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The Gnomon - Sundial

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Author Topic: The Gnomon - Sundial  (Read 13888 times)
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« on: December 16, 2007, 07:42:36 am »


The gnomon is the triangular blade in this sundial.

The gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."

In the northern hemisphere, the shadow-casting edge is normally oriented so that it points north and is parallel to the rotation axis of the Earth. That is, it is inclined to the horizontal at an angle that equals the latitude of the sundial's location. On some sundials, the gnomon is vertical. These were usually used in former times for observing the altitude of the sun, especially when on the meridian.

The style is the part of the gnomon that casts the shadow. This can change as the sun moves. For example, the upper west edge of the gnomon might be the style in the morning and the upper east edge might be the style in the afternoon.

The art of constructing a gnomon sundial is sometimes termed gnomonics. One so skilled would be referred to as a gnomonist.

Gnomon may also imply the design paradigm relationship between an indicator and a dial or other reference, as with a speedometer and needle. In this case, the needle functions as a gnomon against the incremented speedometer background.

Gnomon is also a mathematical term that describes the part of a parallelogram that remains when a similar parallelogram is removed from one of its corners.

Also, gnomon is the name given to an aesthetic process utilised by James Joyce in his set of short stories Dubliners, whereby the whole of the character is revealed by a single part.

Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Greeks. The Chinese also used the gnomon, mentioned in the 2nd century Nine Chapters on the Mathematical Art as being used much earlier by the Duke of Zhou (11th century BC).
« Last Edit: December 16, 2007, 07:44:00 am by Bianca2001 » Report Spam   Logged

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« Reply #1 on: December 16, 2007, 07:46:39 am »


From Wikipedia, the free encyclopedia

The scaphion was a portable gnomon, developed by hellenistic astronomers. They put a gnomon in a metallic hemisphere, which was divided inside in concentric circles. They could use it for determination of geographical coordinates from measured solar altitudes. Using this measuring instrument Eratosthenes of Cyrene (ca. 220 BC) had measured the length of Earth's meridian, and after that they used this instrument to survey smaller regions as well.
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« Reply #2 on: December 16, 2007, 07:50:14 am »

Figure 1. Basic sundial nomenclature.


aberration (of light): the effect by which the apparent direction of distant astronomical bodies is altered by the velocity of the Earth and the finite speed of light. Discovered by James Bradley, it has a value of 20.47 arc-sec and is thus totally insignificant to dialling.

accuracy (of a dial): a measure of how closely the time indicators (lines or points) of a dial indicate the true time. Contrast with resolution. See also precision.

Act of 1751: {1752} refers to an act of the British parliament in that year which finally adopted the Gregorian calendar and set the beginning of the (English) year to 1 January, rather than 25 March. As a result, there can be some confusion about the year, prior to 1752, for dates between January and March. Scotland's New Year's Day had already been set to 1 January since 1600. Dates in the Julian calendar are usually denoted "Old Style", with those in the Gregorian "New Style.
British dials made before 1752 and which have EoT or sunrise/sunset tables show dates 11 days earlier than the current ones, e.g. the vernal equinox is on 10 March instead of 21 March, and the EoT will be shown as zero on 5 April, 3 June, 23 August and 15 December. Note that the Act was passed in 1751 but did not come into operation until the following year, hence the alternative dates sometimes seen.

acute angle: an angle of less than 90º.

age of the moon: see phase of the moon.

almanac: an annual calendar of months and days, with astronomical and other data. They usually include an ephemeris of the Sun and some other celestial bodies, the equation of time, the Sun's declination etc. Almanacs are sometimes inscribed on, or accompany, C16-18 dials.
The annual Nautical Almanac, produced by the Royal Greenwich Observatory, derives from the version first published by Astronomer Royal Nevil Maskelyne in 1767.

almucantar: (pron. al-moo-can-tar) a circle of equal altitude on the celestial sphere. It is a small circle on the celestial sphere, parallel to the horizon.

alidade: the revolving arm of an astrolabe through which sightings of the stars are made. Sometimes used on sundials where a pinhole at one end of the ~ forms an image of the Sun on a plate at the other end carrying an analemma.

altazimuth: {alt-azimuth} a mounting system for an astronomical instrument that allows it to be set in altitude and azimuth. The term is also used to describe the horizon co-ordinate system which uses these two parameters.

altitude (of the sun): {elevation} [a, ALT] the angular distance of the (centre of) the sun's disk above the observer's horizon (negative values indicate that the Sun is below the horizon). It is measured along the principal plane to the sun's centre, and is the complement to the zenith distance. It is part of the horizon co-ordinate system. See Equations. Note that aviators and others use the term altitude to measure a height (distance) above the ground.

anaphoric (clock): a clock with a dial face like an astrolabe, showing seasonal hours.

ante meridiem (a.m.): before noon.

analemma: (pron. ana-lem-a) in modern usage it is a graphical plot with the Equation of Time on one axis and the sun's declination on the other. In appearance, a tall thin figure of eight. The dates of various points around the curve are often shown. The shadow of a point falling onto an arbitrary plane at the same clock time each day will trace out an analemma over the course of a year. Normally seen on the noon line of a dial, but can be on any hour line. The exact appearance of the analemma will depend on the plane upon which it is projected.

Figure 2. The components of the analemma

The word analemma has had several other meanings in the history of astronomy and dialling. In the first century BC, the Roman engineer Vitruvius used the word to refer to a graphical construction, equivalent to today's orthographic projection. In the second century AD Ptolemy used analemma to mean an instrument acting as a nomograph for defining the angles of a dial. The use of a modern analemma on a dial dates to around 1640, and the first treatment in English was by Samuel Foster in 1654.

angle: (units of measurement) may be decimal degrees; degrees, arc-minutes and arc-seconds; radians (2 radians = 360º); or (seldom, military equipment) mils (6400 mils = 360º); or (very rare) grade (1/100th of a right angle). Preferred notations are: [dd.ddº or ddº mm' ss"]. Note that trigonometric functions in computer spreadsheets (e.g. ExcelTM ) are always defined in radians. The mathematical convention is that positive angles are measured counter-clockwise, usually with the zero angle position in the 3 o'clock direction or along the x-axis (see cartesian co-ordinates). In dialling, it is more common to measure angles counter-clockwise from the noon line, although some authors measure from the sub-style line.

Antarctic Circle: the parallel of latitude at 66° 34' S. Note that this defines the northern limit of the region around the S pole having at least one day a year with no night.

antisolar point: the point on the celestial sphere directly opposite the sun's position.

aperture: a small transparent hole in an opaque surface, designed to let a small beam of sunlight through to fall on a dial plate or alidade e.g. for noon dials, ring dials and heliochronometers.

aphelion: (pron. ap-heel-eon) the point where the Earth's orbit takes it furthest from the sun. It occurs during the first week of July.

apogee: (pron. apo-gee) the point in the Moon's (or other satellite's) orbit when it is furthest from the Earth.

arc: a curve which is part of the circumference of a circle.

arc-minutes {or minutes of arc}: an angular measure equal to 1/60th of a degree. Preferred notation [' or arcmin].

arc-seconds {or seconds of arc}: an angular measure equal to 1/60th of an arc-minute. Preferred notation [ " or arcsec].

Arctic Circle: parallel of latitude at 66° 34' N. Note that this defines the southern limit of the region around the N pole having at least one day a year with no night.

Aries (first point of): see equinoxes.

armillary sphere: a skeleton model of the celestial sphere with rings representing the equator, tropics etc. Often finely made in brass, but versions in wood with paper scales were common in 19th century France. It is also the basis of a form of dial - see armillary, dial (types of).

ascendant: rising towards the zenith. Note: astrologers have a different definition.

astro compass: see solar compass.

astroid: (pron. as-troy-d) a mathematical curve which is formed by the envelope of a series of straight lines, and has the equation: x2/3 + y2/3 = 1. In dialling, it is the shape of a vertical gnomon used in the latitude-independent astroid dial. The astroid curve is also one branch of the shape which is traced out by a point on the circumference of a circle as it rolls inside a circle of four times the radius.

ASTROLABE: an early astronomical instrument in the form of a heavy disk (the mater) which was suspended vertically and had an angular scale marked around it (the limb). A coplanar klimata and an alidade rotated about its centre. A fretted rete gave the positions of the brightest fixed stars. The various components were held on the central pivot (the pin or axis) by a small wedge or horse; sometimes dog.

 - The planispheric ~ represents the celestial sphere by a two-dimensional stereographic projection, showing the position of the sun and major stars at different times and dates, as well as different latitudes. A separate plate is required for each latitude. It was probably a Greek invention of the 2nd century BC, but it was developed extensively by the Islamic cultures from the 9th century AD. It fell out of use in the late 17th century in the west.

