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A vertical declining dial (south west) in Eyam Derbyshire England. 53°17′03″N 1°40′29″W / 53.28420, -1.67471

A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style (a thin rod or a sharp, straight edge) onto a flat surface marked with lines indicating the hours of the day. As the sun moves across the sky, the shadow-edge progressively aligns with different hour-lines on the plate. Such designs rely on the style being aligned with the axis of the Earth's rotation. Hence, if such a sundial is to tell the correct time, the style must point towards true North (not magnetic North) and the style's angle with horizontal must equal the sundial's geographical latitude. However, many sundials do not fit this description, and operate on different principles. Look up sundial in Wiktionary, the free dictionary. ... Image File history File links Gnome-globe. ... Northern hemisphere highlighted in yellow. ... Eyam Hall. ... Derbyshire is a county in the East Midlands of England. ... For other uses, see England (disambiguation). ... Sol redirects here. ... Shadows on pavement A shadow is a region of darkness where light is blocked. ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This is about the geographic meaning of North Pole. ... This article is about the geographical term. ...

Introduction

Sundials can be categorized in several ways.^[1] First, some sundials use a spot of light, or a line of light, to indicate the time, where others use the edge or tip of a shadow. In the former case, the spot of light may be formed by allowing the sun's rays through a small hole or reflecting them from a small circular mirror; a line of light may be formed by allowing the rays through a thin slit or focusing them through a cylindrical lens. In the other case, the shadow-casting object — the sundial's gnomon — may be a thin rod, or any object with a sharp tip or a straight edge. Second, sundials employ many types of gnomon. The gnomon may be fixed or moved according to the season; it may be oriented vertically, horizontally, aligned with the Earth's axis, or oriented in an altogether different direction determined by mathematics. Third, sundials may use many types of surfaces to receive the spot or line of light, the shadow-tip or shadow-edge. Planes are the most common surface, but partial spheres, cylinders, cones and even more complicated shapes have been used for greater accuracy or intriguing aesthetics. Fourth, sundials differ in their portability and their need of orientation. The installation of many dials requires knowing the local latitude, the precise vertical direction (e.g., by a level or plumb-bob), and the direction to true North. In contrast, other dials are self-aligning; for example, two dials that operate on different principles, such as a horizontal and analemmatic dial, may be mounted together on one plate, such that their times agree only when the plate is aligned properly. Sundials were an important aspect of the Greek and egypitan civilizations up to the 16th century. In certain applications, it is advantages to focus light (or image) along one direction but not the direction that is perpendicular to this direction. ... The cantilever spar of this cable-stay bridge, the Sundial Bridge at Turtle Bay, forms the gnomon of a large garden sundial The gnomon is the part of a sundial that casts the shadow. ... This article is about the mathematical construct. ... For other uses, see Sphere (disambiguation). ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... This article is about the geometric object, for other uses see Cone. ... This article is about the geographical term. ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

Sundials indicate the local solar time, unless otherwise corrected. To obtain the standard clock time, three types of corrections need to be made. First, the solar time needs to be corrected for the longitude of the sundial relative to the longitude at which the official time zone is defined. For example, a sundial located west of Greenwich, England but within the same time-zone, shows an earlier time than the official time; it will show "noon" after the official noon has passed, since the sun passes overhead later, since the sundial is further in the west. This correction is often made by rotating the hour-lines by an angle equaling the difference in longitudes. Second, the practice of daylight saving time shifts the official time away from solar time by an hour or, in rare cases, by another amount. This correction is usually made by numbering the hour-lines with two sets of numbers. Third, the orbit of the Earth is not perfectly circular and its rotational axis not perfectly perpendicular to its orbit, which together produce small variations in the sundial time throughout the year. This correction — which may be as great as 15 minutes — is described by the equation of time. A more sophisticated sundial design is required to incorporate this correction automatically; alternatively, a small plaque can be affixed to the sundial giving the offsets at various times of the year. Solar time is based on the idea that when the sun reaches its highest point in the sky, it is noon. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... This article is about Greenwich in England. ... For other uses, see England (disambiguation). ... Although DST is common in Europe and North America, most of the worlds people do not use it. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ...

Apparent motion of the Sun

Top view of an equatorial sundial. The hour lines are spaced equally about the circle, and the shadow of the gnomon (a thin cylindrical rod) rotates uniformly. The height of the gnomon is 5/12 the outer radius of the dial. This animation depicts the motion of the shadow from 3 a.m. to 9 p.m. on mid-summer's day, when the sun is at its highest declination (roughly 23.5°). Sunset and sunrise occur at 3am and 9pm, respectively, on that day at geographical latitudes near 57.5°, roughly the latitude of Aberdeen or Gothenburg.

The principles of sundials can be understood most easily from an ancient model of the Sun's motion. Science has established that the Earth rotates on its axis, and revolves in an elliptic orbit about the Sun; however, meticulous astronomical observations and physics experiments were required to establish this. For navigational and sundial purposes, it is an excellent approximation to assume that the Sun revolves around a stationary Earth on the celestial sphere, which rotates every 23 hours and 56 minutes about its celestial axis, the line connecting the celestial poles. Since the celestial axis is aligned with the axis about which the Earth rotates, its angle with the local horizontal equals the local geographical latitude. Unlike the fixed stars, the Sun changes its position on the celestial sphere, being at positive declination in summer, at negative declination in winter, and having exactly zero declination (i.e., being on the celestial equator) at the equinoxes. The path of the Sun on the celestial sphere is known as the ecliptic, which passes through the twelve constellations of the zodiac in the course of a year. For other uses, see Aberdeen (disambiguation). ... For other uses, see Gothenburg (disambiguation). ... Sol redirects here. ... The celestial sphere is divided by the celestial equator. ... The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... This article is about the geographical term. ... The fixed stars (from the Latin stellae fixae) are celestial objects that do not seem to move in relation to the other stars of the night sky. ... In astronomy, declination (abbrev. ... The celestial equator is a great circle on the imaginary celestial sphere, which could be constructed by inflating the Earths equator until it intersects with said sphere. ... For other uses, see Equinox (disambiguation). ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... For other uses, see Zodiac (disambiguation). ...

This model of the Sun's motion helps to understand the principles of sundials. If the shadow-casting gnomon is aligned with the celestial poles, its shadow will revolve at a constant rate, and this rotation will not change with the seasons. This is perhaps the most commonly seen design and, in such cases, the same set of hour lines may be used throughout the year. The hour-lines will be spaced uniformly if the surface receiving the shadow is either perpendicular (as in the equatorial sundial) or circularly symmetric about the gnomon (as in the armillary sphere). In other cases, the hour-lines are not spaced evenly, even though the shadow is rotating uniformly. If the gnomon is not aligned with the celestial poles, even its shadow will not rotate uniformly, and the hour lines must be corrected accordingly. The rays of light that graze the tip of a gnomon, or which pass through a small hole, or which reflect from a small mirror, trace out a cone that is aligned with the celestial poles. The corresponding light-spot or shadow-tip, if it falls onto a flat surface, will trace out a conic section, such as a hyperbola, ellipse or (at the North or South Poles) a circle. This conic section is the intersection of the cone of light rays with the flat surface. This cone and its conic section change with the seasons, as the Sun's declination changes; hence, sundials that follow the motion of such light-spots or shadow-tips often have different hour-lines for different times of the year, as seen in shepherd's dials, sundial rings, and vertical gnomons such as obelisks. Alternatively, sundials may change the angle and/or position of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial. The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... This article is about the geometric object, for other uses see Cone. ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... Elliptical redirects here. ... This article is about the shape and mathematical concept of circle. ...

Terminology

The 'shadow-maker' of the sundial is called a gnomon.^[2] The linear feature that casts the shadow from which the time can be read is often called a style.^[3][2] On a standard garden (horizontal) sundial, this line is the top edge of the gnomon. The style should be parallel to the Earth's axis of rotation, and point to the celestial pole.

The sun casts a shadow from the gnomon or style to a surface called the dial face or dial plate (often shortened to face).

The line on the dial plate perpendicularly beneath the style is called the substyle^[2], that is below the style. The angle the style makes perpendicularly with the dial plate is called the substyle height, an unusual use of the word height to mean an angle. On many wall dials, the substyle is not the same as the noon line. The angle, on the dial plate, the noon line makes to the substyle is called the substyle distance, an unusual use of the word distance to mean an angle.

Some sundials indicate both the time and the date by the shadow of a particular point on the gnomon. That point is called the nodus. The nodus may be the tip of a gnomon with an arbitrary (usually horizontal or vertical) orientation^[2]. A few sundials have both a style and a nodus, with the nodus in the form of a small sphere or a notch on a polar-pointing style.

In addition to the Hour line, the face of the dial can contain further information , such as the horizon, the equator and the tropics. These lines are referred to as the dial furniture.

It is traditional for a sundial to have a motto. The motto is usually in the form of an epigram, and often represents the sense of humor of the dial maker.^[4] For other uses, see Motto (disambiguation). ...

A dial is said to be equiangular if its hour-lines are straight and spaced equally. Most equiangular sundials have a fixed gnomon style aligned with the Earth's rotational axis, as well as a shadow-receiving surface that is symmetrical about that axis; examples include the equatorial dial, the equatorial bow, the armillary sphere, the cylindrical dial and the conical dial. However, some other designs are equiangular, such as the Lambert dial.

Casting light instead of shadow

Benoy Sun Clock showing 6:00pm - 18.00 hours

Most of the sundials described below use shadow to indicate time, whether it be the shadow-edge of the style, or the shadow-point of the nodus. However, light may be used in equivalent ways. Nodus-based sundials may use a small hole or mirror to isolate a single ray of light; the former are sometimes called aperture dials. The oldest example is perhaps the antiborean sundial (antiboreum), a spherical nodus-based sundial that faces true North; a ray of sunlight enters from the South through a small hole located at the sphere's pole and falls on the hour and date lines inscribed within the sphere, which resemble lines of longitude and latitude, respectively, on a globe.^[5] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

Light may also be used to replace the shadow-edge of a gnomon. Whereas the style usually casts a sheet of shadow, an equivalent sheet of light can be created by allowing the sun's rays through a thin slit, reflecting them from a long, slim mirror (usually half-cylindrical), or focusing them through a cylindrical lens. For illustration, the Benoy Dial uses a cylindrical lens to create a sheet of light, which falls as a line on the dial surface. Benoy dials can be seen throughout Great Britain, such as^[6] In certain applications, it is advantages to focus light (or image) along one direction but not the direction that is perpendicular to this direction. ...

