For other uses see Sundial (disambiguation).

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 onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon often a thin rod or a sharp straight edge. As the sun moves across the sky the shadow-edge aligns with different hour-lines. All sundials must be aligned with the axis of the Earth's rotation to tell the correct time. In most designs the style must point towards true celestial north (not the north magnetic pole or south magnetic pole). That is the style's horizontal angle must equal the sundial's geographical latitude.

Unfortunately it is common for inexpensive decorative sundials to have incorrect hour angles and these cannot be adjusted to tell correct time. SSW facing vertical declining sundial on Moot Hall Aldeburgh Suffolk England. Ancient sundial from Marcianopolis Contents 1 Introduction 2 Apparent motion of the Sun 3 Terminology 4 Sundials in the Southern Hemisphere 5 Sundials with fixed axial gnomon 5.1 Equatorial sundials 5.2 Horizontal sundials 5.3 Vertical sundials 5.4 Pocket Sundials 5.5 Polar dials 5.6 Vertical declining dials 5.7 Reclining dials 5.8 Reclining-declining dials 5.9 Spherical sundials 5.10 Cylindrical conical and other non-planar sundials 6 Adjustments to calculate clock time from a sundial reading 6.1 Summer (daylight saving) time correction 6.2 Time-zone (longitude) correction 6.3 Equation of time correction 7 Movable-gnomon sundials 7.1 Universal equinoctial ring dial 7.2 Analemmatic sundials 7.3 Lambert dials 8 Altitude-based sundials 8.1 Human shadows 8.2 Shepherd dials Timesticks 8.3 Ring dials 8.4 Card dials (Capuchin dials) 9 Nodus-based sundials 9.1 Reflection sundials 10 Multiple dials 10.1 Diptych (tablet) sundial 10.2 Multiface (Facet-headed) dials 10.3 Prismatic dials 11 Unusual sundials 11.1 Benoy dials 11.2 Bifilar sundial 11.3 Digital sundial 11.4 Analog calculating sundial 11.5 Globe dial 11.6 Noon marks 11.7 Noon cannon 12 Meridian lines 13 History 14 Sundial mottoes 15 See also 16 References 16.1 Notes 16.2 Bibliography 17 External links Introduction

There are different types of sundials: Some sundials use a line of light to indicate the time. Others use the edge of a shadow. 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.

When the sundial reads by shadows the shadow-casting object the sundial's gnomon may be a thin rod or any object with a sharp tip or a straight edge. 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.

Sundials also may use many types of surfaces to receive the light or shadow. Planes are the most common surface but partial spheres cylinders cones and other shapes have been used for greater accuracy or beauty.

Sundials differ in their portability and their need for 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. Portable dials are self-aligning; for example it may have two dials that operate on different principles such as a horizontal and analemmatic dial mounted together on one plate. In these designs their times agree only when the plate is aligned properly.

Sundials indicate the local solar time unless corrected for some other time. To obtain the official clock time three types of corrections need to be made.

First the orbit of the Earth is not perfectly circular and its rotational axis not perfectly perpendicular to its orbit. The sundial's indicated solar time thus varies from clock time by small amounts that change throughout the year. This correction which may be as great as 15 minutes is described by the equation of time. A sophisticated sundial with a curved style or hour lines may incorporate this correction. Often instead simpler sundials are used with a small plaque that gives the offsets at various times of the year.