 - The universal ~ uses modified projections of the celestial sphere so that they are latitude-independent. The Gemma Frisius type (developed in the west in the early 16th century) retains the stereographic projection but moves the centre to the First point of Aries. The Rojas type (by J. de Rojas of Sarmiento, 1550) uses an orthographic projection with a projection point at infinity. The La Hire type (late 17th century) moved the projection point in an attempt to make it easier to read.

 - The mariner's ~ is a much-simplified instrument designed to measure the sun's altitude, using an open frame and weighted at the bottom to make it more stable onboard ship; it is a precursor to the sextant.

    See Appendix X for further astrolabe terminology.

astronomical triangle: the spherical triangle on the celestial sphere whose vertices are the observer's zenith, the elevated celestial pole, and the position of the Sun (or other celestial body).

atmospheric refraction: see refraction.

autumnal {or fall} equinox: see equinoxes.

axis (of the Earth's rotation) or polar axis: the line running through the true North and South poles about which the Earth rotates.

azimuth (of the sun): [A, AZ] the angle of the sun, measured in the horizontal plane and from true south. Angles to the west are positive, those to the east, negative. Thus due west is 90°, north is ±180°, east –90°. It is part of the horizon co-ordinate system. See Equations. Note that navigators (and some astronomers, but not Meeus) measure azimuth or bearings clockwise from the north.

« Last Edit: December 16, 2007, 04:35:57 pm by Bianca2001 » Report Spam   Logged

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« Reply #3 on: December 16, 2007, 07:53:53 am »


back-staff: an old instrument for measuring the altitude of the Sun while facing away from it. The Davis quadrant, designed by the English captain John Davis, is actually a form of back-staff.

bay (or bay en imy wenut): literally a "palm rib of the observer of the hours". It was an ancient Egyptian instrument or sighting device, used in conjunction with a merkhet to observe and time transits.

Beltane {Beltaine}: an ancient Celtic festival held on the 1st of May, when bonfires were lit. It is one of the cross-quarter days

bissextile: a leap-year (from bis sextus dies, or doubled 24 February).

blue moon: there are at least two possible meanings. It can mean a second full moon in a given calendar month. It seems that this "meaning" was accidentally invented by Sky and Telescope magazine in 1946, but it has passed into wide usage. Alternatively, it may mean that the Moon actually has a blue coloration, due to smoke or other aerosols in the atmosphere. Both phenomena are rare (the second more so), hence the expression "once in a blue moon".

brachiolus: (pron. brak-e-o-lus) from the Latin for "little arm" it is a movable arm which acts as a suspension point for a cord on a card dial.

break of day: see daybreak.

British Summer Time [BST]: see time (types of).
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« Reply #4 on: December 16, 2007, 07:55:05 am »


Candlemas: the festival of the purification of the Virgin Mary, on 2nd February. It also corresponds to the Celtic festival of Imbolic, and is a cross-quarter day.

calendar: a system for counting days and defining the date.

Campbell-Stokes: see sunshine recorder.

Cancer: see tropics.

canting out: see wedging out.

Capricorn: see tropics.

cardinal point (of the compass): North, South, East or West [N, S, E or W]. These points are the intersections of the celestial meridian (N, S) and the prime vertical (E, W) with the horizon. Note that the Latin terms are Septentrio, Meridies, Oriens and Occidens, so that a compass rose on a mediaeval dial simply identifying "S" is ambi guous.

cartesian co-ordinates: see co-ordinates .

celestial equator: the intersection of the extended plane of the Earth's equator with the celestial sphere.

celestial latitude: see ecliptic latitude.

celestial longitude: see ecliptic longitude.

celestial pole: the points on the celestial sphere where it meets the Earth's axis. The stars appear to rotate around these poles.

celestial sphere: an imaginary sphere, arbitrarily large and co-centred with the Earth, on which all the stars appear to be fixed.

centre (of a dial): the point where all the hour lines, and a polar-pointing style, meet. This point does not always exist (e.g. on polar dial and direct E or W dials, the lines meet at infinity). In simple horizontal or vertical dials, this point coincides with the root of a (thin) gnomon. In the case of a thick gnomon having two styles, there are two centres to the dial. The centre is often, but not necessarily, the origin of the co-ordinate system used to describe the dial. See Figure 1.

chapter ring: the ring on a dial face carrying the hour numerals. The term is more widely used for clocks, but it also finds use, for example, on dials with several separate rings for different locations.

chilindrum: see Dial (types of); cylinder ~.

civil time: see Time (types of) civil~.

clinometer: an instrument for measuring the inclination or slope of a surface. Also called an inclinometer.

cloisonné: a term sometimes used to describe the technique of making metal dials by deeply etching the lines and numerals and then filling them with coloured material. It derives from the jewellery method of separating enamels into shallow compartments with metal edges.

co-latitude: equals 90° – latitude.

compass bowl: a bowl sunk into the dial plate of a (portable) horizontal dial to house a magnetic compass.

compass rose: a drawing of the compass directions, showing as a bare minimum the cardinal points, but more usually eight, sixteen or thirty-two points.

compendium: normally used to describe a collection of scientific instruments in one case. Also, Compendium: the journal of the NASS.

conic section: any of the range of geometric curves produced by the intersection of plane with a cone (i.e. circles, ellipses, parabolas and hyperbolas).

co-ordinates: a system of measurements used to describe any point in two or three dimensions.
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« Reply #5 on: December 16, 2007, 07:56:46 am »

Co-ordinate Systems:

Cartesian ~ [x,y,z] in which the axes are mutually perpendicular, are normally used for positions of points within a dial. For simple horizontal dials the preferred axes have x increasing to the E of the dial plane, y increasing to the N of the dial plane and z (in 3-D only) increasing. perpendicularly to the dial plane (upwards). For vertical and other plane dials, x increases to the left, y increases downwards, and z perpendicular to the plane in the direction towards the observer. The origin of the system must be defined explicitly. Note that these definitions produce a conventional right-handed co-ordinate system, and are also those used by the Zonwvlak programs.

ecliptic ~: {celestial ~} [ ,  e ] or [ELAT, ELON] the system of ecliptic (or celestial) latitude and longitude, defined with respect to the ecliptic and the celestial poles. Ecliptic co-ordinates predominated in Western astronomy until the Renaissance but, with the advent of national nautical almanacs, the equatorial system, more suited to observation and navigation, gained ascendancy.

Figure 3. Celestial co-ordinates seen by an observer in mid-northern latitudes.

equatorial ~: [,  ] or [RA, DEC] is the most common astronomical co-ordinate system and is defined by the celestial equator and poles. The right ascension and declination are directly analogous to terrestrial latitude and longitude.

Figure 4. The equatorial system of celestial co-ordinates, showing the right ascension (RA) and declination (dec) of a star.

galactic ~: is used for studying the structure of the galaxy. It is unlikely to be encountered in dialling.

geographic ~: (or terrestrial ~) [,  ] or [Lat, LON] the standard method of determining any location on the Earth's globe, using latitude and longitude.

horizon ~ system: {or altazimuth system} [a,A] or [ALT,AZ] the simplest celestial co-ordinate system, it is based on altitude and azimuth. It is fundamental in navigation as well as in terrestrial surveying. However, for specifying the position of the Sun or other celestial bodies, other co-ordinate systems fixed with respect to the celestial sphere are far more suitable.

Ordnance Survey co-ordinates: (also referred to as the British National Grid, BNG) the system of Eastings and Northings used to define locations in the UK. They are cartesian co-ordinates with a basic grid consisting of 100km squares, each of which has a unique two-letter code (e.g. SZ). See Appendix XI for a map of the grid squares. The full OS grid reference comprises these two letters followed by a three-digit easting and a three digit northing, eg SZeeennn. This gives a resolution of 100m in both directions. Higher resolution ("6-figure" or BNG) references usually replace the letter code with their numerical values, eg eeeeee nnnnnn, giving a 1m resolution. Here, the first two digits of the easting (northing) are the distance in 10 km increments east (north) of the datum point at the bottom left of the map. Note that the OS maps on which the co-ordinates are based use the transverse Mercator projection, with a projection origin at 49º N; 2° W.

polar ~ :[r, ] an angle-based co-ordinate systemal sometimes used for defining points on a dial plane, where r is the distance from the origin and  is measured anti-clockwise from the S. Note: navigators also make use of polar co-ordinates and usually define them as (, r).

Ptolemaic co-ordinates [hec, hor]: an angular co-ordinate system loosely based on the geometry of Ptolemy.

terrestrial : see geographic ~.

