# Sundial

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SSW facing, vertical declining sundial on Moot Hall, Aldeburgh, Suffolk, England.

A sundial is a device that tells the time of day 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 their styles parallel to the axis of the Earth's rotation to tell the correct time throughout the year. The style's angle from the horizontal will thus equal the sundial's geographical latitude. It is common for inexpensive mass-produced decorative sundials to have incorrect hour angles, which cannot be adjusted to tell correct time.[1][2]

## Introduction

A child and a woman looking at a sundial installed at the National Garden of Athens, Greece in 2013

There are different types of sundials. Some sundials use a shadow or the edge of a shadow while others use a line or spot of light to indicate the time.

The shadow-casting object, known as a gnomon, may be a long thin rod, or other 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} With sundials using light to indicate time, a line of light may be formed by allowing the sun's rays through a thin slit or focusing them through a cylindrical lens. A spot of light may be formed by allowing the sun's rays to pass through a small hole or by reflecting them from a small circular mirror.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

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 an earlier 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} ## Apparent motion of the Sun Top view of an equatorial sundial. The hour lines are spaced equally about the circle, and the shadow of the gnomon (a thin cylindrical rod) rotates uniformly. The height of the gnomon is 5/12 the outer radius of the dial. This animation depicts the motion of the shadow from 3 a.m. to 9 p.m. (not accounting for Daylight Saving Time) on or around Solstice, when the sun is at its highest declination (roughly 23.5°). Sunrise and sunset occur at 3am and 9pm, respectively, on that day at geographical latitudes near 57.05°, roughly the latitude of Aberdeen, Scotland or Sitka, Alaska. {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B=

{{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

The principles of sundials are understood most easily from the Sun's apparent motion. The Earth rotates on its axis, and revolves in an elliptical orbit around the Sun. An excellent approximation assumes that the Sun revolves around a stationary Earth on the celestial sphere, which rotates every 24 hours 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} Unlike the fixed stars, the Sun changes its position on the celestial sphere, being at a positive declination in spring and summer, and at a negative declination in autumn and winter, and having exactly zero declination (i.e., being on the celestial equator) at the equinoxes. The Sun's celestial longitude also varies, changing by one complete revolution per year. The path of the Sun on the celestial sphere is called the ecliptic. The ecliptic passes through the twelve constellations of the zodiac in the course of a year.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

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).{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} 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 data—such as the horizon, the equator and the tropics—which 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.[3] 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 parallel to the axis of the celestial sphere, and therefore is 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.[3]Template:Efn 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 substyle,[3] meaning "below the style". The angle the style makes with the plane of 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.Template:SfnTemplate:Sfn 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 Southern-hemisphere sundial in Perth, Australia. Magnify to see that the hour marks run anticlockwise. Note graph of Equation of Time, needed to correct sundial readings. A sundial at a particular latitude in one hemisphere must be reversed for use at the opposite 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. 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 go in opposite directions, so on a horizontal dial they run anti-clockwise rather than clockwise.[7] Sundials which are designed to be used with their plates horizontal in one hemisphere can be used with their plates vertical at the complementary latitude in the other hemisphere. For example, the illustrated sundial in Perth, Australia, which is at latitude 32 degrees South, would function properly if it were mounted on a south-facing vertical wall at latitude 58 (i.e. 90-32) degrees North, which is slightly further North than Perth, Scotland. The surface of the wall in Scotland would be parallel with the horizontal ground in Australia (ignoring the difference of longitude), so the sundial would work identically on both surfaces. Sundials are used much less in the Southern Hemisphere than the Northern.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} One reason for this is the seasonal asymmetry of the equation of time. (See also below.) From early November to mid-February, during the Southern Hemisphere's summer, a sundial loses about half an hour relative to a clock. This adds to the difficulty of using it as a timepiece. The change during the northern summer is only about one-third as great, and is often ignored without causing much error. Since sundials are mainly used during the summer months, they are therefore better suited to the Northern Hemisphere.Template:OR

The most common reason for a sundial to differ greatly 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 a sundial must have been designed for the local geographical latitude and its style must be parallel to the Earth's rotational axis; the style must be aligned with true North and its height (its angle with the horizontal) must equal the local latitude. To adjust the style height, the sundial can often be tilted slightly "up" or "down" while maintaining the style's north-south alignment.Template:Sfn

### 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.

## 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 26°55" above horizontal, reflecting the local latitude.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

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. Template:Coord 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.Template:SfnTemplate:SfnTemplate:Sfn 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).