Second the solar time must be corrected for the longitude of the sundial relative to the longitude of the official time zone. For example a sundial located west of Greenwich England but within the same time-zone shows a later time than the official time. It will show "noon" after the official noon has passed since the sun passes overhead later. This correction is often made by rotating the hour-lines by an angle equal to the difference in longitudes. Last to adjust for daylight saving time the sundial must shift the time away from solar time by some amount usually an hour. This correction may be made in the adjustment plaque or by numbering the hour-lines with two sets of numbers. 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). Sunrise and sunset occur at 3am and 9pm respectively on that day at geographical latitudes near 57.5 roughly the latitude of Aberdeen or Sitka Alaska. The principles of sundials can be understood most easily from the Sun's apparent motion. Scientists have proven that the Earth rotates on its axis and revolves in an elliptic orbit about the Sun; however meticulous observations and experiments were needed. For the purposes of a sundial an excellent approximation assumes 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 celestial axis is the line connecting the celestial poles. Since the celestial axis is aligned with the axis about which the Earth rotates the angle of the axis with the local horizontal is the local geographical latitude. Unlike the fixed stars the Sun changes its position on the celestial sphere being at a positive declination in summer at a 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 called the ecliptic. The ecliptic passes through the twelve constellations of the zodiac in the course of a year. Sundial in Singapore Botanic Gardens. The fact that Singapore is located almost at the equator is reflected in its design. This model of the Sun's motion helps to understand 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 the most common design. In such cases the same 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 circular about the gnomon (as in the armillary sphere). In other cases the hour-lines are not spaced evenly even though the shadow rotates 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 reflect from a small mirror trace out a cone 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. This is 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. Terminology In general sundials indicate the time by casting a shadow or throwing light onto a surface known as a dial face or dial plate. Although usually a flat plane the dial face may also be the inner or outer surface of a sphere cylinder cone helix and various other shapes. The time is indicated where a shadow or light falls on the dial face which is usually inscribed with hour lines. Although usually straight these hour lines may also be curved depending on the design of the sundial (see below). In some designs it is possible to determine the date of the year or it may be required to know the date to find the correct time. In such cases there may be multiple sets of hour lines for different months or there may be mechanisms for setting/calculating the month. In addition to the hour lines the dial face may offer other datasuch as the horizon the equator and the tropicswhich are referred to collectively as the dial furniture. The entire object that casts a shadow or light onto the dial face is known as the sundial's gnomon.1 However it is usually only an edge of the gnomon (or another linear feature) that casts the shadow used to determine the time; this linear feature is known as the sundial's style. The style is usually aligned with the axis of the celestial sphere and therefore aligned with the local geographical meridian. In some sundial designs only a point-like feature such as the tip of the style is used to determine the time and date; this point-like feature is known as the sundial's nodus.12 Some sundials use both a style and a nodus to determine the time and date. The gnomon is usually fixed relative to the dial face but not always; in some designs such as the analemmatic sundial the style is moved according to the month. If the style is fixed the line on the dial plate perpendicularly beneath the style is called the substyle1 meaning "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 (see below). The angle on the dial plate between the noon line and the substyle is called the substyle distance an unusual use of the word distance to mean an angle. By tradition many sundials have a Motto. The motto is usually in the form of an epigram: sometimes sombre reflections on the passing of time and the brevity of life but equally often humorous witticisms of the dial maker.3 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 other designs are equiangular such as the Lambert dial a version of the analemmatic dial with a moveable style. Sundials in the Southern Hemisphere A sundial at a particular latitude in one hemisphere must be reversed for use at the reciprocal latitude in the other hemisphere.4 A vertical direct south sundial in the Northern Hemisphere becomes a vertical direct north sundial in the Southern Hemisphere ; an opposite. To position a horizontal sundial correctly one has to find true North or South. The same process can be used to do both.5 The gnomon set to the correct latitude has to point to the true South in the Southern hemisphere as in the Northern Hemisphere it has to point to the true North.6 Also the hour numbers on a horizontal dial run anti-clockwise rather than clockwise.7 Sundials are not as common in the Southern hemisphere as in the North. This is possibly because when Europeans arrived the mechanical clock was accurate enough for their purposes of time keeping and there was no need to erect sundials.