End of Co-ordinate systems
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« Reply #6 on: December 16, 2007, 07:57:53 am »


cross: for a discussion of the cross sometimes seen on the noon line of a dial, see noon cross and cross patty.

cross-quarter days: days which are (approximately) midway between the Quarter days, hence dividing the year into eight parts. They are occasionally used instead of the zodiac signs for declination lines on dials, and have become adopted as modern celebrations or holidays. See Appendix XII for their names and dates.

cross patty {c. pattée or c. formée}: an heraldic term for a form of square cross shape (  ) sometimes seen instead of XII on the noon line of dials. It is perhaps the most common of the noon crosses.

cross-staff: a simple instrument for determining t he altitude of a celestial body. A cross piece or transom is moved along a staff, calibrated with a cotangent scale, and sighted by eye against the body and the horizon. Old illustrations often show a ~ with three transoms fitted but, in use, only one would be used at a time. Also called a fore-staff or Jacob's staff.

culmination (of the sun): to lie on the meridian or, in more general language, to reach its highest point. Equivalent to the superior transit. From the Latin "culmen", meaning summit.

cursor: a part of a mathematical instrument which slides backwards and forwards over a scale.

cusp: (mathematical) a sharp point where two curves meet e.g. the "horns" of the Moon (strictly, where the second derivative of a curve changes sign).
(astrological) the initial point of an astrological house or sign.

cycloid: (pron. si-cloy-d) a geometric curve which is traced out by a point on the circumference of a circular disk rolling (without slipping) along a straight line.
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« Reply #7 on: December 16, 2007, 07:59:21 am »


daeg mael: one of the Anglo-Saxon tides, it may also have been the word for a dial in the early Anglo-Saxon period.

dagsmork: an Icelandic term ('daymarks') referring to landmarks in the countryside which, when viewed from a fixed location, indicated the direction of the Sun at fixed times of the day.

date: a single day in a chosen calendar system. Note that the agreed international date system (and British Standard 4795) specify "year, month, day" - for example 1951 August 10. Common UK usage is the reverse of this - beware the illogical American usage of month, day, year, especially in all-numeric forms.

Date Line see International Date Line.

dawn: the first light of day, taken as the onset of morning twilight.

day: the period for one rotation of the Earth. Solar ~ : measured between successive transits of the sun: Mean solar ~ :measured between successive transits of the fictitious mean sun. Equal to 24 hours, it is the usual meaning of ~ unless it is further qualified. Sidereal ~ : measured between successive transits of the First point of Aries (or, in everyday language, any 'fixed' star). A sidereal day is 23 hours 56 minutes 4.1seconds. Beware the possible confusion between day and daytime.

daybreak (or break of day): an old term for first light, usually taken as the onset of astronomical twilight.

daytime: that period of a day between sunrise and sunset.

Daylight Saving Time: see time (types of).

declination (of a wall) {sometimes called the declining angle or the deviation, to avoid confusion with the sun's declination}: [d, DEC] the angle, measured in a horizontal plane, that a wall's perpendicular makes with due south (i.e. a wall facing S has d = 0°). Walls declining westward have positive declinations, those eastward, negative. Beware – this is not a universal convention and some authors define the angle with respect to the nearest cardinal point of the compass.

declination (of the sun): [, DELTA, DEC] the angular distance of the Sun above or below the celestial equator. Its value follows an annual sine wave like curve, varying between 0º at the equinoxes and ±23.4º (approx.) at the solstices. It has positive values when the Sun is above the celestial equator (summer in the Northern hemisphere) and negative when below. The same system is used as part of the equatorial co-ordinate system (together with right ascension) to locate other celestial bodies. See Figure 1 and Equations.

declination lines: lines on a dial showing the sun's declination on a particular date. They are read by observing the shadow of a nodus.

degree: [ º or deg] an angle equal to 1/360 of a complete circle.

descendant: falling from the zenith. Note: astrologers have a different definition.

diagonal scale: a device for interpolating between scale divisions, pre-dating the vernier scale. It is constructed by drawing diagonals between individual divisions across a wide band, with a series of equi-spaced arcs parallel to the main scale crossing them. It is read by noting the position of the fiducial line with one of these arcs. Most usually found on astronomical instruments, a similar design was used by Sir Christopher Wren for indicating the minutes on his famous vertical dial on All Souls' College, Oxford.

dial: a Middle English word, apparently deriving from the Latin 'dies' though the medieval Latin 'dialis', used for what is now called a sundial. It later became used for many types of indicators, hence the necessity (from 1599) for the qualifying 'sun' prefix. The word ~ in modern English has now become common again as a shortened version of sundial. Hence dialling {dialing}, the art and science of designing and constructing dials; diallist {dialist}, one who designs or makes dials.
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« Reply #8 on: December 16, 2007, 08:01:12 am »

Dial types:

Ahaz (Dial of Ahaz): supposed refraction dial, from the Bible story (Kings 20 v8-11) which may allude to a dial showing time running backwards.

altitude ~: {or elevation ~} any dial which uses the sun's altitude, rather than its azimuth, for indicating the time. Usually does not need to be aligned N-S. Examples are ring dials, flag dials, and shepherds' dials. Altitude dials were also often incorporated in quadrants and folding rules.

analemmatic ~: (pron. ana-lem-mat-ic) dials consisting of hour points, (rather than lines) laid round an ellipse, and a movable gnomon perpendicular to the dial plane. It may be on any plane, but the most usual form is horizontal. In the horizontal version of the dial, gnomon position lies on the straight N-S minor axis, at a point determined by the sun's declination (i.e., the date). Most usually found set in the ground in parks, where the observer acts as the gnomon. Note that some of these dials show an analemma drawn about the gnomon positioning line. This is a method of indicating the EoT for the appropriate date, but it must be remembered that the gnomon is not positioned on the analemma. The analemmatic dial may be regarded as a projection of the universal equatorial ring dial. Analemmatic dials were once common paired with a horizontal ~ in a self-orienting portable compendium.

analemmic ~: this term has sometimes been used to describe dials which have an analemma-shaped gnomon, or analemmas on the hour lines, enabling them to read mean time. Note, the dials have no direct link to analemmatic ones.

Anglo-Saxon ~ {sometimes just Saxon ~}: a sundial from the Anglo-Saxon period (c 650 – 1050 AD); designed to show unequal hours, or the basic tides, with a horizontal gnomon. Similar to the mass dials which superseded it, a Saxon ~ shows much higher levels of craftsmanship and is often finely decorated. Also, it is invariably engraved in a separate (circular or rectangular) stone, not into a pre-existing wall. Saxon dials are often taken to be the precursors to the later scientific dials. In the early part of the period the semicircle was divided by five lines into four segments. During the latter part of the period it was subdivided into eight or twelve segments and the dial sometimes carried an inscription in Old English. Throughout the period the principal lines had a cross bar near the perimeter giving the appearance of Latin crosses. See Appendix II for the basic time periods shown on the dial.

antiboreum: an ancient form of dial in which a partial-sphere is hollowed into a stone, and a ray of sunlight enters the partial-sphere through a south-facing pinhole through the stone.

armillary: (pron. ar-mil-ar-y) (or armillary dial; some authors also use the term armillary sphere) a form of equinoctial sundial which comprises, as a minimum, two circular bands plus a rod through the poles representing the Earth's axis and acting as the gnomon. One band represents the equator (carrying the hour scale) and the other the local meridian. Usually, other great circles are added representing the Prime meridian and the ecliptic plane, sometimes together with small circles for the tropics and arctic circles. These add artistically, but detract from its clarity as a dial. The gnomon sometimes carries a nodus at the centre of the sphere; this may be used for indicating the date.

astroid ~: a ~ which uses the sun's declination, altitude and azimuth to give the hour angle. It is latitude-independent, and is named after the geometric shape which forms its gnomon.

auxiliary ~: a small equatorial dial used as a mechanical aid to constructing dials on other planes (particularly vertical decliners) by co-mounting on a common gnomon and projecting the hour lines. Often used with a trigon.

azimuthal ~ (or azimuth ~): any dial which uses the sun's azimuth for indicating the time. It usually needs to be aligned N-S, and has a vertical style (if it has no dependence on altitude).

Berossos ~: another term for a hemispherium, named after its inventor Berossus Chaldaeus, a Babylonian astronomer who flourished on the Greek island of Cos around 270 B.C.

bifilar ~: invented in 1922 by Hugo Michnik in its horizontal form, although it can be on any plane. The time is indicated by the intersection on the dial plate, of the shadows of two wires (or other lines in space) stretched above and parallel to it. The wires often run E-W and N-S, with their (different) heights above the plane being a function of the location of the dial. It may have equiangular hour markings, and hence can be delineated to show many kinds of hours.