• Carnfunnock Country Park Antrim Northern Ireland
• Upton Hall British Horological Institute Newark-on-Trent Nottinghamshire UK
• Within the collections of St Edmundsbury Heritage Service Bury St Edmunds^[7] UK
• Longleat Warminster Wiltshire UK
• Jodrell Bank Science Centre and Arboretum
• Birmingham Botanical Gardens Edgbaston UK
• Science Museum UK - (inventory number 1975-318)

Any celestial body, such as a star or the Sun, appears to rotate about the celestial axis over the course of a 24-hour day. Over the course of the year, the stars keep their position on the celestial sphere, but the Sun and planets change their positions. In particular, the Sun appears to move through the zodiac constellations.

Antrim in Northern Ireland may refer to Antrim town. ... Northern Ireland (Irish: , Ulster Scots: Norlin Airlann) is a constituent country of the United Kingdom lying in the northeast of the island of Ireland, covering 5,459 square miles (14,139 km², about a sixth of the islands total area). ... The British Horological Institute (also known as the BHI) is the representative body of the horological industry in the United Kingdom. ... Newark (also Newark-on-Trent) is a town in Nottinghamshire, located on the River Trent. ... Nottinghamshire (abbreviated Notts) is an English county in the East Midlands, which borders South Yorkshire, Lincolnshire, Leicestershire and Derbyshire. ... , Bury St Edmunds is a town in the county of Suffolk, England, and was formerly the county town of West Suffolk. ... This article is about the English town. ... Not to be confused with Wilshire. ... The 76m Lovell Telescope at Jodrell Bank Observatory. ... This article is about a type of botanical garden. ... The Birmingham Botanical Gardens in Birmingham, England were designed in 1829 and opened in 1832. ... Edgbaston constituency shown within Birmingham Edgbaston is an area and ward in the city of Birmingham in England. ... Image:Science Museum bernoulli exhibit. ... This article is about the astronomical object. ... Sol redirects here. ... A planet (from the Greek πλανήτης, planetes or wanderers) is a body of considerable mass that orbits a star and that produces very little or no energy through nuclear fusion. ... For other uses, see Zodiac (disambiguation). ...

Sundials with fixed axial gnomon

The most commonly observed sundials are those in which the shadow-casting style is fixed in position and aligned with the Earth's rotational axis, being oriented with true North and South, and making an angle with the horizontal equal to the geographical latitude. This axis is aligned with the celestial poles, which is closely, but not perfectly, aligned with the (present) pole star Polaris. For illustration, the celestial axis points vertically at the true North Pole, where it points horizontally on the equator. At Jaipur, a famous location for sundials, the gnomons of such sundials are raised 26°55" above horizontal, since that is the local latitude. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ... The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... For other uses of the words Pole star and Polestar see Polestar (disambiguation). ... -1... For other uses, see North Pole (disambiguation). ... World map showing the equator in red For other uses, see Equator (disambiguation). ... , Jaipur   (Hindi: जयपुर), also popularly known as the pink city, is the capital of Rajasthan state, India. ...

The Jantar Mantar in Jaipur is a famous collection of sundials; photographed from the largest, 27-meter sundial, the Samrat Yantra (the Supreme Instrument).26°55′29″N 75°49′29″E / 26.9247, 75.8248

On any given day, the Sun appears to rotate uniformly about this axis, at about 15° per hour, making a full circuit (360°) in 24 hours. A linear gnomon aligned with this axis will cast a sheet of shadow (a half-plane) that, falling opposite to the Sun, likewise rotates about the celestial axis at 15° per hour. The shadow is seen by falling on a receiving surface that is usually flat, but which may be spherical, cylindrical, conical or of other shapes. If the shadow falls on a surface that is symmetrical about the celestial axis (as in an armillary sphere, or an equatorial dial), the surface-shadow likewise moves uniformly; the hour-lines on the sundial are equally spaced. However, if the receiving surface is not symmetrical (as in most horizontal sundials), the surface shadow generally moves non-uniformly and the hour-lines are not equally spaced; one exception is the Lambert dial described below. Image File history File linksMetadata Download high resolution version (1984x1248, 443 KB) I, Knowledge Seeker, took this photograph on December 26, 2002. ... Image File history File linksMetadata Download high resolution version (1984x1248, 443 KB) I, Knowledge Seeker, took this photograph on December 26, 2002. ... Tourists gather at Jantar Mantar The Jantar Mantar is a collection of architectural astronomical instruments, built by Maharaja Jai Singh II at his then new capital of Jaipur between 1727 and 1733. ... , Jaipur   (Hindi: जयपुर), also popularly known as the pink city, is the capital of Rajasthan state, India. ... This article is about the unit of length. ...

Some types of sundials are designed with a fixed gnomon that is not aligned with the celestial poles, such as a vertical obelisk. Such sundials are covered below under the section, "Nodus-based sundials".

Equatorial sundials

An equatorial sundial in the Forbidden City, Beijing. 39°54′57″N 116°23′25″E / 39.9157, 116.3904 The gnomon points true North and its angle with horizontal equals the local latitude. Closer inspection of the full-size image reveals the "spider-web" of date rings and hour-lines.

The distinguishing characteristic of the equatorial dial (also called the equinoctial dial) is the planar surface that receives the shadow, which is exactly perpendicular to the gnomon's style.^[8] This plane is called equatorial, because it is parallel to the equator of the Earth and of the celestial sphere. If the gnomon is fixed and aligned with the Earth's rotational axis, the sun's apparent rotation about the Earth casts a uniformly rotating sheet of shadow from the gnomon; this produces a uniformly rotating line of shadow on the equatorial plane. Since the sun rotates 360° in 24 hours, the hour-lines on an equatorial dial are all spaced 15° apart (360/24). The uniformity of their spacing makes this type of sundial easy to construct. Both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. Near the equinoxes in spring and autumn, the sun moves on a circle that is nearly the same as the equatorial plane; hence, no clear shadow is produced on the equatorial dial at those times of year, a drawback of the design. Download high resolution version (1632x1232, 654 KB)Sundial, Forbidden City File links The following pages link to this file: Sundial Categories: GFDL images ... Download high resolution version (1632x1232, 654 KB)Sundial, Forbidden City File links The following pages link to this file: Sundial Categories: GFDL images ... For other uses, see Forbidden City (disambiguation). ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ... Download high resolution version (1632x1232, 654 KB)Sundial, Forbidden City File links The following pages link to this file: Sundial Categories: GFDL images ... For other uses, see Equinox (disambiguation). ...

A nodus is sometimes added to equatorial sundials, which allows the sundial to tell the time of year. On any given day, the shadow of the nodus moves on a circle on the equatorial plane, and the radius of the circle measures the declination of the sun. The ends of the gnomon bar may be used as the nodus, or some feature along its length. An ancient variant of the equatorial sundial has only a nodus (no style) and the concentric circular hour-lines are arranged to resemble a spider-web.^[9] In astronomy, declination (abbrev. ...

Horizontal sundial in thyme garden (Minnesota.)June 17, 2007 at 12:21. 44°51′39.3″N, 93°36′58.4″W

Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution (2576 × 1932 pixel, file size: 1. ... Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution (2576 × 1932 pixel, file size: 1. ... Species About 350 species, including: Thymus adamovicii Thymus altaicus Thymus amurensis Thymus bracteosus Thymus broussonetii Thymus caespititius Thymus camphoratus Thymus capitatus Thymus capitellatus Thymus camphoratus Thymus carnosus Thymus cephalotus Thymus cherlerioides Thymus ciliatus Thymus cilicicus Thymus cimicinus Thymus comosus Thymus comptus Thymus curtus Thymus disjunctus Thymus doerfleri Thymus glabrescens Thymus... Capital Saint Paul Largest city Minneapolis Largest metro area Minneapolis-St. ... is the 168th day of the year (169th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ...

Horizontal sundials

In the horizontal sundial (also called a garden sundial), the plane that receives the shadow is aligned horizontally, rather than being perpendicular to the style as in the equatorial dial.^[10] Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule^[11]

where λ is the sundial's geographical latitude, θ is the angle between a given hour-line and the noon hour-line (which always points towards true North) on the plane, and t is the number of hours before or after noon. For example, the angle θ of the 3pm hour-line would equal the arctangent of sin(λ), since tan(45°) = 1. When λ equals 90° (at the North Pole), the horizontal sundial becomes an equatorial sundial; the style points straight up (vertically), and the horizontal plane is aligned with the equatorial place; the hour-line formula becomes θ = 15° × t, as for an equatorial dial. However, a horizontal sundial is impractical on the Earth's equator, where λ equals 0°, the style would lie flat in the plane and cast no shadow. This article is about the geographical term. ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. ... Sine redirects here. ... For other uses, see North Pole (disambiguation). ... World map showing the equator in red For other uses, see Equator (disambiguation). ...

The chief advantages of the horizontal sundial are that it is easy to read, and the sun lights the face throughout the year. All the hour-lines intersect at the point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true North and its angle with the horizontal equals the sundial's geographical latitude λ. A sundial designed for one latitude can be used in another latitude, provided that the sundial is tilted upwards or downwards by an angle equal to the difference in latitude. For example, a sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis.^[12] True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ...

Vertical sundials

Two vertical dials at Houghton Hall Norfolk UK 52°49′39″N 0°39′27″E / 52.827469, 0.657616. The left and right dials face South and East, respectively. Both styles are parallel, their angle to the horizontal equaling the latitude. The East-facing dial is a polar dial with parallel hour-lines, the dial-face being parallel to the style.

In the common vertical dial, the shadow-receiving plane is aligned vertically; as usual, the gnomon's style is aligned with the Earth's axis of rotation.^[13] As in the horizontal dial, the line of shadow does not move uniformly on the face; the sundial is not equiangular. If the face of the vertical dial points directly south, the angle of the hour-lines is instead described by the formula^[14] Image File history File links Metadata Size of this preview: 800 × 362 pixelsFull resolution (1040 × 470 pixels, file size: 156 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 800 × 362 pixelsFull resolution (1040 × 470 pixels, file size: 156 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... The facade of Houghton Hall from Colen Campbells Vitruvius Britannicus. ... Norfolk (pronounced ) is a low-lying county in East Anglia in the east of southern England. ... The United Kingdom of Great Britain and Northern Ireland is a country in western Europe, and member of the Commonwealth of Nations, the G8, the European Union, and NATO. Usually known simply as the United Kingdom, the UK, or (inaccurately) as Great Britain or Britain, the UK has four constituent...

where λ is the sundial's geographical latitude, θ is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle θ of the 3pm hour-line would equal the arctangent of cos(λ), since tan(45°) = 1. Interestingly, the shadow moves counter-clockwise on a South-facing vertical dial, whereas it runs clockwise on horizontal and equatorial dials. This article is about the geographical term. ... In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. ... Sine redirects here. ...

An East-facing polar dial in Doubs, France 47°30′N 6°48′E / 47.50, 6.80. It receives no afternoon sunlight; the hour-lines near noon are spaced widely, as the sun's rays become parallel to the dial's face.