>8 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 gnomons are raised 2655" above horizontal reflecting the local latitude. 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. 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. 395457N 1162325E / 39.9157N 116.3904E / 39.9157; 116.3904 (Forbidden City equatorial sundial) 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.9 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. 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.10 Horizontal sundials For a more detailed description of such a dial see Whitehurst & Son sundial (1812). Horizontal sundial in Minnesota. June 17 2007 at 12:21. 445139.3N 933658.4W 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.11 Hence the line of shadow does not rotate uniformly on the dial face; rather the hour lines are spaced according to the rule12 where is the sundial's geographical latitude (and the angle the style makes with horizontal) 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 of the 3pm hour-line would equal the arctangent of sin() since tan(45) 1. When 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 15 t as for an equatorial dial. However a horizontal sundial is impractical on the Earth's equator where equals 0 the style would lie flat in the plane and cast no shadow. 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 . 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.13 Vertical sundials Two vertical dials at Houghton Hall Norfolk UK 524939N 03927E / 52.827469N 0.657616E / 52.827469; 0.657616 (Houghton Hall vertical sundials). 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.14 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 formula15 where is the sundial's geographical latitude 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 of the 3pm hour-line would equal the arctangent of cos() 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. Dials that face due South North East or West are called vertical direct dials.16 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.17 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. Pocket Sundials This portable folding German sundial has a string gnomon (pointer) adjustable for accuracy at any latitude. As shadows fall across the sundial the smaller dials show Italian and Babylonian hours. The dial also indicates the length of the day and the position of the sun in the zodiac. Polar dials In polar dials the shadow-receiving plane is aligned parallel to the gnomon-style.18 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 +; this occurs when the sun's rays become parallel to the plane. 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.19 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 between the noon hour-line and another hour-line is given by the formula20 where is the sundial's geographical latitude t is the time before or after noon and is the angle of declination from true South. When such a dial faces South (0) this formula reduces to the formula given above tan cos tan(15 t). 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 between the substyle and the noon hour-line is given by the formula20 If a vertical sundial faces true South or North (0 or 180 respectively) the correction 0 and the substyle is aligned with the noon hour-line. The height of the gnomon (that is the angle the style makes to the plate) is 21 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.22 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 above23 where is the desired angle of reclining is the sundial's geographical latitude 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 of the 3pm hour-line would equal the arctangent of sin(+) since tan(45) 1. When equals 90 (in other words a South-facing vertical dial) we obtain the vertical formula above since sin(+90) cos(). 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.24 The angle between the noon hour-line and another hour-line has two components 1 + 2 described by the formulae25 where is the sundial's geographical latitude t is the time before or after noon and and are the angles of inclination and declination respectively. As in the simpler declining dial the gnomon-substyle is not aligned with the noon hour-line.26 The general formula for the angle between the substyle and the noon-line is given by27 Spherical sundials Equatorial bow sundial in Hasselt505547N 52031E / 50.92972N 5.34194E / 50.92972; 5.34194 (Hasselt equatorial bow sundial) Flanders in 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 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.28 However some equiangular sundials such as the Lambert dial described below are based on other principles. 