Bloud ~ : a portable, magnetic azimuth ~ made mostly in Dieppe by makers such as Charles Bloud.

book ~ {open book ~}: a modification of the polar ~, with the dial plate consisting of two planes set in a vee, with their intersection line lying parallel to the Earth's axis. A polar gnomon can be placed bisecting the angle of the two planes. Alternatively it may be arranged so that the outer edge of each plane acts as the gnomon for the other. The term book ~ can also be applied to diptych dials which are designed to look like a book when closed.

Butterfield ~: a pocket sundial by, or in the style of, Michael Butterfield (Paris, 17th century). Typically it consists of an octagonal silver horizontal dial with a gnomon of adjustable angle, often with a bird's head pointer, with several rings of hour lines for cities of different latitudes. A magnetic compass is fitted in the same case.

cannon ~: see noon gun.

Capuchin ~ {or Capucine ~}: a latitude-specific card dial, related to the Regiomontanus dial. So-called because the outline of the hour-lines is said to resemble a hooded Capuchin monk.

card ~: a class of portable dials built on a single plane, e.g. a card which is suspended in the vertical plane. They usually have a sun sighting device along one edge, and a cord with a bead which hangs vertically below a movable suspension point.

ceiling ~{also known as a mirror ~ or reflected ~}: a dial marked on a ceiling where the time and date are indicated by a beam of sunlight reflected from a small horizontal mirror placed on a windowsill.

chalice ~ (or cup, bowl etc.): a form of refraction ~ where the hourlines are drawn on the inside of a drinking vessel. Early examples, often in precious metals are rare and valuable.

Chinese ~: a wide range of dials have been used in China, from the vertical gnomon of the mythical astronomer Xi, through equiangular ~ with sun-pointers and 100-segment time scales from the 1st - 2nd centuries BC, equatorial dials for equal hours in the Ming dynasty (1368 to 1664), to conventional horizontal dials in the 19th century.

compass ~: a portable horizontal dial with an accompanying compass to allow it to be correctly oriented. The compass is often below the pierced dial plate, and the gnomon is hinged for packing. Beware: the term compass dial is often used to mean a magnetic dial.

complementary ~: a (hypothetical) horizontal ~ used as an aid to designing a vertical declining and/or reclining dial. Its gnomon and hour lines are calculated not for the site of the proposed (real) dial, but for the location where the Earth's surface is parallel to the dial plate of the proposed dial. For a simple direct south dial, the complementary dial would be located at the co-latitude.

cone ~: a term used to describe several entirely different types of dial.(a) a class of dials where the dial plate is an inverted, truncated cone, giving dials similar to a scaphe dial or a hemicyclium, or (b) a class of modern dials which use a cone lying on its side as the gnomon. Many varieties, including sidereal, exist.

cross ~: (or cruciform ~ or crucifix ~) a dial in the form of a cross, usually of stone, with the "front" surface of the cross parallel to the equatorial plane, and the top pointing south. The side surfaces of the cross can each form a dial plane, with its gnomon being a corresponding edge of the cross itself. Usually found as churchyard memorials. Rare. Portable cross dials have the long arm parallel to the polar axis and the short arm E-W.

cube ~: a (set of) dials on the surfaces of a cube. There may be up to 6 dials, but more often 5 e.g. direct N, S, E, and W, together with a horizontal on the top surface. Alternatively, it is possible to set the cube so that its top surface is parallel to the equatorial plane, i.e. the base makes an angle equal to the co-latitude with the horizontal. Both portable (usually adjustable) and monumental versions are known.

cycloid (polar) ~: a variation of the standard polar dial in which the gnomon has a cycloid shape, with the result that the hour lines are equally spaced.

cylinder ~ (also known as a shepherd's ~ or pillar ~): a portable, altitude dial in which hour lines for different dates are delineated around the surface of a cylinder, which is allowed to hang or stand vertically. A horizontal gnomon projects radially from the top of the cylinder, and is adjusted to the appropriate date around its periphery. Sometimes two gnomon are supplied; a long one for winter and a short one for summer. The dial is held with the gnomon facing the Sun so that the shadow falls vertically. Latitude specific. This was the chilindrum of Chaucer's monk.

declining ~: a vertical dial which does not face any of the cardinal points of the compass. The sub-style will be displaced from the noon line, although the latter will still lie vertically below the dial centre.

diametral ~ : one of the equatorial projection dials, first described by Samuel Foster of Gresham College in the 17th century, it is a horizontal dial with a moveable style and hour points which lie along a straight line lying E-W.

diffraction ~: a dial invented in 1999 by M. Catamo & C. Lucarini. It has no gnomon, but the dial plate consists of a circular diffraction pattern, which forms a bright, multicoloured diametrical line pointing at the Sun when viewed perpendicularly to the centre of the dial plate. Horizontal, altitude and equinoctial versions are possible. The dial plate is usually made from a CD (compact disc), hence "CD dial".

digital ~: an ingenious 20th century dial. The "gnomon" consists of a rectangular sandwich of shadow masks set parallel to the polar axis. This gnomon casts a shadow in which digits representing the time are sunlit. Patented, and requires great precision in manufacture.

diptych ~: (pron. dip-tich or dip-tic) a portable (pocket) dial in which a vertical and horizontal dial are hinged together, and a common cord gnomon running between them also ensures that they open to a right angle. Latitude specific. This term is, confusingly, sometimes also used to describe a monumental open book dial.

direct ~: a vertical dial which directly faces one of the cardinal points of the compass e.g. direct S.

double horizontal ~ : a horizontal dial with (usually) a combined polar pointing gnomon and a vertical one showing the time/date on a stereographic projection of the sky onto the horizontal plate. Capable of self orientating, although normally fixed in position. Usually attributed to William Oughtred in the early 17th century, early hand-engraved versions are very fine.

Egyptian ~: a range of sundials from ancient Egypt (portable and fixed) exists, the earliest being from the time of Tuthmosis III (1479-1425 BC). The portable devices appear as a long, thin 3-D letter "L", laid with the long shaft horizontal along the sun's azimuth, with the upturned foot casting a shadow onto the shaft. It is very similar to the merkhet but has a dedicated hour scale

equant ~: (pron. ek-want) a modified horizontal ~ in which the hour-lines are replaced by hour points. These points are arranged round a geometric curve chosen so that the points are equally spaced, allowing the use of a vernier scale and more accurate interpolation of times. Not related to Ptolemy's equant point.

equatorial ~: a dial in which the dial plate is set parallel to the equatorial plane and the polar-pointing gnomon is perpendicular to it. The dial has hour lines equally spaced at 15º intervals around the gnomon, and hence the dial plate may be rotated to account for EoT, longitude and BST/DST corrections. Sunlight falls on the underside of the dial plate from the autumnal equinox until the vernal equinox. For this period, the gnomon must project below the dial plate, which is delineated on both sides. An alternative form replaces the dial plate by a narrow hour ring (or half-ring) allowing the scale, inscribed on its inner circumference, to be read throughout the year. With this form, special analemma-shaped gnomons can be used to show mean time. Note: some authorities insist that this dial should be called an equinoctial ~.

equiangular ~: a term used for dial types where the hour points are placed at equal angles (15º) around a circle (or part of). If the dial plane is not parallel to the equatorial plane, the mounting of the gnomon, (which does not need to be polar) must be movable to accommodate this.

equatorial projection ~: a class of dials obtained by projecting a universal equatorial ring dial onto any plane. Members of the class include analemmatic, diametral, Foster-Lambert and Parent dials.

equinoctial ~: (pron. ec-we-noc-te-al) another (historical) name for an equatorial ~, preferred by some authors.

flag ~: an altitude ~, formed by "unwrapping" the scale of a shepherd's ~ into a flat plane which can be shaped like a flag or pennant and is positioned perpendicular to the sun.

Foster-Lambert ~: a form of equatorial projection dial, with the projection arranged to produce a circular ring of equiangular hour points. A good example is the large reclining dial (now back at Herstmonceux Castle after a period at Cambridge) designed in 1975 by Gordon Taylor for the Royal Greenwich Observatory.

geographical ~: a dial in which the dial plate shows a map of the world, with curved hour lines allowing the time at any location to be indicated.

globe ~ (or spherical ~): a class of dial in which the "dial plate" is a globe or sphere, usually set with its axis parallel to the Earth's polar axis and often with the observer's position at the top. The gnomon is in the form of a thin semi-circular vane which can swivel around the globe about its axis. In use, the vane is rotated until the shadow is minimised and the time read from an equiangular scale around the equator. It indicates the meridian of longitude where it is currently noon. An alternative type of globe dial (a terrella) simply uses the globe itself to form the shadow, and the time is indicated by the terminator. Transparent globe ~ are also possible (the Wenger ~). where the shadow of a movable point on the surface is made to fall on the centre of the globe.

