. It occurs as foliated to fibrous masses, and in an exceptionally rare crystal form. It has a perfect basal cleavage, and the folia are not elastic, although slightly flexible. The Mohs scale of mineral hardness, based


title: Truck content: Truck A truck or lorry is a motor vehicle designed to transport cargo. Trucks vary greatly in size, power, and configuration; smaller varieties may be mechanically similar to some automobiles. Commercial trucks can be very large and powerful, and may be configured to mount specialized equipment, such as in the case of fire trucks, concrete mixers, and suction excavators. Modern trucks are largely powered by diesel engines, although small to medium size trucks with gasoline engines exist in the US, Canada, and Mexico. In the European Union, vehicles with a gross combination mass of up to are known as light