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.29 Among the most precise sundials ever made are two equatorial bows constructed of marble found in Yantra mandir.30 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. Cylindrical conical and other non-planar sundials Precision sundial in Btgenbach Belgium. (Precision 30 seconds)502523N 61206E / 50.4231N 6.2017E / 50.4231; 6.2017 (Belgium) (Google Earth) 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.31 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. 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. 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. Equation of time correction Main article: Equation of time 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. 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.32 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. 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 and the tilt of the Earth's axis 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. 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. Universal equinoctial ring dial 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. A universal equinoctial ring dial (sometimes called a ring dial for brevity although the term is ambiguous) is a portable version of an armillary sundial33 or was inspired by the mariner's astrolabe.34 It was likely invented by William Oughtred around 1600 and became common throughout Europe.35 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. These bars are sometimes an addition to a set of Gemma's rings. 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. 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.36 Analemmatic sundials Main article: Analemmatic sundial Analemmatic sundial on a meridian line in the garden of the abbey of Herkenrode in Hasselt (Flanders in Belgium) The "Eye of Time" an analemma calendar sculpture at the University of Leicester Analemmatic sundials are a common feature at science museums planetariums and public parks. They exploit the fact that the sun travels in a predictable pattern over the course of a year called the Analemma and trace the projection of an object's shadow to measure time not only the hours as in normal sundials but also weeks and months. Lambert dials The Lambert dial is another movable-gnomon sundial.37 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 45 - (/2) where 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 where R is the radius of the Lambert dial and 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. 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.38 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. Chaucer evokes this method a few times in his Canterbury Tales as in his Parson's Tale It was four o'clock according to my guess Since eleven feet a little more or less my shadow at the time did fall Considering that I myself am six feet tall. An equivalent type of sundial using a vertical rod of fixed length is known as a backstaff dial. Shepherd dials Timesticks 19th century Tibetan Shepherd's Timestick A shepherd's dial also known as a shepherds' column dial839 pillar dial cylinder dial or chilindre is a portable cylindrical sundial with a knife-like gnomon that juts out perpendicularly.40 It is normally dangled from a rope or string so the cylinder is vertical. The gnomon can be twisted to be above a month or day indication on the face of the cylinder. This corrects the sundial for the equation of time. The entire sundial is then twisted on its string so that the gnomon aims toward the sun while the cylinder remains vertical. The tip of the shadow indicates the time on the cylinder. The hour curves inscribed on the cylinder permit one to read the time. Shepherd's dials are sometimes hollow so that the gnomon can fold 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 "Goth now your wey" quod he "al stille and softe And lat us dyne as sone as that ye may; for by my chilindre it is pryme of day." Similarly the shepherd's dial is evoked in Shakespeare's Henry VI Part 3 O God! methinks it were a happy life To be no better than a homely swain; To sit upon a hill as I do now To carve out dials quaintly point by point Thereby to see the minutes how they run-- How many makes the hour full complete How many hours brings about the day How many days will finish up the year How many years a mortal man may live. The cylindrical shepherd's dial can be unrolled into a flat plate. In one simple version41 the front and back of the plate each have three columns corresponding to pairs of months with roughly the same solar declination (JuneJuly MayAugust AprilSeptember MarchOctober FebruaryNovember and JanuaryDecember). The top of each column has a hole for inserting the shadow-casting gnomon a peg. Often only two times are marked