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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