Dials that face due South, North, East or West are called vertical direct dials.^[15] If the face of a vertical dial does not face due South, the hours of sunlight that the dial receives may be limited. For example, a vertical dial that faces due East will tell time only in the morning hours; in the afternoon, the sun does not shine on its face. Vertical dials that face due East or West are polar dials, which will be described below. Vertical dials that face North are rarely used, since they tell time only before 6am or after 6pm, by local solar time. For non-direct vertical dials — those that face in non-cardinal directions — the mathematics of arranging the hour-lines becomes more complicated, and is often done by observation; such dials are said to be declining dials.^[16] Doubs is a département in eastern France named after the Doubs River. ...

Vertical dials are commonly mounted on the walls of buildings, such as town-halls, cupolas and church-towers, where they are easy to see from far away. In some cases, vertical dials are placed on all four sides of a rectangular tower, providing the time throughout the day. The face may be painted on the wall, or displayed in inlaid stone; the gnomon is often a single metal bar, or a tripod of metal bars for rigidity. If the wall of the building does not face in a cardinal direction such as due South, the hour lines must be corrected. Since the gnomon's style is aligned with the Earth's rotation axis, it points true North and its angle with the horizontal equals the sundial's geographical latitude; consequently, its angle with the vertical face of the dial equals the colatitude, or 90°-latitude. Cupola of St Peters Basilica, Rome In architecture, a cupola consists of a dome-shaped ornamental structure located on top of a larger roof or dome, often used as a lookout or to admit light and provide ventilation. ... True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ... In spherical coordinates, colatitude is the complementary angle of the latitude. ...

Polar dials

In polar dials, the shadow-receiving plane is aligned parallel to the gnomon-style.^[17] Thus, the shadow slides sideways over the surface, moving perpendicularly to itself as the sun rotates about the style. As with the gnomon, the hour-lines are all aligned with the Earth's rotational axis. When the sun's rays are nearly parallel to the plane, the shadow moves very quickly and the hour lines are spaced far apart. The direct East- and West-facing dials are examples of a polar dial. However, the face of a polar dial need not be vertical; it need only be parallel to the gnomon. Thus, a plane inclined at the angle of latitude (relative to horizontal) under the similarly inclined gnomon will be a polar dial. The perpendicular spacing X of the hour-lines in the plane is described by the formula

where H is the height of the style above the plane, and t is the time (in hours) before or after the center-time for the polar dial. The center time is the time when the style's shadow falls directly down on the plane; for an East-facing dial, the center time will be 6am, for a West-facing dial, this will be 6pm, and for the inclined dial described above, it will be noon. When t approaches ±6 hours away from the center time, the spacing X diverges to infinity; this occurs when the sun's rays become parallel to the plane. For other uses, see Infinity (disambiguation). ...

Vertical declining dials

Effect of declining on a sundial's hour-lines. A vertical dial, at a latitude of 51° N, designed to face due South (far left) shows all the hours from 6am to 6pm, and has converging hour-lines symmetrical about the noon hour-line. By contrast, a West-facing dial (far right) is polar, with parallel hour lines, and shows only hours after noon. At the intermediate orientations of South-Southwest, Southwest, and West-Southwest, the hour lines are asymmetrical about noon, with the morning hour-lines ever more widely spaced.

A declining dial is any non-horizontal, planar dial that does not face in a cardinal direction, such as (true) North, South, East or West.^[18] As usual, the gnomon's style is aligned with the Earth's rotational axis, but the hour-lines are not symmetrical about the noon hour-line. For a vertical dial, the angle θ between the noon hour-line and another hour-line is given by the formula^[19] A modern compass card. ... Look up North in Wiktionary, the free dictionary. ... For other uses, see South (disambiguation). ... A compass rose For other uses, see East (disambiguation). ... A compass rose with west highlighted This article refers to the cardinal direction; for other uses see West (disambiguation). ...

where λ is the sundial's geographical latitude, t is the time before or after noon, and η is the angle of declination from true South. When such a dial faces South (η=0°), this formula reduces to the formula given above, tan θ = cos λ tan(15° × t). This article is about the geographical term. ... For other uses, see South (disambiguation). ...

When a sundial is not aligned with a cardinal direction, the substyle of its gnomon is not aligned with the noon hour-line. The angle β between the substyle and the noon hour-line is given by the formula^[20]

tanβ = sinηcotλ

If a vertical sundial faces true South or North (η=0° or 180°, respectively), the correction β=0° and the substyle is aligned with the noon hour-line.

Reclining dials

The sundials described above have gnomons that are aligned with the Earth's rotational axis and cast their shadow onto a plane. If the plane is neither vertical nor horizontal nor equatorial, the sundial is said to be reclining or inclining.^[21] Such a sundial might be located on a South-facing roof, for example. The hour-lines for such a sundial can be calculated by slightly correcting the horizontal formula above^[22]

where χ is the desired angle of reclining, λ is the sundial's geographical latitude, θ is the angle between a given hour-line and the noon hour-line (which always points due north) on the plane, and t is the number of hours before or after noon. For example, the angle θ of the 3pm hour-line would equal the arctangent of sin(λ+χ), since tan(45°) = 1. When χ equals 90° (in other words, a South-facing vertical dial), we obtain the vertical formula above, since sin(λ+90°) = cos(λ). This article is about the geographical term. ... In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. ... Sine redirects here. ... Sine redirects here. ... Sine redirects here. ...

Some authors use a more specific nomenclature to describe the orientation of the shadow-receiving plane. If the plane's face points downwards towards the ground, it is said to be proclining or inclining, whereas a dial is said to be reclining when the dial face is pointing away from the ground.

Reclining-declining dials

Some sundials both decline and recline, in that their shadow-receiving plane is not oriented with a cardinal direction (such as true North) and is neither horizontal nor vertical nor equatorial. For example, such a sundial might be found on a roof that was not oriented in a cardinal direction. The formulae describing the spacing of the hour-lines on such dials are rather complicated.^[23] The angle θ between the noon hour-line and another hour-line has two components θ = θ₁ + θ₂, described by the formulae^[24] True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

tanθ₁ = tanηtanχ

where λ is the sundial's geographical latitude, t is the time before or after noon, and χ and η are the angles of inclination and declination, respectively. This article is about the geographical term. ...

As in the simpler declining dial, the gnomon-substyle is not aligned with the noon hour-line.^[25] The general formula for the angle β between the substyle and the noon-line is given by^[26]

Spherical sundials

Equatorial bow sundial in Hasselt 50°55′47″N, 5°20′31″E,Belgium. The rays pass through the narrow slot, forming a uniformly rotating sheet of light that falls on the circular bow. The hour-lines are equally spaced; in this image, the local solar time is roughly 15:00 hours (3 pm). On September 10, a small ball, welded into the slot casts a shadow on centre of the hour band.

The surface receiving the shadow need not be a plane, but can can have any shape, provided that the sundial maker is willing to mark the hour-lines. If the style is aligned with the Earth's rotational axis, a spherical shape is convenient since the hour-lines are equally spaced, as they are on the equatorial dial above; the sundial is equiangular. This is the principle behind the armillary sphere and the equatorial bow sundial.^[27] However, some equiangular sundials — such as the Lambert dial described below — are based on other principles. Hasselt municipality and district in the province Limburg Hasselt is a Belgian city and municipality, and capital of the Flemish province of Limburg. ...

In the equatorial bow sundial, the gnomon is a bar, slot or stretched wire parallel to the celestial axis. The face is a semicircle (corresponding to the equator of the sphere, with markings on the inner surface. This pattern, built a couple of meters wide out of temperature-invariant steel invar, was used to keep the trains running on time in France before World War I.^[28] Invar, also called FeNi36, is an alloy of iron (64%) and nickel (36%) with some carbon and chromium. ...

Among the most precise sundials ever made are two equatorial bows constructed of marble found in Yantra mandir.^[29] This collection of sundials and other astronomical instruments was built by Maharaja Jai Singh II at his then-new capital of Jaipur, India between 1727 and 1733. The larger equatorial bow is called the Samrat Yantra (The Supreme Instrument); standing at 27 meters, its shadow moves visibly at 1 mm per second, or roughly a hand's breadth (6 cm) every minute.-1... Tourists gather at Jantar Mantar The Yantra Mandir (often called the Jantar Mantar, especially in the tourist trade) is a collection of architectural astronomical instruments, built by Maharaja Jai Singh II at his then new capital of Jaipur between 1727 and 1733. ... Maharaja Sawai Jai Singh (November 3, 1688-September 21, 1743) was ruler of the kingdom of Amber (later called Jaipur. ... , Jaipur   (Hindi: जयपुर), also popularly known as the pink city, is the capital of Rajasthan state, India. ... This article is about the unit of length. ...

Cylindrical dial with central style. 41°38′26″N, 2°21′34″E Cardedeu, Spain.

Cylindrical, conical, and other non-planar sundials

Other non-planar surfaces may be used to receive the shadow of the gnomon. For example, the gnomon may be aligned with the celestial poles and located also along the symmetry axis of a cone or a cylinder. Due to the symmetry, the hour lines on such surfaces will be equally spaced, as on an equatorial dial or an armillary sphere. The conical dial is very old, and was the basis for one type of chalice sundial; the style was a vertical pin within a conical goblet, within which were inscribed the hour lines.

As an elegant alternative, the gnomon may be located on the circumference of a cylinder or sphere, rather than at its center of symmetry. In that case, the hour lines are again spaced equally, but at double the usual angle, due to the geometrical inscribed angle theorem. This is the basis of some modern sundials, but it was also used in ancient times; in one type, the edges of a half-cylindrical gnomon served as the styles.^[30] In geometry, an inscribed angle is formed when two secant lines of a circle (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. ...

Just as the armillary sphere is largely open for easy viewing of the dial, such non-planar surfaces need not be complete. For example, a cylindrical dial could be rendered as a helical ribbon-like surface, with a thin gnomon located either along its center or at its periphery.

Adjustments to calculate clock time from a sundial reading

The most common reason for a sundial to differ from clock time is that the sundial has not been oriented correctly or its hour lines have not been drawn correctly. For example, most commercial sundials are designed as horizontal sundials as described above. To be accurate such sundials must have been designed for that latitude and their style must be parallel to the Earth's rotational axis; the style must be aligned with true North and its angle with the horizontal must equal the local geographical latitude. To align the style, the sundial can sometimes be tilted slightly on its north south axis. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ...

Summer (daylight saving) time correction

Some areas of the world practice daylight saving time, which shifts the official time, usually by one hour. This shift must be added to the sundial's time to make it agree with the official time. Although DST is common in Europe and North America, most of the worlds people do not use it. ...