on the column below one for noon and the other for mid-morning/mid-afternoon. Timesticks clock spear8 or shepherds' time stick8 are based on the same principles as dials.839 The time stick is carved with eight vertical time scales for a different period of the year each bearing a time scale calculated according to the relative amount of daylight during the different months of the year. Any reading depends not only on the time of day but also on the latitude and time of year.39 A peg gnomon is inserted at the top in the appropriate hole or face for the season of the year and turned to the Sun so that the shadow falls directly down the scale. Its end displays the time.8 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.42 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. To adjust for the equation of time the hole is usually on a loose ring within the ring so that the hole can be adjusted to reflect the current month. Card dials (Capuchin dials) Card dials are another form of altitude dial.43 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 Krakw. 500341N 195624E / 50.0614N 19.9400E / 50.0614; 19.9400 (Krakw sundial) The shadow of the cross-shaped nodus moves along a hyperbola which shows the time of the yearindicated 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). 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.44 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.45 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. If the mirror is parallel to the Earth's equator and the ceiling is horizontal then the resulting angles are those of a conventional horizontal sundial. Using the ceiling as a sundial surface exploits unused space and the dial may be large enough to be very accurate. 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. Diptych (tablet) sundial Diptych sundial in the form of a lute circa 1612. The gnomons-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.46 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.47 Multiface (Facet-headed) dials A common multiple dial is to place sundials on every face of a Platonic solid usually a cube.48 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. 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.49 Examples include a three-dimensional cross or star of David on gravestones. Unusual sundials Benoy dials Benoy Sun Clock time shown: 6:00pm - 18.00 hours The Benoy Dial was invented by Walter Gordon Benoy of Collingham in Nottinghamshire. 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 as50 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 Edmunds51 UK Longleat Warminster Wiltshire UK Jodrell Bank Science Centre and Arboretum Birmingham Botanical Gardens Edgbaston UK Science Museum UK - (inventory number 1975-318) 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.5253 The intersection of the two threads' shadows gives the solar time. Digital sundial A digital sundial found in the Sundial Park of Genk (Flanders in Belgium). 505756N 53053E / 50.9655N 5.5146E / 50.9655; 5.5146 (Genk Sundial Park 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. 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. 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. Noon marks Noon-mark from Ste. Marie-Madeleine church in Avenches Switzerland. 465250N 70226E / 46.8805N 7.0405E / 46.8805; 7.0405 (Ste. Marie-Madeleine church noon mark) The analemma is the narrow figure-8 shape which plots the equation of time (in degrees not time 14minutes) 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. 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. Noon cannon A noon cannon sometimes called a 'meridian cannon' is a specialized sundial that is designed to create an 'audible noonmark' by automatically igniting a quantity of gunpowder at noon. These were novelties rather than precision sundials sometimes installed in parks in Europe mainly in the late 18th or early 19th century. They typically consist of a horizontal sundial which has in addition to a gnomon a suitably mounted lens set up to focus the rays of the sun at exactly noon on the firing pan of a miniature cannon loaded with some gunpowder (but no bullet). To function properly the position and angle of the lens must be adjusted seasonally. Meridian lines A horizontal line aligned on a meridian with a gnomon facing the noon-sun is termed a meridian line and does not indicate the time but instead the day of the year. Historically they were used to accurately determine the length of the solar year. Examples are the Bianchini meridian line in Santa Maria degli Angeli e dei Martiri in Rome and the Cassini line in San Petronio Basilica at Bologna. History For more details on this topic see History of sundials. The earliest sundials known from the archaeological record are the obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egyptian astronomy and Babylonian astronomy. 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. The Roman writer Vitruvius lists dials and shadow clocks known at that time. 