Graeco-Roman ~: a general class of dial from about the 3rd century BC (Greek) to the 4th century AD (Roman). Made of stone, they include the hemispherium, the hemicyclium, and some conical dials.

great decliner: usually indicates a declining dial which nearly, but not quite, faces E or W. The centre of the dial falls off the dial plate and, as a consequence, it does not show a noon line.

hâfir dial: an Islamic dial with unequal hours, vertical gnomon and equiangular date scale of 12 segments.

halazûn dial: an Islamic dial with unequal hours, vertical gnomon and a date scale of 6 segments (each representing two signs of the zodiac).

hat ~: an altitude dial comprising a circular disk mounted concentrically on top of a vertical cylinder. The dial is read by the maximum vertical length of the disk's shadow on the outside of the cylinder.

heliochronometer: a precision sundial which incorporates some means to allow it to read civil (or mean) time. This is usually achieved by incorporating an EoT cam (as in the Pilkington and Gibbs heliochronometers), or by projecting a spot of light onto an analemma. Note: some authors use this term to describe any precision sundial.

hemispherium: an ancient dial with the dial surface formed by a hemisphere hollowed into a horizontal (or occasionally vertical) stone face. The gnomon is a vertical spike (length equal to the radius of the sphere) set in the bottom of the hemisphere. It is essentially a horizontal altitude dial, with a shaped dial plate which prevents sunrise and sunset being at infinite distances.

hemicyclium: similar to the hemispherium, but with the south-facing part of the hemisphere cut away, and with the gnomon now projecting horizontally from the N edge.

horizontal ~: the common or garden sundial with a horizontal dial plate and polar-pointing gnomon. Latitude specific.

inclining ~: usually applied to portable dials in which a horizontal dial, designed for a high latitude, typically 60º , may be inclined by raising its southern edge (in the N hemisphere) so that it may be used at locations with lower latitudes. The opposite arrangement is also sometimes found. The term is also sometimes confusingly used for near-vertical dials where the top leans away from the observer.

Islamic ~: a ~ with unequal hours and showing the Islamic prayer times.

Lambert ~: see Foster-Lambert ~.

Little Ship of Venice {or Navicula}. A portable dial in the shape of a Venetian ship with a central mast. Based on the Regiomontanus dial, the few early examples are valuable.

magnetic ~ {or magnetic compass ~} : a small portable ~ in which a complete horizontal ~ is mounted on a compass card, and hence is self-orienting. In principle, the magnetic variation of the place and date where it will be used can be accommodated by rotating the dial from the magnetic N-S line of the compass. Beware: this type of dial is sometimes described as just a compass dial.

magnetic azimuth ~: a portable ~, usually in diptych form. There is no string gnomon but instead the lid is lined up to fall exactly on the base, the time being read from the compass needle on a chapter ring. The chapter ring position is moved in a N-S direction from a calendar volvelle on the under side.

mass ~ (or mass clock. Also known as a scratch ~): a rather basic dial from the medieval period scratched or engraved into the south-facing stonework of a church or similar building, often near the main door or the priest's door. Although later than Anglo-Saxon dials, they are generally less well executed. Usually circular or semicircular in form, with a hole in the centre to accommodate a horizontal gnomon rod (invariably missing). Delineated, probably empirically, to show some form of unequal hours, there is a huge variety of design types. Some are event markers rather than true sundials.

mechanical universal equinoctial ~ (sometimes minute ~): a ~ that uses gearing to show accurate time on a clock face, i.e. a solar clock.

mirror ~: a ~ having no gnomon, but using a small, appropriately angled mirror to reflect a small spot of sunlight onto the dial face. The dial may be on a vertical wall facing N or within a building. See also ceiling dial or reflecting dial (separate definitions).

monofilar ~: a ~ in which time is marked by the point where the shadow of a thread ( or other thin gnomon) held between the dial face and the Sun intersects a set of date lines.

moon ~: a sundial calibrated in some way so that it can tell the time by moonlight. No change to the basic dial is required, but a correction factor for the time is required which accounts for the age or phase of the Moon. Never very accurate because of the complex nature of the Moon's orbit, they generally require a nearly full Moon to be able to be read clearly. Purpose-built moon dials have either spiral hour lines or a table of moon phases (as in the famous Queens' College, Cambridge, dial).

multiple ~: simply more than one dial physically incorporated into the same dial structure.

multiple gnomon ~: a ~ in which there is a separate shadow casting element (gnomon) for each hour line. The elements can be points, lines or planes.

navicula de Venitiis: see Dial Types ( Little Ship of Venice)

noon (or meridian) dial or line: a dial which has only one hour line, for noon. It has a nodus rather than a full gnomon. This may be in the form of a small ball on the end of a shaft or, more usually, an aperture in a plate or window opening into a building. Very long, accurately-levelled meridian lines (running N-S) built into cathedrals were intended for the accurate determination of the equinoxes, solstices and other solar parameters. A noon dial (as opposed to noon line) is usually taken to mean a complete noon analemma, possibly including dates.

noon gun: a small cannon mounted such that focussed sunlight from an appropriately angled lens falls on the touch-hole and fires the gun at noon. A novelty rather than an accurate time indicator.

noon mark: a stone, or line marked on a stone, set to receive the noon shadow of a building or other feature. The term is, however, often used interchangeably with a noon ~.

Nuremberg ~: a loose collective term used for the diptych dials made around Nuremberg, Germany, during the 16th and 17th centuries. The majority were made of ivory, featured a compass bowl in the lower leaf and had a string gnomon.

Oughtred ~: another name for a double horizontal dial.

Parent ~: a form of analemmatic ~, with the dial plane parallel to the Earth's axis so that the ellipse of hour points becomes a segment. First designed by Parent in 1701.

pelekinon ~: a form of ~ attributed to the Greeks around 100 BC. In appearance, the dial resembles a butterfly or double-headed axe, and was delineated to show unequal hours.

pillar ~: see cylinder ~. Sometimes also confusingly used to describe monumental dials mounted on tall pillars.

poke ~: an old term for a pocket or portable dial.

polar ~: a ~ in which the dial plate is set along the E-W direction and reclines so that it is parallel to the polar axis. The standard polar-pointing gnomon is thus also parallel to the dial plate. Simple to construct, but the hour lines disappear to infinity when the Sun is in the plane of the dial. For a south-facing polar dial, the theoretical limits at the summer solstice are 6am to 6pm.

polarised light ~: a gnomon-less dial which detects the orientation of the polarised skylight. Its polariser/analyser system is best arranged to view a region of the sky near the N celestial pole (S in the southern hemisphere), allowing the hour lines to follow a standard 15º per hour scale. Although not particularly accurate, it has the advantage that it does not require direct sunlight to work as long as there is clear sky towards the N celestial pole. Thought to have been invented by Sir Charles Wheatstone in 1848.

polyhedron ~: a multiple dial in the form of a solid polyhedron, with a separate dial on each face. Usually each dial is some form of decliner/recliner, but may include scaphe and polar dials as well. Particularly common as the monumental Scottish stone lectern and obelisk dials.

portable ~: simply a dial meant to be moved from place to place, either as a pocket dial or simply being transportable. In most forms, some means of orienting the dial is included, and they are often either universal or capable of being read at a number of fixed latitudes.

prism ~: a term occasionally used to describe a multiple dial with two or three dial faces set on the sides of a triangular prism.

proclining ~: a term sometimes used to describe a dial which is approximately upright but which leans forward towards the observer. A dial which leans forward by 10º will have an inclination of +100º. They are sometimes also called inclining dials, although that term is best reserved for dials derived from a horizontal ~.

reclining ~ : strictly, an approximately vertical dial which leans backwards away from the observer. However, often used as a catch-all term for any non-vertical dial. The angle is defined from the horizontal towards the observer, so a dial which leans backwards by 10º from the vertical has an inclination +80º.

reflecting ~: these dials have no gnomon, but reflect sunlight by means of a semi-cylindrical mirror, set with the axis of the mirror parallel to the polar axis. The mirror reflects the light to form a caustic curve amongst the hour points. For the special case of the mirror having a cycloid shape, the hour points are equally spaced. Note that the term reflecting dial may also be used for ceiling dials.

refraction ~: dials which use a clear liquid in a solid cup to compress the hour lines. Sometimes drawn on the inside of a drinking cup - a chalice dial - (see Dial of Ahaz) or on the bottom of a fountain basin or swimming pool. A second form uses a cylindrical lens to focus sunlight onto a curved dial plate.

Regiomontanus ~: a universal form of card dial, usually with the suspension point of the cord movable in two dimensions in the card plane. It is the basis for many other variants of dial.

ring ~ : a portable, altitude dial in the form of a ring, with a small aperture in its circumference. The ring is suspended in a vertical place such that the aperture faces the sun. The time is then indicated on a time/date scale on the inside of the dial. The suspension point may be adjustable on the circumference to allow for latitude changes. Not very accurate, due to their usually small size and the fact that a very compressed date scale is needed to prevent the ring becoming too wide. These dials were known by Vitruvius in the first century BC. Beware: this term is also sometimes loosely used to described a universal equinoctial ring dial.