Time-zone (longitude) correction

A time zone can cover 60° of longitude, so any point within that zone will experience time difference with the reference longitude, equivalent to 4 minutes of time per degree. For illustration, sunsets and sunrises occur at a later "official" time in the far western edge of a time-zone, compared to those observed at the far eastern edge. As an example, if a sundial is located at a longitude 5° west of the reference longitude, its time will read 20 minutes slow, since the sun appears to revolve around the Earth at 15° per hour. This is a constant correction throughout the year. For equiangular dials such as the equatorial, spherical or Lambert dials, this correction can be made by rotating the dial surface by an angle equalling the difference in longitude, without changing the gnomon position or orientation. However, this method does not work for other dials, such as a horizontal dial; the correction must be applied by the viewer. Timezone and TimeZone redirect here. ...

Equation of time correction

The Equation of Time - above the axis the dial will appear fast, and below the dial will appear slow.

Although the Sun appears to rotate nearly uniformly about the Earth, it is not perfectly uniform, due to the ellipticity of the Earth's orbit (the fact that the Earth's orbit about the Sun is not perfectly circular) and the tilt (obliquity) of the Earth's rotational axis relative to the plane of its orbit. Therefore, sundials time varies from standard clock time. On four days of the year, the correction is effectively zero, but on others, it can be as much as a quarter-hour early or late. The amount of correction is described by the equation of time. This correction is universal; it does not depend on the local latitude of the sundial. File links The following pages link to this file: Equation of time Categories: Public domain images ... File links The following pages link to this file: Equation of time Categories: Public domain images ... Look up meantime in Wiktionary, the free dictionary. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ...

In some sundials, the equation of time correction is provided as a plaque affixed to the sundial. In more sophisticated sundials, however, the equation can be incorporated automatically. For example, some equatorial bow sundials are supplied with a small wheel that sets the time of year; this wheel in turn rotates the equatorial bow, offsetting its time measurement. In other cases, the hour lines may be curved, or the equatorial bow may be shaped like a vase, which exploits the changing altitude of the sun over the year to effect the proper offset in time.^[31] A heliochronometer is a precision sundial that corrects apparent solar time to mean solar time or another standard time. Heliochronometers usually indicate the minutes to within 1 minute of Universal Time. See this discussion of the limits of Sundial Accuracy. Solar time is based on the idea that when the sun reaches its highest point in the sky, it is noon. ... Solar time is based on the idea that, when the sun reaches its highest point in the sky, it is noon. ... Standard time is the result of synchronizing clocks in different geographical locations within a time zone to the same time rather than using the local meridian as in local mean time or solar time. ... Universal Time (UT) is a timescale based on the rotation of the Earth. ...

An analemma may be added to many types of sundials to correct apparent solar time to mean solar time or another standard time. These usually have hour lines shaped like "figure eights" (analemmas) according to the equation of time. This compensates for the slight eccentricity in the Earth's orbit that causes up to a 15 minute variation from mean solar time. This is a type of dial furniture seen on more complicated horizontal and vertical dials. Solar time is based on the idea that, when the sun reaches its highest point in the sky, it is noon. ... Standard time is the result of synchronizing clocks in different geographical locations within a time zone to the same time rather than using the local meridian as in local mean time or solar time. ... Theoretical rendering of the analemma, looking east in the northern hemisphere. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ...

Movable-gnomon sundials

In addition to the sundials have a gnomon that is designed to be moved over the course of the year. In other words, the position of the gnomon relative to the center of the hour lines can vary. The advantage of such dials is that the gnomon need not be aligned with the celestial poles and may even be perfectly vertical (the analemmatic dial). A second advantage is that such dials, when combined with a fixed-gnomon sundial, allow the user to determine true North with no other aid; the two sundials are correctly aligned if and only if the time on the two sundials agrees. This is a useful property for portable sundials. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

Universal ring dial. The dial is suspended from the cord shown in the upper left; the suspension point on the vertical meridian ring can be changed to match the local latitude. The center bar is twisted until a sunray passes through the small hole and falls on the horizontal equatorial ring.

Universal equinoctial ring dial

A universal equinoctial ring dial (sometimes called a ring dial for brevity, although the term is ambiguous) is a portable version of an armillary sundial,^[32] or was inspired by the mariner's astrolabe.^[33] It was likely invented by William Oughtred around 1600 and became common throughout Europe.^[34] This article is about the Mariners astrolabe. ... William Oughtred William Oughtred (March 5, 1575 – June 30, 1660) was an English mathematician. ...

In its simplest form, the style is a thin slit that allows the sun's rays to fall on the hour-lines of a equatorial ring. As usual, the style is aligned with the Earth's axis; to do this, the user may orient the dial towards true North and suspend the ring dial vertically from the appropriate point on the meridian ring. Such dials may be made self-aligning with the addition of a more complicated central bar, instead of a simple slit-style. This bar could pivot about its end points and held a perforated slider that was positioned to the month and day according to a scale scribed on the bar. The time was determined by rotating the bar towards the sun so that the light shining through the hole fell on the equatorial ring. This forced the user to rotate the instrument, which had the effect of aligning the instrument's vertical ring with the meridian. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

When not in use, the equatorial and meridian rings can be folded together into a small disk.

In 1610, Edward Wright created the sea ring, which mounted a universal ring dial over a magnetic compass. This permitted mariners to determine the time and magnetic variation in a single step.^[35]

Analemmatic sundials

Analemmatic sundial

A typical analemmatic sundial, also known as a 'Human Sundial'. The person acts as the gnomon, standing in the proper position for the month. This sundial has a second, inner dial to show the daylight saving time.

An analemmatic sundial uses a vertical gnomon and its hour lines are the vertical projection of the hour lines of a circular equatorial sundial onto a flat plane.^[36] Therefore, the analemmatic sundial is an ellipse, where the short axis is aligned North-South and the long axis is aligned East-West. The noon hour line points true North, where as the hour lines for 6am and 6pm point due West and East, respectively; the ratio of the short to long axes equals the sine sin(λ) of the local geographical latitude, denoted λ. All the hour lines converge to a single center; the angle θ of a given hour line with the noon hour is given by the formula^[37] Image File history File links Analemmatic_(Human_Sundial). ... Image File history File links Analemmatic_(Human_Sundial). ... Although DST is common in Europe and North America, most of the worlds people do not use it. ... Elliptical redirects here. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... This article is about the geographical term. ...

where t is the time (in hours) before or after noon. However, the vertical gnomon does not always stand at the center of the hour lines; rather, to show the correct time, the gnomon must be moved northwards from the center by the distance^[38]

Y = Wcos(λ)tan(δ)

where W is the width of the ellipse and δ is the Sun's declination at that time of year. The declination measures how far the sun is above the celestial equator; at the equinoxes, δ=0 whereas it equals roughly ±23.5° at the summer and winter solstices. In astronomy, declination (abbrev. ... The celestial equator is a great circle on the imaginary celestial sphere, which could be constructed by inflating the Earths equator until it intersects with said sphere. ... For other uses, see Equinox (disambiguation). ... For other uses, see Solstice (disambiguation). ...

Accurate dials of this type fit nicely in a public square, using a ball at the tip of a flagpole as the nodus, with the face painted on or inlaid in the pavement. A less accurate version of the sundial is to lay out the hour marks on concrete, and then let the user stand in a square marked with the month. In middle latitudes, the ellipse with the hour-marks should be about six meters wide, so the shadow of the head of the beholder will fall near it most of the time.^[39] The month squares are arranged to correct the sundial for the time of year. The user's head then forms the gnomon of the dial. If the sundial is molded into the concrete, it resists vandalism and is engaging and reasonably accurate. ^[40]

Lambert dials

The Lambert dial is another movable-gnomon sundial.^[41] In contrast to the elliptical analemmatic dial, the Lambert dial is circular with evenly spaced hour lines, making it an equiangular sundial, similar to the equatorial, spherical, cylindrical and conical dials described above. The gnomon of a Lambert dial is neither vertical or aligned with the Earth's rotational axis; rather, it is tilted northwards by an angle α = 45° - (λ/2), where λ is the geographical latitude. Thus, a Lambert dial located at latitude 40° would have a gnomon tilted away from vertical by 25° in a northerly direction. To read the correct time, the gnomon must also be moved northwards by a distance This article is about the geographical term. ...

Y = Rtan(α)tan(δ)

where R is the radius of the Lambert dial and δ again indicates the Sun's declination for that time of year.

Altitude-based sundials

Altitude dials measure the height of the sun in the sky, rather than its rotation about the celestial axis. They are not oriented towards true North, but rather towards the sun and generally held vertically. The sun's elevation is indicted by the position of a nodus, either the shadow-tip of a gnomon, or a spot of light. The time is read from where the nodus falls on a set of hour-curves that vary with the time of year. Since the sun's altitude is the same at times equally spaced about noon (e.g., 9am and 3pm), the user had to know whether it were morning or afternoon. Many of these dials are portable and simple to use, although they are not well-suited for travelers, since their hour-curves are specific for a given latitude. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ... This article is about the geographical term. ...

Human shadows

The length of a human shadow (or of any vertical object) can be used to measure the sun's elevation and, thence, the time.^[42] The Venerable Bede gave a table for estimating the time from the length of one's shadow in feet, on the assumption that a monk's height is six times the length of his foot. Such shadow lengths will vary with the geographical latitude and with the time of year. For example, the shadow length at noon is short in summer months, and long in winter months. Bede, commonly known as the Venerable Bede, (c. ... This article is about the geographical term. ...

Chaucer evokes this method a few times in his Canterbury Tales, as in his Parson's Tale Chaucer: Illustration from Cassells History of England, circa 1902 Chanticleer the rooster from an outdoor production of Chanticleer and the Fox at Ashby_de_la_Zouch castle Geoffrey Chaucer (ca. ... Canterbury Tales Woodcut 1484 The Canterbury Tales is a collection of stories written by Geoffrey Chaucer in the 14th century (two of them in prose, the rest in verse). ...

An equivalent type of sundial using a vertical rod of fixed length is known as a backstaff dial. The backstaff, or back-quadrant, is a navigational tool that was used to determine latitude. ...

Shepherd dials

A shepherd's dial consists of curved hour-lines drawn on a cylinder. The horizontal pointer is placed over the date and pointed at the sun to determine the time.

A shepherd's dial — also known as a pillar dial, a cylinder dial or chilindre — is a portable cylindrical sundial with a gnomon that juts out perpendicularly.^[43] When held vertically and pointed at the Sun, it measures the altitude of the Sun, from which the hour can be calculated if the day is known. The hour curves are inscribed on the cylinder for reading the time. Shepherd's dials are sometimes hollow, so that the gnomon can be stored within when not in use.