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 Sundial mottoes Further information: List of sundial mottoes The association of sundials with time has inspired their designers over the centuries to display mottoes as part of the design. Often these cast the device in the role of memento mori inviting the observer to reflect on the transience of the world and the inevitability of death. "Do not kill time for it will surely kill thee." Other mottoes are more whimsical: "I count only the sunny hours" and "I am a sundial and I make a botch / of what is done far better by a watch." Collections of sundial mottoes have often been published through the centuries. See also Foucault pendulum Francesco Bianchini Horology Moondial Nocturnal device for determining time by the stars at night. Scottish sundial the ancient renaissance sundials of Scotland. Tide (time) divisions of the day on early sundials. Wilanw Palace Sundial created by Johannes Hevelius in about 1684. References Notes a b c British Sundial Society. "BSS Glossary.". Archived from the original on 2007-10-10. http://web.archive.org/web/20071010085501/http://www.sundialsoc.org.uk/glossary/alpha.htm#S. Retrieved 2011-05-02.  In some technical writing the word "gnomon" can also mean the perpendicular height of a nodus from the dial plate. The point where the style intersects the dial plate is called the gnomon root. Rohr (1965) pp. 126129; Waugh (1973) pp. 124125. Sabanski Carl. "The Sundial Primer". http://www.mysundial.ca/tsp/northvssouth.html. Retrieved 2008-07-11.  Sunshine in your pocket!. "Making a sundial for the Southern hemisphere.". http://solar.physics.montana.edu/YPOP/Classroom/Lessons/Sundials/south.html. Retrieved 2008-07-11.  Sunshine in your pocket!. "Making a sundial for the Southern hemisphere.". http://solar.physics.montana.edu/cgi-bin/novlessonS.cgi. Retrieved 2008-07-11.  British Sundial Society. "The Sundial Register.". http://www.sundialsoc.org.uk/glossary/frameset.htm. Retrieved 2008-01-05. dead link a b c d e f National Maritime Museum; Lippincott Kristen; Eco Umberto; Gombrich E. H. (1999). The Story of Time. London: Merrell Holberton in association with National Maritime Museum. pp. 4243. ISBN 1-85894-072-9.  Rohr (1965) pp. 4649; Waugh (1973) pp. 2934; Mayall and Mayall (1994) p. 5556 9698 138141. Schaldach K (2004). "The arachne of the Amphiareion and the origin of gnomonics in Greece". Journal of the History of Astronomy 35: 435445. ISSN 0021-8286.  Rohr (1965) pp. 4953; Waugh (1973) pp. 3551; Mayall and Mayall (1994) pp. 56 99101 143144. Rohr (1965) p. 52; Waugh (1973) p. 45. Many ornamental sundials are designed to be used at 45 degrees north. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base so that its style or gnomon is parallel to the Earth's axis of rotation and pointing in the direction of the north celestial pole in the northern hemisphere or the south celestial pole in the southern hemisphere. Some mass-produced garden sundials fail to correctly calculate the hourlines so can never be corrected. A local standard time zone is nominally 15 degrees wide but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer and in cool colors for winter. Rohr (1965) pp. 5369; Waugh (1973) pp. 5299; Mayall and Mayall (1994) pp. 5758 102107 141143 146151. Rohr (1965) p. 55; Waugh (1973) p. 52. Rohr (1965) pp. 5455; Waugh (1973) pp. 5269 Rohr (1965) pp. 5569; Waugh (1973) pp. 7499; Mayall and Mayall (1994) p. 58. Rohr (1965) p. 72; Waugh (1973) pp. 7073; Mayall and Mayall pp. 58 107112. Rohr (1965) pp. 5569; Waugh (1973) pp. 7499; Mayall and Mayall (1994) pp. 58 112117 145146. a b Rohr (1965) p. 79. Mayall and Mayall p. 238. Rohr (1965) pp. 7081; Waugh (1973) pp. 100107; Mayall and Mayall (1994) pp. 5960 117122 144145. Rohr (1965) p. 77; Waugh (1973) pp. 101103; Capt. Samuel Sturmy (1683). The Art of Dialling. London: Unknown publisher.  Rohr (1965) pp. 7681; Waugh (1973) pp. 106107; Mayall and Mayall 122125. Rohr (1965) pp. 7778. Rohr (1965) pp. 7879; Waugh (1973) pp. 106107; Mayall and Mayall 5960. Rohr (1965) p. 78. Rohr (1965) pp. 114 124125; Waugh (1973) pp. 174180; Mayall and Mayall pp. 60 126129 151155. Rohr (1965) p. 17. Rohr (1965) pp. 118119; Mayall and Mayall (1994) pp. 215216. An example of such a half-cylindrical dial may be found at Wellesley College in Massachusetts. (Mayall and Mayall p. 94.) The Claremont CA Bowstring Equatorial. "Photo Info". http://www.wsanford.com/wsanford/exo/sundials/ca/claremont/info.html. Retrieved 2008-01-19.  Waugh (1973) p. 157. Swanick Lois Ann. An Analysis Of Navigational Instruments In The Age Of Exploration: 15th Century To Mid-17th Century MA Thesis Texas A&M University December 2005 Turner 1980 p25 May William Edward A History of Marine Navigation G. T. Foulis & Co. Ltd. Henley-on-Thames Oxfordshire 1973 ISBN 0 85429 143 1 Mayall and Mayall pp. 190192. Rohr (1965) p. 15; Waugh (1973) pp. 13. a b c St. Edmundsbury Borough Council. "Telling the story of time measurement: The Beginnings". http://www.stedmundsbury.gov.uk/sebc/visit/beginnings.cfm. Retrieved 2008-06-20.  