${\displaystyle H_{E}=15^{\circ }\times t(hours)}$

The uniformity of their spacing makes this type of sundial easy to construct. If the dial plate material is opaque, both sides of the equatorial dial must be marked, since the shadow will be cast from below in winter and from above in summer. With translucent dial plates (e.g. glass) the hour angles need only be marked on the sun-facing side, although the hour numberings (if used) need be made on both sides of the dial, owing to the differing hour schema on the sun-facing and sun-backing sides. Another major advantage of this dial is that equation of time (EoT) and daylight saving time (DST) corrections can be made by simply rotating the dial plate by the appropriate angle each day. This is because the hour angles are equally spaced around the dial. For this reason, an equatorial dial is often a useful choice when the dial is for public display and it is desirable to have it show the true local time to reasonable accuracy. The EoT correction is made via the relation :

${\displaystyle Correction^{\circ }={\frac {EoT(minutes)+60\times \Delta DST(hours)}{15}}}$

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.[11]

### Horizontal sundials

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

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.Template:Sfn Template:Sfn Template:Sfn Hence, the line of shadow does not rotate uniformly on the dial face; rather, the hour lines are spaced according to the rule Template:Sfn Template:Sfn

${\displaystyle \tan H_{H}=\sin L\tan(15^{\circ }\times t)}$

where L is the sundial's geographical latitude (and the angle the style makes with horizontal), ${\displaystyle H_{H}}$ 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 ${\displaystyle H_{H}}$ of the 3pm hour-line would equal the arctangent of sin L, since tan 45° = 1. When L 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 plane; the hour-line formula becomes ${\displaystyle H_{H}}$ = 15° × t, as for an equatorial dial. A horizontal sundial at the Earth's equator, where L equals 0°, would require a (raised) horizontal style and would be an example of a polar sundial (see below).

Detail of horizontal sundial outside Kew Palace in London, United Kingdom

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 L. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base 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. {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} Many ornamental sundials are designed to be used at 45 degrees north. Some mass-produced garden sundials fail to correctly calculate the hourlines and so can never be corrected. A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles. To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter. {{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} Since the hour angles are not evenly spaced, the equation of time corrections cannot be made via rotating the dial plate about the gnomon axis. These types of dials usually have an equation of time correction tabulation engraved on their pedestals or close by. Horizontal dials are commonly seen in gardens, churchyards and in public areas.

### Vertical sundials

Two vertical dials at Houghton Hall Norfolk UK Template:Coord. 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.Template:Sfn Template:Sfn Template:Sfn 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 formulaTemplate:Sfn Template:Sfn

${\displaystyle \tan H_{V}=\cos L\tan(15^{\circ }\times t)}$

where L is the sundial's geographical latitude, ${\displaystyle H_{H}}$ 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 ${\displaystyle H_{H}}$ of the 3pm hour-line would equal the arctangent of cos L, since tan 45° = 1. Interestingly, the shadow moves counter-clockwise on a South-facing vertical dial, whereas it runs clockwise on horizontal and equatorial north-facing dials.

Dials with faces perpendicular to the ground and which face directly South, North, East, or West are called vertical direct dials.Template:Sfn Template:Sfn It is widely believed, and stated in respectable publications, that a vertical dial cannot receive more than twelve hours of sunlight a day, no matter how many hours of daylight there are.Template:Sfn However, there is an exception. Vertical sundials in the tropics which face the nearer pole (e.g. north facing in the zone between the Equator and the Tropic of Cancer) can actually receive sunlight for more than 12 hours from sunrise to sunset for a short period around the time of the summer solstice. For example, at latitude 20 degrees North, on June 21, the sun shines on a north-facing vertical wall for 13 hours, 21 minutes.[12] Vertical sundials which do not face directly South (in the northern hemisphere) may receive significantly less than twelve hours of sunlight per day, depending on the direction they do face, and on the time of year. For example, a vertical dial that faces due East can 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 uncommon, because they tell time only during the spring and summer, and do not show the midday hours except in tropical latitudes (and even there, only around midsummer). For non-direct vertical dials — those that face in non-cardinal directions — the mathematics of arranging the style and the hour-lines becomes more complicated; it may be easier to mark the hour lines by observation, but the placement of the style, at least, must be calculated first; such dials are said to be declining dials.Template:Sfn Template:Sfn Template:Sfn

"Double" sundials in Nové Město nad Metují, Czech Republic; the observer is facing almost due north.

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 faces toward the South, but does not face due South, the gnomon will not lie along the noon line, and the hour lines must be corrected. Since the gnomon's style must be parallel to the Earth's axis, it always "points" true North and its angle with the horizontal will equal the sundial's geographical latitude; on a direct south dial, its angle with the vertical face of the dial will equal the colatitude, or 90° minus the latitude.Template:Sfn

### 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 sundial,Template:Sfn or was inspired by the mariner's astrolabe.[15] It was likely invented by William Oughtred around 1600 and became common throughout Europe.Template:Sfn

In its simplest form, the style is a thin slit that allows the sun's rays to fall on the hour-lines of an 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.[16]

### Analemmatic sundials

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Analemmatic sundial on a meridian line in the garden of the abbey of Herkenrode in Hasselt (Flanders in Belgium)

Analemmatic sundials are a type of horizontal sundial that has a vertical gnomon and hour markers positioned in an elliptical pattern. There are no hour lines on the dial and the time of day is read on the ellipse. The gnomon is not fixed and must change position daily to accurately indicate time of day. Analemmatic sundials are sometimes designed with a human as the gnomon. Human gnomon analemmatic sundials are not practical at lower latitudes where a human shadow is quite short during the summer months. A 66 inch tall person casts a 4 inch shadow at 27 deg latitude on the summer solstice. [17]

### Lambert dials

The Lambert dial is another movable-gnomon sundial.Template:Sfn 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 nor aligned with the Earth's rotational axis; rather, it is tilted northwards by an angle α = 45° - (Φ/2), where Φ 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

${\displaystyle Y=R\tan \alpha \tan \delta \,}$

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

## Altitude-based sundials

### Diptych (tablet) sundial

Diptych sundial in the form of a lute, c. 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.[27] 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.[28]

A common multiple dial is to place sundials on every face of a Platonic solid, usually a cube.[29] 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.