Shepherd's dials appear in several works of literature. For example, in the Chaucer's Canterbury Tales, the monk says, Chaucer: Illustration from Cassells History of England, circa 1902 Chanticleer the rooster from an outdoor production of Chanticleer and the Fox at Ashby_de_la_Zouch castle Geoffrey Chaucer (ca. ... Canterbury Tales Woodcut 1484 The Canterbury Tales is a collection of stories written by Geoffrey Chaucer in the 14th century (two of them in prose, the rest in verse). ...

Similarly, the shepherd's dial is evoked in Shakespeare's Henry VI, Part 3, Shakespeare redirects here. ... Henry VI Part III is the third of William Shakespeares plays set during the lifetime of King Henry VI of England, and prepares the ground for one of his best-known and most controversial plays: the tragedy of King Richard III (Richard III of England). ...

The cylindrical shepherd's dial can be unrolled into a flat plate. In one simple version,^[44] the front and back of the plate each have three columns, corresponding to pairs of months with roughly the same solar declination (June-July, May-August, April-September, March-October, February-November, and January-December). The top of each column has a hole for inserting the shadow-casting gnomon, a peg. Only two times are marked on the column below, one for noon and the other for mid-morning/mid-afternoon.

Ring dials

In a ring dial (also known as an Aquitaine or a perforated ring dial), the ring is hung vertically and oriented sideways towards the sun.^[45] A beam of light passes through a small hole in the ring and falls on hour-curves that are inscribed on the inside of the ring.

Card dials (Capuchin dials)

Card dials are another form of altitude dial.^[46] A card is aligned edge-on with the sun and tilted so that a ray of light passes through an aperture onto a specified spot, thus determining the sun's altitude. A weighted string hangs vertically downwards from a hole in the card, and carries a bead or knot. The position of the bead on the hour-lines of the card gives the time. In more sophisticated versions such as the Capuchin dial, there is only one set of hour-lines, i.e., the hour lines do not vary with the seasons. Instead, the position of the hole from which the weighted string hangs is varied according to the season.

Nodus-based sundials

Kraków. 50°03′41″N 19°56′24″E / 50.0614, 19.9400 The shadow of the cross-shaped nodus moves along a hyperbola which shows the time of the year,indicated here by the zodiac figures. It is 1:50pm on the 16th July, 25 days after the summer solstice.

Another type of sundial follows the motion of a single point of light or shadow, which may be called the nodus. For example, the sundial may follow the sharp tip of a gnomon's shadow, e.g., the shadow-tip of a vertical obelisk (e.g., the Solarium Augusti) or the tip of the horizontal marker in a shepherd's dial. Alternatively, sunlight may be allowed to pass through a small hole or reflected from a small (e.g., coin-sized) circular mirror, forming a small spot of light whose position may be followed. In such cases, the rays of light trace out a cone over the course of a day; when the rays fall on a surface, the path followed is the intersection of the cone with that surface. Most commonly, the receiving surface is a geometrical plane, so that the path of the shadow-tip or light-spot traces out a conic section such as a hyperbola or an ellipse. The collection of hyperbolae was called a pelekonon (axe) by the Greeks, because it resembles a double-bladed ax, narrow in the center (near the noonline) and flaring out at the ends (early morning and late evening hours). In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... Illumination of Earth by the sun on the northern hemisphere summer solstice The summer solstice is an astronomical term regarding the position of the sun in relation to the celestial equator. ... The Luxor obelisk in the Place de la Concorde in Paris Obelisk outside Santa Maria sopra Minerva in Rome. ... The Solarium Augusti in a 19th century representation The Solarium Augusti, the largest sundial the ancient world has known,[1] was erected in Rome by Emperor Augustus, with a 30-metre Egyptian red granite obelisk that he had imported from Heliopolis. ... This article is about the geometric object, for other uses see Cone. ... Look up plane in Wiktionary, the free dictionary. ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ... Elliptical redirects here. ...

Reflection sundials

Isaac Newton developed a convenient and inexpensive sundial, in which a small mirror is placed on the sill of a south-facing window.^[47] The mirror acts like a nodus, casting a single spot of light on the ceiling. Depending on the geographical latitude and time of year, the light-spot follows a conic section, such as the hyperbolae of the pelikonon. Using the ceiling as a sundial surface has several advantages; it exploits unused space and may be very accurate, if large. Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... This article is about the geographical term. ...

Multiple dials

Sundials are sometimes combined into multiple dials. If two or more dials that operate on different principles — say, such as an analemmatic dial and a horizontal or vertical dial — are combined, the resulting multiple dial becomes self-aligning. In other words, the direction of true North need not be determined; the dials are oriented correctly when they read the same time. This is a significant advantage in portable dials. However, the most common forms combine dials based on the same principle, and thus are not self-aligning. True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...

Several sundials arrayed on the faces of a cube. The styles are all parallel and meant to be aligned with the Earth's rotation axis. Such an array of sundials is not self-aligning, however.

Diptych (tablet) sundial

Diptych sundial in the form of a mandolin, circa 1612. The gnomon-style is a string stretched between a horizontal and vertical face. This sundial also has a small nodus (a bead on the string) that tells time on the hyperbolic pelikinon, just above the date on the vertical face.

The diptych consisted of two small flat faces, joined by a hinge.^[48] Diptychs usually folded into little flat boxes suitable for a pocket. The gnomon was a string between the two faces. When the string was tight, the two faces formed both a vertical and horizontal sundial. These were made of white ivory, inlaid with black lacquer markings. The gnomons were black braided silk, linen or hemp string. With a knot or bead on the string as a nodus, and the correct markings, a diptych (really any sundial large enough) can keep a calendar well-enough to plant crops. A common error describes the diptych dial as self-aligning. This is not correct for diptych dials consisting of a horizontal and vertical dial using a string gnomon between faces, no matter the orientation of the dial faces. Since the string gnomon is continuous, the shadows must meet at the hinge; hence, any orientation of the dial will show the same time on both dials.^[49] Download high resolution version (1200x948, 136 KB)C:Sundial in the form of a mandolin - Project Gutenberg eText 15050. ... Download high resolution version (1200x948, 136 KB)C:Sundial in the form of a mandolin - Project Gutenberg eText 15050. ... This article is about the musical instrument. ... Ivory consular diptych of Areobindus, Byzantium, 506 AD, Louvre museum A diptych is any object with two flat plates attached at a hinge. ...

Multiface (Facet-headed) dials

A common multiple dial is to place sundials on every face of a Platonic solid, usually a cube.^[50] Extremely ornate sundials can be composed in this way, by applying a sundial to every surface of a solid object. In some cases, the sundials are formed as hollows in a solid object, e.g., a cylindrical hollow aligned with the Earth's rotational axis (in which the edges play the role of styles) or a spherical hollow in the ancient tradition of the hemisphaerium or the antiboreum. (See the History section below.) In some cases, these multiface dials are small enough to sit on a desk, whereas in others, they are large stone monuments. In geometry, a Platonic solid is a convex regular polyhedron. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ...

Such multiface dials have the advantage of receiving light (and, thus, telling time) at every hour of the day. They can also be designed to give the time in different time-zones simultaneously. However, they are generally not self-aligning, since their various dials generally use the same principle to tell time, that of a gnomon-style aligned with the Earth's axis of rotation. Self-aligning dials require that at least two independent principles are used to tell time, e.g., a horizontal dial (in which the style is aligned with the Earth's axis) and an analemmatic dial (in which the style is not). In many cases, the multiface dials are erected never to be moved and, thus, need be aligned only once.

Prismatic dials

Prismatic dials are a special case of polar dials, in which the sharp edges of a prism of a concave polygon serve as the styles and the sides of the prism receive the shadow.^[51] Examples include a three-dimensional cross or star of David on gravestones. In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. ... Look up polygon in Wiktionary, the free dictionary. ...

Unusual sundials

A digital sundial found in the Sundial Park of Genk in Flanders, Belgium. 50°33′44″N 4°41′51″E / 50.5622, 4.6975 The sun's rays are filtered by a carefully designed set of screens to produce different digits over the course of the day. The golden style points towards true North and the style's angle with horizontal equals the sundial's geographical latitude.

Image File history File linksMetadata Digitalsundial. ... Image File history File linksMetadata Digitalsundial. ... Geography Country Belgium Community Flemish Community Region Flemish Region Province Limburg Arrondissement Hasselt Coordinates , , Area 87. ... For other uses, see Flanders (disambiguation). ...

Bifilar sundial

Discovered by the German mathematician Hugo Michnik, the bifilar sundial has two non-intersecting threads parallel to the dial. Usually the second thread is orthogonal to the first.^[52][53]

The intersection of the two threads' shadows gives the solar time.

Digital sundial

Main article: Digital sundial

A digital sundial uses light and shadow to 'write' the time in numerals rather than marking time with position. One such design uses two parallel masks to screen sunlight into patterns appropriate for the time of day. Digital sundial is a clock that indicates the current time with numerals formed by the sunlight. ... Digital sundial is a clock that indicates the current time with numerals formed by the sunlight. ...

Analog calculating sundial

A horizontal sundial with a face cut on a cardioid keeps clock time, while still resembling a conventional garden sundial. The cardioid shape connects the intersections between the solar-time marks of a conventional sundial, and the equal-angles of a true clock-time face. The place where The shadow crosses the cardioid's edge, and the clock time can be read from the underlying clock-time dial. The sundial is adjusted for daylight saving time by rotating the underlying equal-angle clock-time face. The sun-time face does not move. In geometry, the cardioid is an epicycloid which has one and only one cusp. ...

Globe dial

The globe dial is a sphere aligned with the Earth's rotational axis, and equipped with a spherical vane.^[54] Similar to sundials with a fixed axial style, a globe dial determines the time from the Sun's azimuthal angle in its apparent rotation about the earth. This angle can be determined by rotating the vane to give the smallest shadow. This style of sundial was popularized by Thomas Jefferson at his home in Monticello. Thomas Jefferson (13 April 1743 N.S.–4 July 1826) was the third President of the United States (1801–09), the principal author of the Declaration of Independence (1776), and one of the most influential Founding Fathers for his promotion of the ideals of Republicanism in the United States. ... This is about the Jefferson residence. ...

Noon marks

Noon-mark from Ste. Marie-Madeleine church in Avenches, Switzerland. 46°52′50″N 7°02′26″E / 46.8805, 7.0405 The analemma is the narrow figure-8 shape, which plots the equation of time (in degrees, not time, 1°=4minutes) versus the altitude of the sun at noon at the sundial's location. The altitude is measured vertically, the equation of time horizontally.

The simplest sundials do not give the hours, but rather note the exact moment of 12:00 noon.^[55] In centuries past, such dials were used to correct mechanical clocks, which were sometimes so inaccurate as to lose or gain significant time in a single day. Avenches is a commune in the Canton of Vaud, Switzerland, seat of the district with the same name. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ...