Saxon ~: see Anglo-Saxon ~.

scaphe ~: (pron. sk-af-e) {skafe, scaphion} a dial in which the dial plate is a shallow dish in any plane (usually a horizontal or, rarer, vertical one). The name comes from the Greek word for boat, and the dial itself is thought to have developed from the hemispherium. Normally with a vertical gnomon.

scientific ~: a term usually taken to mean a dial which is designed to show equal hours, or at least in which the effect of latitude been mathematically accounted for. Thus any dial with a polar-pointing gnomon is scientific, but, for example a mass dial is not. Mostly, they date from the 16th century onwards.

scratch ~: see mass dials.

self-orienting ~ : any dial which, when correctly adjusted for he latitude and/or date, can be used to find the direction of south. Sometimes also called "self-southing".

shadow plane ~: a class of dial in which the gnomon is movable and is set by the observer so that it, and its shadow, lie in the sun's hour plane. The gnomon may be a plane, line or point. The dial plate can, if required, be any surface. A globe dial with a movable vane is an example of a shadow plane ~.

shepherd's ~: see cylinder dial for the usual meaning. A second type of shepherd's dial is a set of marks cut in the turf, so that the shepherd's crook could be used as a vertical gnomon – see Shakespeare's Henry VI part 3, act 2, scene 5.

sidereal ~: (pron. sy-deer-e-al) a ~ designed to show sidereal time by means of introducing a variable offset to the time shown by the solar shadow on an equiangular dial. The dials are rare, with no known public dial in the UK(?)

solar clock (or solar chronometer): an instrument in which a sighting of the sun, through a movable telescope or open sights, is made to display the time on a clock face by a set of gears. A famous example by Sir Charles Wheatstone is in the Science Museum. Note: this term is often used as a synonym for heliochronometer, but is best reserved for the definition given here.

spherical ~: see globe dial.

spoon ~: a rare form of scaphe ~ delineated in the bowl of a spoon.

stained glass ~: a (generally vertical) dial in which the dial face is of stained glass, and is viewed from the back, i.e. through the glass from inside the building. The gnomon remains on the outside of the building, and frequently causes cracking of the glass if supported directly from it. Typically, they were incorporated into church windows in the 17th century, although most are now in museums and there are some notable modern examples.

standing ring ~: a form of universal equinoctial ring dial mounted on a stand, usually including a compass.

Star of David ~: a monumental dial similar in concept to the cross dial, except that the six-pointed star with 60º angles gives opportunities for numerous dials.

sun clock: see solar chronometer, dial (types of).

tidal ~: a dial delineated to give the times of the marine tides. Based on some form of equiangular dial (e.g. an equatorial dial). It bears the compass points in a circle with the names of various ports written against them. The 'establishment' of a port is given as a compass point and, together with the hour markers, indicate the interval of time between the passage of the Moon over the meridian of the port and its high tide. Not to be confused with dials showing the Anglo-Saxon tides.

universal ~: any portable dial with a means of allowing it to work at, or be adjusted for, any latitude. Note: sometimes the range of usage is limited to one hemisphere. The term is also sometimes applied, with qualifications, to dials which operate over a more limited range of latitudes, e.g. dials with, say, 30º- 60ºN scales.

universal equatorial ring ~ (or - equinoctial - ): a portable dial which looks similar to a folding version of an armillary dial, but with a movable suspension point to provide latitude adjustment. A stylised version of the hour ring and gnomon forms the BSS logo. In some versions, an aperture gnomon mounted on the central axis is used, the position of the aperture being adjusted to suit the sun's declination. This form is self-orienting. Large well-made versions are accurate and valuable.

vertical ~: any dial in which the dial plate is vertical.

window ~: (or projecting ~) a ~ in which the hour lines are marked on a window in such a way that their shadows fall across a single reading point inside the room. The lines, as drawn on the window, form an inverted, mirror-imaged vertical dial. This form is related to stained glass and mirror (or ceiling) ~.

- End of Dial types -
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« Reply #9 on: December 16, 2007, 08:02:23 am »

dialling scales: ruler-like (or rule-like) scales designed to help in the geometrical layout of dial. Their non-linear scales are effectively analogue computers for solving dialling equations. Standard scales, following George Serle's original version of 1657, and themselves developed from Samuel Foster's 1638 work, have separate scales for : hours, latitude (prime) and latitude (meridian).

dial plane: the plane in which the dial plate, and the hour indicators, lie.

dial plate (or ~ face): the physical plate on which the hour lines and furniture lie. It (usually) supports the gnomon.

diffraction grating: a plate with a set of closely spaced slits (usually parallel and equi-distant) which disperses incoming light into its constituent wavelengths (i.e. colours). The surface of a CD acts as a circular reflection diffraction grating.

dioptra {dioptera}: a form of alidade, used as the index of a volvelle (and also sometimes of a quadrant or an astrolabe), rotating against an angle scale.

dip (of the horizon): the angle of the observed horizon (due to the curve of the Earth's surface and the height of the observer, but neglecting refraction) below the true or astronomical horizon. It is given by:

dip (arc-minutes) = 1.811 x height (metres).
dip (magnetic): the angle that the Earth's magnetic field makes with the horizontal. It varies with geographical location and (slowly) with the date. See Appendix IX for values. It is measured with an inclinometer.

dipleidoscope: (pron. dip-ly-do-skop) from the Greek words for "double image viewer". Devised by James Bloxham and patented by Edward Dent in 1843. It is an instrument for observing the transit of the Sun to an accuracy of a few seconds. Essentially, it comprises a hollow equilateral prism, with the front, semi-reflecting face facing south and parallel to the polar axis. At noon, the reflection of the Sun from this surface exactly coincides with a second image doubly reflected from the other two faces.

diptych: literally, two leaves or pages. See dial types, diptych .

diurnal: daily, or occupying one day. Can also mean of the daytime (as opposed to nocturnal: of the nighttime).

domifying circles: (from the Latin Domus Coelestris - celestial house.) Circles on the celestial sphere which show the hourly position of the Sun in the six Regiomontanus (astrological) houses that are above the horizon. On a vertical south dial, they are represented by straight lines emanating from the intersection of the noon line and the horizon line (i.e. the horizontal line on the dial plate perpendicular to the nodus). The domifying lines are angled similarly to the hour lines, but are numbered in the reverse direction as DOM. VII (horizontal, E),DOM.VIII, DOM.IX, DOM.X (along the noon line), DOM.XI, DOM.XII and DOM.I (horizontal, W). On a horizontal dial, these lines all lie parallel to the noon line. See Appendix V.

Dominical cycle: a letter-cycle originating in the Roman period, when each day of the year was allocated the letters A,B,C,D,E,F and G in a repeating sequence. In a given year, every weekday (e.g. Monday) has the same letter, and the cycle repeats with the 28-year Julian leapyear cycle. The Dominical letter (for Sundays) is often found on portable dials, and is used with the Golden Number to find Easter.

dusk: the evening twilight period.
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« Reply #10 on: December 16, 2007, 08:03:26 am »


earthshine: the illumination resulting from sunlight reflected from the Earth, particularly when providing low-level illumination of the "dark" portion of the Moon.

East: the point on the horizon 90º (measured clockwise) from the North. The Sun appears to rise from the East point on the equinoxes.