Rohr (1965) pp. 109111; Waugh (1973) pp. 150154; Mayall and Mayall pp. 162166. Waugh (1973) pp. 166167. Rohr (1965) p. 111; Waugh (1973) pp. 158160; Mayall and Mayall (1994) pp. 159162. Rohr (1965) p. 110; Waugh (1973) pp. 161165; Mayall and Mayall (1994) p. 166185. Rohr (1965) p. 14. Waugh (1973) pp. 116121. Rohr (1965) p. 112; Waugh (1973) pp. 154155; Mayall and Mayall pp. 2324. Waugh (1973) p. 155. Rohr (1965) p. 118; Waugh (1973) pp. 155156; Mayall and Mayall p. 59. Waugh (1973) pp. 181190. List correct as of British Sundial Register 2000. British Sundial Society. "The Sundial Register.". http://www.sundialsoc.org.uk/register.htm. Retrieved 2008-01-05.  St. Edmundsbury Borough Council. "Telling the story of time measurement.". http://www.stedmundsbury.gov.uk/sebc/visit/Telling-the-Story-of-Time-Measurement.cfm. Retrieved 2008-01-05.  Bifilar sundial Cadran Bifilaire Rohr (1965) pp. 114115. Waugh (1973) pp. 1828. Mayall and Mayall p. 26. 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 ed.). 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):334351 1978 Turner Gerard L'E Antique Scientific Instruments Blandford Press Ltd. 1980 ISBN 0-7137-1068-3 J. L. Heilbron The sun in the church: cathedrals as solar observatories Harvard University Press 2001 ISBN 978-0-674-00536-5. 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. Ralf Kern: Wissenschaftliche Instrumente in ihrer Zeit. Vom 15. 19. Jahrhundert. Verlag der Buchhandlung Walther Knig 2010 ISBN 978-3-86560-772-0 Trait abrg de gnomonique Francis Ziegeltrum auto-dition 2010 ISBN 978-2-7466-1913-5 External links Wikimedia Commons has media related to: Sundials The Ancient Vedic Sun Dial Analemmatic Sundial at Tanglewood Asociacin Amigos de los Relojes de Sol (AARS) - Spanish Sundial Society British Sundial Society La Commission des Cadrans Solaires du Qubec (CCSQ) - Commission on Sundials of Quebec Commission des Cadrans Solaires de la Socit Astronomique de France Coordinamento Gnomonico Italiano (CGI) - Italian Sundial Society Derbyshire Sundials - Sundial Calculators North American Sundial Society Register of Scottish Sundials Societat Catalana de Gnomnica - Catalonian Sundial Society De Zonnewijzerkring - Dutch Sundial Society (in English) Zonnewijzerkring Vlaanderen - Flemish Sundial Society v d eTime 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  Astrarium  History of timekeeping devices  Horology  Marine chronometer  Sundial  Water clock Calendar  Day  Week  Month  Year  Tropical year  Gregorian  Islamic  Julian Intercalation  Leap second  Leap year Chronology Astronomical chronology  Calendar era  Chronicle  Dating methodologies  Geochronology Geologic Time  Geological history  Periodization  Regnal year  Timeline Religion and mythology Dreamtime  Kla  Kalachakra  Prophecy  Time and fate deities  Wheel of time Philosophy A-series and B-series  B-Theory of time  Causality  Endurantism  Eternal return  Eternalism  Event Perdurantism  Presentism  Temporal finitism  Temporal parts  The Unreality of Time Physical sciences Time in physics  Absolute time and space  Arrow of time  Chronon  Coordinate time Planck epoch  Planck time  Proper time  Spacetime  Theory of relativity Time dilation  Gravitational time dilation  Time domain  T-symmetry Biology Chronobiology  Circadian rhythms Psychology Mental chronometry  Sense of time  Specious present Sociology and anthropology Long Now Foundation  Time discipline  Time use research Economics Time value of money  Time-based currency  Time Banking Related topics Carpe diem  Duration  Hexadecimal time  Metric time  Space  System time  Tempus fugit Time capsule  Time signature  Time travel v d eTime measurement and standards Major subjects Time  Chronometry  Orders of magnitude  Metrology International standards UTC  UTC offset  UT  DUT1  IERS  ISO 31-1  ISO 8601  TAI  12-hour clock  24-hour clock  Barycentric Coordinate Time  Civil time  Daylight saving time  Geocentric Coordinate Time  International Date Line  Leap second  Solar time  Terrestrial Time  Time zone Obsolete standards Barycentric Dynamical Time  Ephemeris time  Greenwich Mean Time  Prime Meridian Time in physics Absolute time and space  Spacetime  Chronon  Continuous time  Coordinate time  Cosmological decade  Discrete time  Planck epoch  Planck time  Proper time  Theory of relativity  Time dilation  Gravitational time dilation  Time domain  T-symmetry Horology Clock  Astrarium  Atomic clock  Complication  Equation of time  History of timekeeping devices  Hourglass  Marine chronometer  Marine sandglass  Radio clock  Sundial  Watch  Water clock Calendar Astronomical  Calculating the day of the week  Dominical letter  Epact  Equinox  Gregorian  Intercalation  Islamic  Julian  Leap year  Lunar  Lunisolar  Seven-day week  Solar  Solstice  Tropical year  Week-day names Archaeology & geology Dating methodologies  Geologic time scale  International Commission on Stratigraphy Astronomical chronology Galactic year  Nuclear time scale  Precession  Sidereal time Units of time Century  Day  Decade  Fortnight  Hour  Jiffy  Lustrum  Millennium  Minute  Month  Saeculum  Second  Shake  Tide  Week  Year Related topics Chronology  Duration  Mental chronometry  Metric time  System time  Time value of money  Timekeeper