In U.S. colonial-era houses, a noon-mark can often be found carved into a floor or windowsill.^[56] Such marks indicate local noon, and they provide a simple and accurate time reference for households that do not possess accurate clocks. In modern times, some Asian countries, post offices have set their clocks from a precision noon-mark. These in turn provided the times for the rest of the society. The typical noon-mark sundial was a lens set above an analemmatic plate. The plate has an engraved figure-eight shape., which corresponds to plotting the equation of time (described above) versus the solar declination. When the edge of the sun's image touches the part of the shape for the current month, this indicates that it is 12:00 noon. Theoretical rendering of the analemma, looking east in the northern hemisphere. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ...

History

The earliest sundials known from the archaeological record are obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egypt and Babylon. Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the Old Testament describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings 20:11 — which was likely of Egyptian or Babylonian design. Sundials are believed to have existed in China since ancient times, but very little is known of their history. For the obelisk punctuation mark, see dagger (typography). ... For other uses, see Babylon (disambiguation). ... Topics in Christianity Movements · Denominations · Other religions Ecumenism · Preaching · Prayer Music · Liturgy · Calendar Symbols · Art · Criticism Important figures Apostle Paul · Church Fathers Constantine · Athanasius · Augustine Anselm · Aquinas · Palamas · Luther Calvin · Wesley Arius · Marcion of Sinope Archbishop of Canterbury · Catholic Pope Coptic Pope · Ecumenical Patriarch Christianity Portal This box:      Note: Judaism...

Hemispherical Greek sundial from Ai Khanoum, Afghanistan, 3rd-2nd century BCE.

The ancient Greeks developed many of the principles and forms of the sundial. Sundials are believed to have been introduced into Greece by Anaximander of Miletus, c. 560 BC. According to Herodotus, the Greeks sundials were initially derived from the Babylonian counterparts. The Greeks were well-positioned to develop the science of sundials, having founded the science of geometry, and in particular discovering the conic sections that are traced by a sundial nodus. The mathematician and astronomer Theodosius of Bithynia (ca. 160 BC-ca. 100 BC) is said to have invented a universal sundial that could be used anywhere on Earth. Image File history File linksMetadata No higher resolution available. ... Image File history File linksMetadata No higher resolution available. ... Hellenistic foot fragment of a giant statue, from Ai-Khanoum, 2nd century BCE. Ai-Khanoum or Ay Khanum (lit. ... This article is about the Pre-Socratic philosopher. ... Herodotus of Halicarnassus (Greek: Hēródotos Halikarnāsseús) was a Greek historian who lived in the 5th century BC (c. ... For other uses, see Geometry (disambiguation). ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... Theodosius of Bithynia (ca. ...

The Romans adopted the Greek sundials, so much so that Plautus complained in one of his plays about his day being "chopped into pieces" by the ubiquitous sundials. Writing in ca. 25 BC, the Roman author Vitruvius listed all the known types of dials in Book IX of his De Architectura, together with their Greek inventors.^[57] All of these are believed to be nodus-type sundials, differing mainly in the surface that receives the shadow of the nodus. Titus Macchius Plautus, generally referred to simply as Plautus, was a playwright of Ancient Rome. ... Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He was the author of De Architectura, known today as The Ten Books of Architecture, a treatise in Latin on architecture, and perhaps the first work about this discipline. ... De architectūra (Latin: On architecture) was a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus. ...

• the hemicyclium of Berosus the Chaldean: a truncated, concave, hemispherical surface
• the hemispherium or scaphe of Aristarchus of Samos: a full, concave, hemispherical surface
• the discus (a disc on a plane surface) of Aristarchus of Samos: a fully circular equatorial dial with nodus
• the arachne (spiderweb) of Eudoxus of Cnidus or Apollonius of Perga: half a circular equatorial dial with nodus
• the plinthium or lacunar of Scopinas of Syracuse: an example in the Circus Flaminius)
• the pros ta historoumena (universal dial) of Parmenio
• the pros pan klima of Theodosius of Bithynia and Andreas
• the pelekinon of Patrocles: the classic double-bladed axe design of hyperbolae on a planar surface
• the cone of Dionysodorus: a concave, conical surface
• the quiver of Apollonius of Perga
• the conarachne
• the conical plinthium
• the antiboreum: a hemispherium that faces North, with the sunlight entering through a small hole.

The nodus-based obelisk sundial, Solarium Augusti, in a 19th century representation, with the Mausoleum of Augustus in the background (left).

The Romans built a very large sundial in 10 BC, the Solarium Augusti, which is a classic nodus-based obelisk casting a shadow on a planar pelekinon.^[58] Berossus (also Berossos or Berosus; Greek: Βήρωσσος) was a Hellenistic Babylonian writer and astronomer who was active at the beginning of the 3rd century BC. // Berossus published the Babyloniaca (hereafter, History of Babylonia) some time around 290-278 BCE for the Macedonian/Seleucid king, Antiochus I. Certain astrological fragments recorded in... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... In geometry, a disk is the region in a plane contained inside of a circle. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Not to be confused with Eudoxus of Cyzicus. ... Apollonius of Perga [Pergaeus] (ca. ... A page of fanciful balusters Arcade a passage or walkway covered over by a succession of arches or vaults supported by columns. ... Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... The Circus Flaminius was a race-track in Ancient Rome. ... Parmenion (c 400 BC - Ecbatana, 330 BC) was a Macedonian general in the service of Philip II of Macedon and Alexander the Great. ... Theodosius of Bithynia (ca. ... Andreas is a common male name in Cyprus, Greece, Germany, Flanders and Scandinavia. ... In Greek mythology, Patroclus, or Pátroklos (gr. ... This article is about the geometric object, for other uses see Cone. ... Dionysodorus of Caunus (ca. ... Apollonius of Perga [Pergaeus] (ca. ... The Luxor obelisk in the Place de la Concorde in Paris Obelisk outside Santa Maria sopra Minerva in Rome. ... The entryway to the Mausoleum of Augustus. ... The Solarium Augusti in a 19th century representation The Solarium Augusti, the largest sundial the ancient world has known,[1] was erected in Rome by Emperor Augustus, with a 30-metre Egyptian red granite obelisk that he had imported from Heliopolis. ...

A modern hemispherium in Gyeongbok Palace in Seoul, South Korea. 37°34′43″N 126°58′38″E / 37.578611, 126.977222 The tip of the pointer serves as the nodus; the height of the nodus-shadow within the bowl gives the time of the year. Since the picture was taken on 24 November, the sun is low in the sky, and the nodus-shadow higher in the bowl.

The Greek dials were inherited and developed further by the Islamic Caliphate cultures and the post-Renaissance Europeans. Since the Greek dials were nodus-based with straight hour-lines, they indicated unequal hours — also called temporary hours — that varied with the seasons, since every day was divided into twelve equal segments; thus, hours were shorter in winter and longer in summer. The idea of using hours of equal time length throughout the year was the innovation of Abul-Hasan near the beginning of the 13th century, based on developments in trigonometry by Albategni. The concept became known in western sundials at least from the year 1400. However, it is unknown when the practice of aligning the style with the Earth's rotational axis was introduced. Gyeongbok Palace (경복궁, Gyeongbokgung) is a palace located in northern Seoul, South Korea. ... Short name Statistics Location map Map of location of Seoul. ... This is a sub-article of Islamic science and astronomy. ... Al Battani (ca. ...

The onset of the Renaissance saw an explosion of new designs. Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial, with accompanying illustrations. Giovanni Padovani (or Paduani) (b. ... Giuseppe Biancani (in Latin, Josephus Blancanus) (1566-1624) was an Italian Jesuit astronomer, mathematician, and selenographer, after whom the Blancanus crater, on the Moon, is named. ...

The oldest sundial in England is incorporated into the Bewcastle Cross ca. 800 AD. The dial is divided into four tides, covering the parts of the working day in areas influenced by the Vikings, a maritime culture which noted the passage of time in the progression of the two high and two low tides each day. A tide is an obsolete or archaic term for time, period or season, such as eventide, shrovetide, Eastertide, etc. ... The Bewcastle Cross is a runic monument in Cumbria, England, from the late 7th or early 8th century. ...

The custom of measuring time by one's shadow has persisted since ancient times. In Aristophanes' play, Assembly of Women, Praxagora asks her husband to return when his shadow reaches 10 feet (3.0 m). The Venerable Bede also gave instructions to his follows, how to interpret their shadow lengths to know what time it is For other uses, see Aristophanes (disambiguation). ... For other uses, see Bede (disambiguation). ...

Sundial mottoes

Further information: List of sundial mottoes

Illustration of Father Time and a sundial motto: "Grow old along with me; the best is yet to be."

Sundials are associated with the passage of time, and it has become common to inscribe a motto into a sundial, often one that prompts the viewer to reflect on the transience of the world and the inevitability of death, e.g., "Do not kill time, for it will surely kill thee." A more cheerful popular motto is "I count only the sunny hours." Another is "I am a sundial, and I make a botch of what is done far better by a watch." Various collections of sundial mottoes have been published over the past few centuries. This article is about the personification of time. ...

See also

• Foucault pendulum
• Francesco Bianchini
• Moondial
• Nocturnal - device for determining time by the stars at night.
• Scottish sundial — the ancient renaissance sundials of Scotland.
• Tide (time) - devisions of the day on early sundials.

Foucaults Pendulum in the Panth̩on, Paris. ... Francesco Bianchini (December 13, 1662 РMarch 2, 1729) was an Italian philosopher and scientist. ... Moondial is also the name of a television series. ... A nocturnal is an instrument used to determine the time based on the position of a certain star in the night sky. ... The renaissance sundials of Scotland are not just more numerous than in any other country they are also stylistically unique. ... A tide is an obsolete or archaic term for time, period or season, such as eventide, shrovetide, Eastertide, etc. ...

Footnotes

2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance with the Gregorian calendar. ... is the 19th day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance with the Gregorian calendar. ... is the 5th day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance with the Gregorian calendar. ... is the 5th day of the year in the Gregorian calendar. ... ISSN, or International Standard Serial Number, is the unique eight-digit number applied to a periodical publication including electronic serials. ... This article is about the geographical term. ... The cantilever spar of this cable-stay bridge, the Sundial Bridge at Turtle Bay, forms the gnomon of a large garden sundial The gnomon is the part of a sundial that casts the shadow. ... The two celestial poles are the imaginary points where the Earths spin axis intersects the imaginary rotating sphere of gigantic radius, called the celestial sphere. ... Timezone and TimeZone redirect here. ... Although DST is common in Europe and North America, most of the worlds people do not use it. ... For other uses, see Wellesley College (disambiguation). ... This article is about the U.S. state. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance with the Gregorian calendar. ... is the 19th day of the year in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 188th day of the year (189th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 250th day of the year (251st in leap years) in the Gregorian calendar. ... Ara Pacis:Detail of the processional frieze showing members of the Julio-Claudian family (north face) The Ara Pacis Augustae (Latin, Altar of Majestic Peace; commonly shortened to Ara Pacis) is an altar to Peace, envisioned as a Roman goddess. ...