### Globe dial

The globe dial is a sphere aligned with the Earth's rotational axis, and equipped with a spherical vane.Template:Sfn 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.

### Noon marks

Noon mark from the Greenwich Royal Observatory. The analemma is the narrow figure-8 shape, which plots the equation of time (in degrees, not time, 1°=4 minutes) 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. Template:Sfn 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.Template:Sfn 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.

Template:Rellink 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.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }} ## Using a sundial as a compass If a horizontal-plate sundial is portable and is made for the latitude in which it is being used, and if the user has a watch and the necessary information to calculate the local sundial time from its reading, the sundial can be used to find the directions of True North, South, etc. The sundial should be placed on a horizontal surface, and rotated about a vertical axis until it shows the correct time. The gnomon will then be pointing to the North, in the northern hemisphere, or to the South in the southern hemisphere. This method is much more accurate than using the watch as a compass (see watch) and can be used in places where the magnetic declination is large, making a magnetic compass unreliable.{{ safesubst:#invoke:Unsubst||date=__DATE__ |$B= {{#invoke:Category handler|main}}{{#invoke:Category handler|main}}[citation needed] }}

An Angbuilgu, (National Museum of Korea)

## References

### Citations

1. Template:Cite web
2. Template:Cite web
3. Template:Cite web
4. Template:Cite web
5. Template:Cite web
6. Template:Cite web
7. Template:Cite web
8. Template:Cite web
9. Template:Cite web
10. {{#invoke:citation/CS1|citation |CitationClass=book }}
11. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
12. Template:Cite web
13. Rohr (1965), pp. 70–81; Waugh (1973), pp. 100–107; Mayall and Mayall (1994), pp. 59–60, 117–122, 144–145.
14. Rohr (1965), p. 77; Waugh (1973), pp. 101–103; {{#invoke:citation/CS1|citation |CitationClass=book }}
15. 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
16. May, William Edward, A History of Marine Navigation, G. T. Foulis & Co. Ltd., Henley-on-Thames, Oxfordshire, 1973, ISBN 0-85429-143-1
17. Analemmatic sundials: How to build one and why they work by C.J. Budd and C.J. Sangwin
18. Rohr (1965), p. 15; Waugh (1973), pp. 1–3.
19. {{#invoke:citation/CS1|citation |CitationClass=book }}
20. Rohr (1965), pp. 109–111; Waugh (1973), pp. 150–154; Mayall and Mayall, pp. 162–166.
21. Waugh (1973), pp. 166–167.
22. Rohr (1965), p. 111; Waugh (1973), pp. 158–160; Mayall and Mayall (1994), pp. 159–162.
23. Rohr (1965), p. 110; Waugh (1973), pp. 161–165; Mayall and Mayall (1994), p. 166–185.
24. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
25. Waugh (1973), pp. 116–121.
26. Rohr (1965), p. 112; Waugh (1973), pp. 154–155; Mayall and Mayall, pp. 23–24.
27. Waugh (1973), p. 155.
28. Rohr (1965),, p. 118; Waugh (1973), pp. 155–156; Mayall and Mayall, p. 59.
29. List correct as of British Sundial Register 2000. Template:Cite web
30. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
32. Digital sundial

### Bibliography

• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• {{#invoke:citation/CS1|citation

|CitationClass=book }} Reprint of the 1902 book published by Macmillan (New York).

• Heilbron, J. L. : The sun in the church: cathedrals as solar observatories, Harvard University Press, 2001 ISBN 978-0-674-00536-5.
• A.P. Herbert, Sundials Old and New, Methuen & Co. Ltd, 1967.
• Kern, Ralf : Wissenschaftliche Instrumente in ihrer Zeit. Vom 15. – 19. Jahrhundert. Verlag der Buchhandlung Walther König 2010, ISBN 978-3-86560-772-0
• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• Hugo Michnik, Theorie einer Bifilar-Sonnenuhr, Astronomishe Nachrichten, 217(5190), p. 81-90, 1923
• {{#invoke:citation/CS1|citation

|CitationClass=book }} 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).

• Savoie, Denis: Sundials, Design, Construction, and Use, Springer, 2009, ISBN 978-0-387-09801-2.
• Frederick W. Sawyer, Bifilar gnomonics, JBAA (Journal of the British Astronomical association), 88(4):334–351, 1978
• {{#invoke:citation/CS1|citation

|CitationClass=book }}

• Walker, Brown: Make A Sundial, (The Education Group British Sundial Society) Editors Jane Walker and David Brown, British Sundial Society 1991 ISBN 0-9518404-0
• {{#invoke:citation/CS1|citation

|CitationClass=book }}