Easter: the requirement to set the date of this Christian festival drove much of the early astronomy and calendar reforms. The standard astronomical algorithm for the date is now "the first Sunday after the full moon (paschal moon) that occurs upon, or next after, the vernal equinox". However, because the rules were set by the Christian clergy before the dates of the equinoxes could be defined accurately, the vernal equinox for this calculation is always taken as 21 March. See Meeus or Duncan in Sources for a full algorithm. The extreme dates of Easter are 22 March and 25 April

eccentricity (of the Earth's orbit): [ec, EC] a measure of the relative sizes of the major and minor axes of the Earth's elliptical orbit. ec = 0.01671... in the year 2000 and is slowly decreasing. ec = 0 would imply a circular orbit. The earliest accurate value was found by John Flamsteed, the first Astronomer Royal, in about 1700 (most of his results were only published after his death in 1707).

eclipse (of the Moon or the Sun): the phenomenon which occurs when the Earth (or at least the observer's location), Sun and Moon lie on a straight line. If the Moon lies in the ecliptic plane between the Sun and the Earth, a solar eclipse occurs (either full, partial or annular, depending on the relative distances). If the Earth lies between the Sun and the Moon (i.e. at a full moon) a lunar eclipse is seen.

ecliptic (plane): (pron. e-clip-tic) the plane that the Earth's orbit traces during a year. The orbits of the Moon and the planets are also close to this plane. It is the plane in which eclipses occur since, by definition, the Sun is always on the ecliptic. It is a great circle on the celestial sphere.

ecliptic latitude: {celestial latitude} [, ELAT] is the position of a body on the celestial sphere, measured along the great circle from the ecliptic. Positive to the north, negative to the south, range –90º to +90º. It is part of the ecliptic co-ordinate system.

ecliptic longitude: {celestial longitude} [,  e, ELON] is the position of a body on the celestial sphere measured around the ecliptic from the vernal equinox positive to the east. Range 0º to 360º. It is part of the ecliptic co-ordinate system.

elevation: see altitude.

ellipse: a conic section and the path the Earth follows during a year (neglecting only the small perturbations caused by the moon and the other planets). It is defined by two foci, and by a major and a minor axis. A circle is a special case of an ellipse with the two foci coincident, and the major and minor axes equalling the diameter. The elongation of an ellipse is characterised by its eccentricity. Also, the outline shape of an analemmatic dial.

ellipsoid: a closed geometric surface obtained by rotating an ellipse around its major or minor axis.

elongation (of the Moon): the angle of the Moon relative to the Sun, as viewed from an observer on the Earth. The term may also be applied to the planets. An elongation of 180º implies a full Moon.

epact (number): the number of days past the full moon on the 1st January of any year in a 19-year metonic cycle (the period before the Sun and the Moon are again in the same relative positions in the constellations). Epact tables are found on old dials, particularly portable ones, in conjunction with lunar volvelles and calendars. In conjunction with an almanac, they can be used to predict the date of Easter.

ephemeris: (pron. ef-em-er-is) a table of predicted positions of celestial objects as a function of time. Astronomical almanacs invariably include an ephemeris for the Sun.

ephemeris second: an obsolete definition of a second used between 1955 and 1965, based on the Earth's speed of rotation. Now replaced – see second (of time).

epicycle: a small circle whose centre moves around the circumference of a larger one. It was proposed as the shape of the orbit of some of the planets by Ptolemy.

epoch: a particular fixed instant used as a reference point on a time scale for astronomical calculations, e.g. J2000.0 or noon 1 Jan 2000 (2451545.0 JD). The word epoch also occurs on some dials, for example, in tables for calculating Easter.

Equation of Time: [E, EoT] the time difference between Local Apparent Time (apparent solar time) and mean solar time at the same location. Its value varies between extremes of about +14 minutes in February and –16 minutes in October. It arises because of the elliptical orbit of the Earth, and the tilt of the Earth's axis to the ecliptic. The preferred usage by diallists is:

mean solar time = apparent solar time + EoT
but this sign convention is by no means universal and the opposite sign is used in modern almanacs. Irrespective of the sign convention adopted, sundials will always appear slow compared to mean time in February, and fast in October/November. See Equations.

Figure 5. The Equation of Time and its components.

EoT varies continuously, but is usually tabulated for noon each day at a particular location. Hence values for America (e.g. as printed in the NASS Compendium) can be a few seconds different from those in Europe. The noon EoT on a particular day varies slightly over the leap year cycles (4, 100, 400 years), and more significantly over millennia.

The first published tabulation of the EoT was by Christiaan Huygens in 1665, but the knowledge of its existence probably goes back to Ptolemy. The first Astronomer Royal, John Flamsteed (1646-1719) produced the first English tables in 1672.

EoT can also be expressed as an equivalent hour angle

equant point [Ea,EOTA]: a point in Ptolemy's model of the solar system around which the Sun and the planets rotate.

equator: the great circle of the Earth (or other celestial body) which is equidistant from the poles. It has, by definition, a latitude of 0º.

equatorial mount: a mount for an instrument (e.g. a telescope) which has one axis parallel to the polar axis and another at 90º to this (the declination axis). The diurnal motion of a celestial body can be followed by rotation about the polar axis alone. A polar-pointing gnomon could act as the axle for such a mount.

equatorial plane: the plane through the Earth defined by the equator.

equinoctial plane: the plane of the equator extended to the celestial sphere, i.e. defined by the celestial equator.

equinoctial line (on a dial): is the line followed by the shadow of a nodus on the equinoxes. For a plane dial, it is a straight line perpendicular to the sub-style.

equinoxes: (vernal or spring ~, autumnal or fall ~) literally "equal nights" i.e. equal amounts of daylight and night-time. Astronomically, the points where the plane of the ecliptic cuts the celestial equator, or the moments when the Sun is at these positions. The vernal ~, around 20-21 March, is also called the First point of Aries and represents the zero of ecliptic longitude and right ascension. Thus the Sun has an ecliptic longitude of 0º or 180º at the ~. Day numbers of the Earth's orbit are usually counted from this point. The autumnal equinox is around 22-23 September, and has a right ascension of 12h. The Sun's declination at the equinoxes is 0º. See Figure 1.

establishment (of a port): the interval between the time of the moon passing the meridian and high tide at the port. It is indicated on some equiangular dials which can indicate the times of the tides (tidal dials).
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« Reply #11 on: December 16, 2007, 08:04:25 am »


fiducial line (or ~ edge): (pron. fid-oo-shal) the edge of an index plate or pointer against which a scale is read.

filem: an old term for a plumbline, particularly on a card dial, to show the vertical.

First point of Aries: see the definition for equinoxes. Note that, because of the precession of the equinoxes, this point currently lies in the constellation of Pisces.

fleur-de-lis {fleur-de-lys}: an heraldic symbol of a stylised Madonna Lily, composed of three petals bound together near their bases. Often used on dials to denote the half-hour lines.

furniture: all features on a dial plate other than the hour lines and their numerals are referred to as dial ~. This may include declination lines, compass rose, EoT graphs or tables, mottoes etc. Other common furniture includes: date, maker's and/or benefactor's name, coats of arms, and latitude and (rarer) longitude. See Figure 1.
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« Reply #12 on: December 16, 2007, 08:05:29 am »


Geographic Position (GP): the point on the Earth's surface directly beneath a celestial body (i.e. where a line to the body from the centre of the Earth intersects the surface).

geoid: the Earth's shape, formed by the mean sea level and its supposed extension under the land masses. It cannot sensibly be represented mathematically, and is often approximated by one of many ellipsoids. Those most likely to be encountered are the Airy 1836 ellipsoid, used to define Ordnance Survey maps, and the WGS 84 ellipsoid, used in the GPS system.

globe: a spherical chart of the Earth. Note that although the Earth's geoid is actually a flattened ellipsoid (i.e. slightly melon-shaped with an equatorial radius of 6378 km, and a polar radius of 6357 km) the spherical representation is used for all dialling activities with the exception, for example, of the model used by the GPS system.

gnomon: (pron. no-mon) the physical structure of a sundial which casts the shadow (from the Greek for "indicator"). The gnomon today is most-often polar pointing (sometimes described as an "axial gnomon"), although it may also be horizontal or vertical. The special properties of a polar pointing gnomon were known to the Moorish astronomer Abdul Hassan Ali in the first half of the 13th century, but its first use may be earlier. The distinction between gnomon and style made (and encouraged in this Glossary) in modern dialling literature is not the one used in early works, and the two words are still sometimes used interchangably. Originally (in English from 1546), gnomon meant a vertical pillar or rod which cast a time-indicating shadow. See Figure 1.

Hence gnomonics: the science of sundialling and gnomonist (seldom used): a person who practices gnomonics.

Golden Number: a number sequence (1-19) used to describe the year number in the metonic cycle. It was used, together with the Dominical letters, to find Easter, and is often found on portable dials.

grade (or grada or gons (obsolete)): [grad] a unit of angular measurement, equal to 1/100th of a right angle, or  /200 radians. Used particularly in France in the 18th and 19th centuries.

great circle: a circle on the surface of a sphere whose diameter is equal to the diameter of that sphere. Thus the circle has the same centre as the sphere. The shortest route between two points on the surface of a (solid) sphere lies on the circumference of the great circle connecting them.

GPS (Global Positioning System): a system of polar-orbiting satellites, run by the US Dept. of Defense, which allows hand-held radio receivers to provide accurate 3-D location information anywhere on (or near) the Earth's surface. It also provides a highly accurate clock, based on UTC. The system uses the WGS84 co-ordinate system and description of the Earth's geoid.

grazing incidence: a term used to describe illumination in which the rays are parallel to the receiving surface. The shadow of a point above the surface falls at infinity.

green flash: an atmospheric phenomenon occasionally observed during the final phase of sunset, when the upper limb of the Sun shows as a green flash due to the complex wavelength-dependence of atmospheric refraction.