Bibliography

• Earle AM (1971). Sundials and Roses of Yesterday. Rutland, VT: Charles E. Tuttle. ISBN 0-8048-0968-2, LCCN 74-142763.  Reprint of the 1902 book published by Macmillan (New York).
• A.P.Herbert, Sundials Old and New,Methuen & Co. Ltd, 1967.
• Mayall RN, Mayall MW (1994). Sundials: Their Construction and Use, 3rd ed., Cambridge, MA: Sky Publishing. ISBN 0-933346-71-9. 
• Hugo Michnik, Theorie einer Bifilar-Sonnenuhr, Astronomishe Nachrichten, 217(5190), p.81-90, 1923
• Rohr RRJ (1996). Sundials: History, Theory, and Practice, translated by G. Godin, New York: Dover. ISBN 0-486-29139-1.  Slightly amended reprint of the 1970 translation published by University of Toronto Press (Toronto). The original was published in 1965 under the title Les Cadrans solaires by Gauthier-Villars (Montrouge, France).
• Frederick W. Sawyer, Bifilar gnomonics, JBAA (Journal of the British Astronomical association), 88(4):334–351, 1978
• Gerard L'E. Turner, Antique Scientific Instruments, Blandford Press Ltd. 1980 ISBN 0-7137-1068-3
• Make A Sundial, (The Education Group British Sundial Society) Editors Jane Walker and David Brown, British Sundial Society 1991 ISBN 0-9518404-0
• Waugh AE (1973). Sundials: Their Theory and Construction. New York: Dover Publications. ISBN 0-486-22947-5. 
• "Illustrating Shadows", Simon Wheaton-Smith, ISBN 0-9765286-8-1, LCN: 2005900674
  • also see "Illustrating More Shadows", Simon Wheaton-Smith, both books are over 300 pages long.

The Library of Congress Control Number or LCCN is a serially based system of numbering books in the Library of Congress in the United States. ...

External links

Wikimedia Commons has media related to:

Sundials

Sundial Societies, Groups and Organizations

• British Sundial Society
• North American Sundial Society
• De Zonnewijzerkring - Dutch Sundial Society (in English)
• Societat Catalana de Gnomònica - Catalonian Sundial Society
• Zonnewijzerkring Vlaanderen - Flemish Sundial Society
• Coordinamento Gnomonico Italiano (CGI) - Italian Sundial Society
• La Commission des Cadrans solaires du Québec (CCSQ) - Commission on Sundials of Quebec
• Asociación de Amigos de los Relojes de Sol (AARS) - Spain, Association of Friends of the Sundial

General sundial links

• Sundial Websites Catalogue An indexed and edited site of Sundial related sites.
• Sunbeams and Sundials Children's guide to the sun, the seasons and sundials.
• The Sundial Primer Details of all aspects of sundial maths.
• A major source of information Information about sundial design and building, small indoor, glass, clay, and concrete, designing programs in many languages for sundials, and VRML models.
• Sundial links a collection of sundial links ordered by date.
• Article by Denis Roegel on drawing sundials with the Metapost graphical language.
• The Analemmas of Vitruvius and Ptolemy describes the use of these ancient analemmas in laying out shadow traces for different days on horizontal sundials.
• (Polish) Wilanów Palace Sundial.
• Daniela Bonanome: The sundial of Grottaferrata (Rome)

v • d • e   Time   Major concepts Time · Eternity · Arguments for eternity · Immortality Deep time · History · Past · Present · Future · Futurology Time Portal Measurement and Standards Chronometry · UTC · UT · TAI · Second · Minute · Hour · Sidereal time · Solar time · Time zone Clock · Horology · History of timekeeping devices · Astrarium · Marine chronometer · Sundial · Water clock Logo turtle graphic The Logo programming language is a functional programming language. ... MetaPost refers to both a programming language and the only known interpreter of the MetaPost programming language. ... This article is about the concept of time. ... This article is about the concept of time. ... While in the popular mind, eternity often simply means existing for an infinite, i. ... Arguments for eternity composed a particularly important area of philosophical debate among Greek, Jewish, Islamic, and Christian philosophers during the ancient and medieval periods. ... 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Wikipedia does not yet have an article with this exact name. ... UTC redirects here. ... Universal Time (UT) is a timescale based on the rotation of the Earth. ... International Atomic Time (TAI, from the French name Temps Atomique International) is a high-precision atomic time standard that tracks proper time on Earths geoid. ... This article is about the unit of time. ... This article is about the unit of time, angle and right ascension. ... The hour (symbol: h) is a unit of time. ... Sidereal time is time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical with, the motion of stars. ... Solar time is based on the idea that when the sun reaches its highest point in the sky, it is noon. ... Timezone and TimeZone redirect here. ... For other uses, see Clock (disambiguation). ... Horology is the study of the science and art of timekeeping devices. ... An astrarium, also called a planetarium, is the mechanical representation of the cyclic nature of astronomical objects in one timepiece. ... A marine chronometer is a timekeeper precise enough to be used as a portable time standard, used to determine longitude by means of celestial navigation. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... Calendar · Day · Week · Month · Year · Tropical year · Julian · Gregorian · Islamic For other uses, see Calendar (disambiguation) A page from the Hindu calendar 1871–1872. ... Look up day in Wiktionary, the free dictionary. ... For more details on each day of the week, see days of the week. ... Look up Month in Wiktionary, the free dictionary. ... A year (from Old English gÄ“r) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... The Julian calendar was a reform of the Roman calendar which was introduced by Julius Caesar in 46 BC and came into force in 45 BC (709 ab urbe condita). ... For the calendar of religious holidays and periods, see liturgical year. ... The Islamic calendar or Muslim calendar (Arabic: التقويم الهجري; at-taqwÄ«m al-hijrÄ«; Persian: تقویم هجري قمری ‎ taqwÄ«m-e hejri-ye qamari; also called the Hijri calendar) is the calendar used to date events in many predominantly Muslim countries, and used by Muslims everywhere to determine the proper day on which to celebrate...   Intercalation · Leap second · Leap year Chronology Astronomical chronology · Geologic Time · Geological history · Geochronology · Archaeological dating Calendar era · Regnal year · Chronicle · Timeline · Periodization Religion and Mythology Time and fate deities · Wheel of time · Kāla · Kalachakra · Prophecy · Dreamtime Philosophy Causality · Eternalism · Eternal return · Event · The Unreality of Time · A-series and B-series · B-Theory of time Endurantism · Four dimensionalism · Perdurantism · Presentism · Temporal finitism · Temporal parts Physical Sciences Time in physics · Spacetime · Absolute time and space · T-symmetry Arrow of time · Chronon · Fourth dimension · Planck epoch · Planck time · Time domain Intercalation is the insertioffn of an extra day, week or month into some calendar years to make the calendar follow the seasons. ... A leap second is a one-second adjustment to civil time in order to keep it close to the mean solar time. ... For the 1921 film starring Fatty Arbuckle, see Leap Year (film). ... For the novel by Michael Crichton, see Timeline (novel). ... Diagram of geological time scale. ... Geological time scale. ... Geochronology is the science of determining the age of rocks, fossils, and sediments. ... Dating material drawn from the archaeological record can made by a direct study of a artifact or may be deduced by association with materials found in the context the item is drawn from or inferred by its point of discovery in the sequence relative to datable contexts. ... A calendar era is the year numbering system used by a calendar. ... Regnal year: the year of the reign of a sovereign. ... Generally a chronicle (Latin chronica, from Greek Χρόνος) is historical account of facts and events in chronological order. ... For other uses, see Timeline (disambiguation). ... 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Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. ... Causality or causation denotes the relationship between one event (called cause) and another event (called effect) which is the consequence (result) of the first. ... Eternalism is a philosophical approach to the ontological nature of time. ... Eternal return or sometimes eternal recurrence is a concept originating from ancient Egypt and developed in the teachings of Pythagoras. ... This page is a candidate for speedy deletion because: this page is a test If you disagree with its speedy deletion, please explain why on its talk page or at Wikipedia:Speedy deletions. ... Wikisource has original text related to this article: The Unreality of Time To meet Wikipedias quality standards, this article or section may require cleanup. ... 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For other uses of this term, see Spacetime (disambiguation). ... In physics, the concept of absolute time and absolute space are hypothetical models in which time either runs at the same rate for all the observers in the universe or the rate of time of each observer can be scaled to the absolute time by multiplying the rate by a... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... This article or section does not cite its references or sources. ... A chronon is a hypothetical concept in theoretical physics intended to describe a quantum of time. ... For other uses, see Fourth dimension (disambiguation). ... Named after Max Planck, in cosmology the Planck epoch (or Planck Era) is the earliest period of time in the history of the universe, from zero to 10-43 seconds (one Planck time), during which all four fundamental forces were unified and elementary particles did not yet exist. ... In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. ... Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... Theory of relativity · Time dilation · Gravitational time dilation · Coordinate time · Proper time Psychology Consciousness and spacetime · Mental chronometry · Reaction time · Sense of time · Specious present Sociology and Anthropology Futures studies · Long Now Foundation · Time discipline · Time use research Economics Newtonian time in economics · Time value of money Related topics Space · Duration · Time capsule · Time travel · Time signature · System time · Metric time · Carpe diem · Tempus fugit