Greenwich Mean Time (GMT): see GMT, time (types of)

Greenwich Meridian: the line of longitude (or half a great circle) passing through the centre of the Airy transit circle at the old Royal Greenwich Observatory in London, and which defines the origin of Longitude (º = 0º). It is now designated the Prime Meridian. Note: prior to 1884, there was no single fixed prime meridian, and hence early sundials sometimes refer to different origins, notably Paris.

Gregorian calendar: the calendar first introduced by Pope Gregory XIII in 1582 AD and now the accepted calendar throughout the vast majority of the world. It introduced the modern system of leap years which results in an error of only 3 days in 10,000 years. Note that adoption of this calendar throughout Europe took an extended period. Its introduction in Britain in 1752 produced a step change of 11 days which can be seen in the difference between EoT tables on dials earlier than this and those on later ones.
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« Reply #13 on: December 16, 2007, 08:06:37 am »


halcyon days: (pron. hal-ce-on) originally, 14 days about the winter solstice. Now taken as simply calm, peaceful.

Hallomas (Halloween in USA): All Saints' day on 1st of November. It is one of the cross-quarter days.

hectemoros angle: [hec] (pron. hec-tem-or-os) the angle from the western horizon to the sun's position, measured around the hectemoros circle. Part of the ptolemaic co-ordinate system, and related to the seasonal hours.

hectemoros circle: the great circle that passes through the E-W points on the horizon and through the sun's position.

heliacal rising: (pron. he-le-ac-l) the instant of the earliest visibility of a star in the East at dawn. The heliacal rising of the star Sirius was used by the ancient Egyptians to predict the coming of the annual Nile flood. Since their year had 365 days, this occurrence had a variable date.

height (of a style): see style height.

heliocentric: an adjective to describe a model of the solar system which places a stationary Sun in the centre, with the planets revolving around it.

heliograph: has two distinct meanings: (i) a device for transmitting morse signals over extended distances by using an accurately aligned mirror to send flashes of sunlight to the receiving station. For long messages, the ~ has a mechanism for tracking the sun's motion. (ii) an astronomical instrument for studying sunspots, as built by George Airy at Kew in 1873.

heliometer: a telescope which produces two images of the Sun which can be manipulated to determine its angular size accurately. Invented in 1754 by John Dollond of London, it is also used to measure angular distances between stars.

heliostat: a scientific instrument which holds an image of the Sun stationary, allowing extended observation (e.g. for solar spectrometry).

hemisphere (northern ~ and southern ~): one half of the Earth's globe, either north of or south of the equator. Note that a sundial at a particular latitude in one hemisphere must be reversed for use at the reciprocal latitude in the other hemisphere.

horarius circle: (pron. hor-ar-e-us) the great circle that passes through the N-S points on the horizon and through the sun's position.

horarius angle: [hor] the angle from the southern horizon to the sun's position, measured around the horarius circle. One of the ptolemaic co-ordinates.

horizon: the line of intersection between the sky and the Earth. For normal astronomical purposes, the observer's horizon is taken to be the great circle on the celestial sphere on which every point is 90º from the observer's zenith. The observed horizon (accounting for the curve of the earth and the height of the observer above its surface, but excluding refraction) is below the astronomical horizon by an angle called the dip. This can have a significant affect on the times of sunrise/sunset.

horologia: the collective Latin name for dials, water-clocks and sand-glasses, used in the Middle Ages.

horologium: a name used to describe medieval manuscripts listing shadow lengths, deriving from the Latin name for timepieces. Modern versions have also been produced. In modern astronomy, it is also the name of a faint southern constellation ("the Clock").

hour: usually means 1/24th of a mean solar day, unless otherwise stated. Scientifically, it is defined as 3600 standard seconds. See Hour (types of) for other definitions. The word derives from the Latin "hora", which was synonomous with prayer.

hour angle: [h, HA] the angle corresponding to the sun's position around its daily (apparent) orbit. Measured westward from local noon, it increases at a rate of 15º per hour. Thus 3pm (Local Apparent Time) is 45º and 9 am is –45º.

hour circle: a great circle on the celestial sphere that passes through the celestial poles. It is orthogonal to the celestial equator.

hour line: the line on a dial plate indicating the shadow position at a particular time (includes fractional as well as whole hours). See Figure 1.

hour line angle: [X, HLA] the angle that an hour line on a dial plate makes with the noon line. The angle increases with time (i.e. positive for the p.m. hours). Thus, for a horizontal dial, the angle increases clockwise (hence the origin of the term) whereas for a vertical south-facing dial, it increases counter-clockwise . Beware, this convention is not used by all authors, and some define the angle with respect to the sub-style line.

hour point: a point on the dial plane indicating the crossing of the gnomon's shadow at a particular time. Hour points replace hour lines on dials where the shadow edge does not pass through the dial centre.

hour plane: the plane which, at any instant, contains the sun, the observer and the N celestial pole. The style and the appropriate hour line lie in the hour plane.
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« Reply #14 on: December 16, 2007, 08:10:27 am »

Hours (types of):

antique ~: same as unequal hours or seasonal hours.

Babylonian ~: number of hours elapsed since sunrise, with 24 equal hours per day. The origin of the term is unclear, but may be related to the fact that the ancient Babylonians originated the base-60 counting system for angles etc. They are sometimes written as "horae ab ortu solis" or H. AB ORT." on dials. See Equations for conversion from equal hours to Babylonian hours.

biblical ~: same as unequal hours or seasonal hours.

Bohemian ~ : same as Babylonian ~.

Canonical ~: the seven times of the day (as opposed to time periods) used to define the services or divine offices in the medieval church. These offices were based on the sixth century Rule of St. Benedict. See Appendix IV for details.

An alternative definition of the term canonical hours, sometimes applied to lines on early Italian dials, is the system of putting equi-angular hour lines around the base of a horizontal gnomon on a vertical south dial.

common ~: the standard 2 x 12 equal hour system, also called German or French ~. In Latin "horae communes", they are often labelled "kleine uhr" (small hours) on Nuremberg dials.

decimal ~: an hour system with ten equal hours per day (as sometimes used by the Chinese and ancient Egyptians, and during the French Revolution).

equal ~: any hour system where the length of an hour is independent of the date, and the same during daytime and night-time.

French ~: an early name for the equal hour system with 2 x 12 hours per day, beginning at midday and midnight. Sometimes written "Oltramontane".

French revolution ~: the equal hours according to French Revolution time.

Great ~: a term for any of the unequal hour systems. Often labelled "grosse uhr" on Nuremberg dials.

Greek ~: same as Babylonian ~.

Italian ~: {sometimes Italic ~} the number of hours that have elapsed since the most recent sunset (hour 0), with 24 equal hours per day. They were used in many European countries during the period 1200 to 1800. They are sometimes written "horae ab occasu solis" or "H. AB OCC." on dials. The two terms (Italian and Italic) are often used synonymously in modern works but there is some evidence in older works that Italian hours were counted from 30 minutes after sunset. See Equations for conversion from equal hours to Italian hours.

modern ~: the equal hours as used in modern time systems. They may occasionally be referred to as common, European, French, German or vulgar hours.

Nuremberg ~: a hybrid equal hour system. The daylight hours were measured using the Babylonian ~ system, starting with 1 at sunrise, while the night hours started with 1 at sunset and used the Italian ~ system. In Latin, "horae norimbergenses".

octaval ~: a time system with the period of daylight divided into eight hours. Probably introduced by the Romans, circa 250AD. See Appendix III for the names of the daylight periods.

planetary ~: a planetary hour is the time needed for 15º of the celestial equator to rise above the horizon, counting from sunrise. As there is always 180º of the celestial equator above the horizon, there are 12 planetary hours from sunrise to sunset but they are unequal not only from day to day but also from hour to hour. Note: this definition is based on the writings of Sacrobosco, but some authors use planetary hours simply as another form of seasonal hours, with the hours associated with the "planets". See Appendix VIII for the symbols of the planets and this association. The Zonwvlak program uses the definition of the German scholar Joseph Drecker (1925) who defines a planetary hour as the time for 15º of the ecliptic to rise above the horizon (counting from sunrise) and are hence very irregular.

seasonal ~: a form of unequal hours, usually with 12 daytime and 12 night-time hours. Named from the fact that the length of an hour varies with the seasons.

temporal ~ or temporary ~: an unequal hour system with 12 hours from sunrise to sunset, and 12 hours (of a different duration) from sunset to sunrise.

unequal ~: an hour system where the duration of an hour depends on the date and is different from day-time to night (except at the equinoxes). The number of hours during day-time is usually 12, but may be 8 and just possibly 10 (e.g. on some mass dials). Counting of the daytime hours begins at sunrise.

Welsch ~: i.e. foreign. Same as Italian ~.

End of Hours (types of)
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