v • d • e Time measurement and standards Major subjects Time · Chronometry · Orders of magnitude · Units of time · Metrology Time Portal International standards UTC · UT · TAI · ISO 31-1 · Second · DUT1 · Leap second · IERS Terrestrial Time · Geocentric Coordinate Time · Barycentric Coordinate Time -1... Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... Coordinate time is the interval of time independent of relativistic time dilation. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... Space-time theories of consciousness relate the geometrical features of conscious experience, such as viewing things in space-time at a point, to the geometrical properties of the universe itself. ... // Definition and history Psychologists have investigated mental chronometry for over 100 years. ... Reaction time (RT) is the elapsed time between the presentation of a sensory stimulus and the subsequent behavioral response. ... Although the sense of time is not associated with a specific sensory system, the work of psychologists and neuroscientists indicates that our brains do have a system governing the perception of time. ... The specious present is the time duration wherein ones perceptions are considered to be in the present. ... Future studies reflects on how today’s changes (or the lack thereof) become tomorrow’s reality. ... The Long Now Foundation, established in 1996, is a private organization that seeks to become the seed of a very long-term cultural institution. ... In sociology and anthropology, time discipline is the general name given to social and economic rules, conventions, customs, and expectations governing the measurement of time, the social currency and awareness of time measurements, and peoples expectations concerning the observance of these customs by others. ... Time use research is a developing interdisciplinary field of study dedicated to knowing how people allocate their time during an average day. ... The time value of money is the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal. ... This article is about the idea of space. ... A duration is an amount of time or a particular time interval. ... For other uses, see Time capsule (disambiguation). ... Time travel is a concept that has long fascinated humanity—whether it is Merlin experiencing time backwards, or religious traditions like Mohammeds trip to Jerusalem and ascent to heaven, returning before a glass knocked over had spilt its contents. ... The time signature (also known as meter signature) is a notational convention used in Western musical notation to specify how many beats are in each measure and what note value constitutes one beat. ... In computer science and computer programming, system time represents a computer systems notion of the passing of time. ... Metric time is the measure of time interval using the metric system, which defines the second as the base unit of time, and multiple and submultiple units formed with metric prefixes, such as kiloseconds and milliseconds. ... For other uses, see Carpe diem (disambiguation). ... Tempus fugit on a sundial Tempus fugit is a Latin expression meaning time flees, more commonly translated as time flies. It is frequently used as an inscription on clocks. ... A time scale specifies divisions of time. ... This article is about the concept of time. ... Wikipedia does not yet have an article with this exact name. ... // The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). ... Metrology (from Greek metron (measure), and -logy) is the science of measurement. ... Image File history File links Portal. ... UTC redirects here. ... Universal Time (UT) is a timescale based on the rotation of the Earth. ... International Atomic Time (TAI, from the French name Temps Atomique International) is a high-precision atomic time standard that tracks proper time on Earths geoid. ... ISO 31-1 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to space and time. ... This article is about the unit of time. ... The time correction DUT1 is the difference between the Universal Time scale UT1 (which corresponds to the Earths rotation) and the Coordinated Universal Time (UTC) (which corresponds, except for a constant offset, to International Atomic Time (TAI)). DUT1 = UT1 - UTC DUT1 is maintained in the range -0. ... A leap second is a one-second adjustment to civil time in order to keep it close to the mean solar time. ... The International Earth Rotation and Reference Systems Service is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter (EOP) and International Celestial Reference System (ICRS) groups. ... Terrestrial Time (TT) is the modern time standard for time on the surface of the Earth. ... Geocentric Coordinate Time (TCG) is a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth. ... Barycentric Coordinate Time (TCB) was defined in 1991 by the International Astronomical Union as one of the replacements for the ill-defined Barycentric Dynamical Time (TDB). ... Civil time · Minute · Hour · 12-hour clock · 24-hour clock · ISO 8601 Civil time is another name for mean solar time reckoned from midnight. ... This article is about the unit of time, angle and right ascension. ... The hour (symbol: h) is a unit of time. ... The 12-hour clock is a timekeeping convention in which the 24 hours of the day are divided into two periods called ante meridiem (a. ... The 24-hour clock is a convention of time keeping in which the day runs from midnight to midnight and is divided into 24 hours, numbered from 0 to 23. ... ISO 8601 is an international standard for date and time representations issued by the International Organization for Standardization (ISO). ... International Date Line · Solar time · Time zone · Daylight saving time · Time offset · Annum Obsolete standards Ephemeris time · Barycentric Dynamical Time · Greenwich Mean Time · Prime Meridian Time in physics Spacetime · Chronon · Cosmological decade · Planck epoch · Planck time · T-symmetry Theory of relativity · Time dilation · Gravitational time dilation · Coordinate time · Proper time “Date line” redirects here. ... Solar time is based on the idea that when the sun reaches its highest point in the sky, it is noon. ... Timezone and TimeZone redirect here. ... Although DST is common in Europe and North America, most of the worlds people do not use it. ... A time offset is defined by international convention as a number of hours and minutes from Coordinated Universal Time in Greenwich, England. ... Annum is a Latin noun meaning year. ... Ephemeris Time (ET) is a now obsolete time scale used in ephemerides of celestial bodies, in particular the Sun (as observed from the Earth), Moon, planets, and other members of the solar system. ... Barycentric Dynamical Time (TDB) was defined by the International Astronomical Union (IAU) in 1976 to be used as the relativistic replacement for the non-relativistic Ephemeris Time which had been used in the ephemerides starting in 1960. ... GMT redirects here. ... Location of the Prime Meridian Image:Prime Meridian. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... For other uses of this term, see Spacetime (disambiguation). ... A chronon is a hypothetical concept in theoretical physics intended to describe a quantum of time. ... A cosmological decade ( CÐ ) is a division of the lifetime of the cosmos. ... Named after Max Planck, in cosmology the Planck epoch (or Planck Era) is the earliest period of time in the history of the universe, from zero to 10-43 seconds (one Planck time), during which all four fundamental forces were unified and elementary particles did not yet exist. ... In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... -1... Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential; the higher the local distortion of spacetime due to gravity, the slower time passes. ... Coordinate time is the interval of time independent of relativistic time dilation. ... In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. ... Time domain · Continuous time · Discrete time · Absolute time and space Horology Clock · Astrarium · Atomic clock · Hourglass · Marine chronometer · Radio clock · Sundial · Watch · Water clock History of timekeeping devices · Equation of time · Complication Calendar Day · Week · Month · Year · Decade · Century · Millennium Astronomical · Julian · Gregorian · Islamic · Lunisolar · Solar · Lunar · Epact · Intercalation · Leap year Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... A continuous signal or a continuous time signal is a varying quantity (a signal) that can be, or is expressed, as a continuous function of an independent variable, usually time. ... Discrete time is non-continuous time. ... In physics, the concept of absolute time and absolute space are hypothetical models in which time either runs at the same rate for all the observers in the universe or the rate of time of each observer can be scaled to the absolute time by multiplying the rate by a... Horology is the study of the science and art of timekeeping devices. ... For other uses, see Clock (disambiguation). ... An astrarium, also called a planetarium, is the mechanical representation of the cyclic nature of astronomical objects in one timepiece. ... “Nuclear Clock” redirects here. ... For other uses, see Hourglass (disambiguation). ... A marine chronometer is a timekeeper precise enough to be used as a portable time standard, used to determine longitude by means of celestial navigation. ... A radio clock A radio clock is a clock that is synchronized by a time code bit stream transmitted by a radio transmitter connected to a time standard such as an atomic clock. ... For other uses, see Watch (disambiguation). ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ... The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. ... In horology terms, a complication in a mechanical timepiece is any feature beyond that of a simple hours, minutes, and seconds movement. ... For other uses, see Calendar (disambiguation) A page from the Hindu calendar 1871–1872. ... Look up day in Wiktionary, the free dictionary. ... For more details on each day of the week, see days of the week. ... Look up Month in Wiktionary, the free dictionary. ... A year (from Old English gÄ“r) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... For other senses of this word, see decade (disambiguation). ... A century (From the Latin cent, one hundred) is one hundred consecutive years. ... A millennium (pl. ... Astronomical year numbering is based on BCE/CE (or BC/AD) year numbering, but follows normal decimal integer numbering more strictly. ... The Julian calendar was a reform of the Roman calendar which was introduced by Julius Caesar in 46 BC and came into force in 45 BC (709 ab urbe condita). ... For the calendar of religious holidays and periods, see liturgical year. ... The Islamic calendar or Muslim calendar (Arabic: التقويم الهجري; at-taqwÄ«m al-hijrÄ«; Persian: تقویم هجري قمری ‎ taqwÄ«m-e hejri-ye qamari; also called the Hijri calendar) is the calendar used to date events in many predominantly Muslim countries, and used by Muslims everywhere to determine the proper day on which to celebrate... A lunisolar calendar is a calendar whose date indicates both the moon phase and the time of the solar year. ... A solar calendar is a calendar whose dates indicate the position of the earth on its revolution around the sun (or equivalently the apparent position of the sun moving on the celestial sphere). ... A lunar calendar is a calendar that is based on cycles of the moon phase. ... The epact (from Greek: epaktai hèmerai = added days) is, as the second Canon of the Gregorian Calendar reform puts it, nothing else than the number of days which the common solar year of 365 days surpasses the common lunar year of 354 days (Latin: Epacta nihil aliud est quam... Intercalation is the insertioffn of an extra day, week or month into some calendar years to make the calendar follow the seasons. ... For the 1921 film starring Fatty Arbuckle, see Leap Year (film). ... Tropical year · Equinox · Solstice · Days of the week · Calculating the day of the week · Dominical letter Archaeology & geology International Commission on Stratigraphy · Geologic Time · Archaeological dating Astronomical chronology Nuclear time scale · Precession · Sidereal time · Galactic year Unusual units Fortnight · Jiffy · Lustrum · Saeculum · Shake · Tide Related topics Chronology · Duration · System time · Metric time · Mental chronometry · Time value of money · Timekeeper

A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... For other uses, see Equinox (disambiguation). ... For other uses, see Solstice (disambiguation). ... This article is about days of the week. ... This article details various mathematical algorithms to calculate the day of the week for any particular date in the past or future. ... The days of the year are sometimes designated letters A, B, C, D, E, F and G in a cycle of 7 as an aid for finding the day of week of a given calendar date and in calculating Easter. ... The International Commission on Stratigraphy concerns itself with stratigraphy on a global scale. ... Diagram of geological time scale. ... Dating material drawn from the archaeological record can made by a direct study of a artifact or may be deduced by association with materials found in the context the item is drawn from or inferred by its point of discovery in the sequence relative to datable contexts. ... The precession of Earths axis of rotation with respect to inertial space is also called the precession of the equinoxes. ... Sidereal time is time measured by the apparent diurnal motion of the vernal equinox, which is very close to, but not identical with, the motion of stars. ... // Galactic time NGC 4414, a typical spiral galaxy alike our Milky Way Galactic time, not to confuse with siderial time, is the time that is described by our spin relative to the center of the galaxy. ... Look up fortnight in Wiktionary, the free dictionary. ... The term jiffy (or jiffie) is used in different applications for various different short periods of time, usually 1/60 of a second. ... Lustrum was a sacrifice for expiation and purification offered by one of the censors of Rome in name of the Roman people at the close of the taking of the census, and which took place after a period of five years, so that the name came to denote a period... A saeculum is a length of time roughly equal to the lifetime of a person, or about 90 years. ... A shake is an informal unit of time equal to 10 nanoseconds, or 10-8 seconds. ... A tide is an obsolete or archaic term for time, period or season, such as eventide, shrovetide, Eastertide, etc. ... For the novel by Michael Crichton, see Timeline (novel). ... A duration is an amount of time or a particular time interval. ... In computer science and computer programming, system time represents a computer systems notion of the passing of time. ... Metric time is the measure of time interval using the metric system, which defines the second as the base unit of time, and multiple and submultiple units formed with metric prefixes, such as kiloseconds and milliseconds. ... // Definition and history Psychologists have investigated mental chronometry for over 100 years. ... The time value of money is the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal. ... Look up timekeeper in Wiktionary, the free dictionary. ...