aberration (de la lumière): effet par lequel la direction apparente des corps célestes distants est modifié en raison de la vitesse de la Terre et de la vitesse finie de la lumière. Découvert par James Bradley, elle a une valeur de 20.47 arc-sec et est totalement sans signification pour la gnomonique.

accuracy (d'un cadran): une mesure de combien proche les indicateurs de temps (lignes ou points) d'un cadran indiquent l'heure juste. Différent de résolution. Voir aussi précision.

Act of 1751: {1752} fait référence à un Acte du Parlement Britannique de l'année 1751 qui adopte finalement le calendrier Gregorien et fait commencer l'année (anglaise) le 1er Janvier, plutôt que le 25 Mars. En conséquence, il peut y avoir quelque confusion, les années antérieures à 1752, pour les dates comprises entre Janvier et Mars. Le premier jour de l'année en Ecosse avait déjà été porté au 1er janvier depuis 1600. Les dates données dans le calendrier Julien sont dites de l'"Ancien Style", et celles données dans le Gregorien du "Nouveau Style".
Les cadrans anglais fabriqués avant 1752 et qui ont des tables de EoT ou Lever/Coucher montrent des dates de 11 jours plus tôt que celles habituelles, car l'équinoxe de printemps isest le 10 Mars au lieu du 21 Mars, et EoT aura pour valeur zéro les5 Avril, 3 Juin, 23 Aoûtt and 15 Decembre. Noter que cet Act promulgué en 1751 n'entra en vigueur que l'année suivante, d'où les dates différentes parfois rencontrées.

angle aigü: un angle de moins de 90º.

age de la lune: voir phase de la lune.

almanach: un calendrier annuel de mois et jours avec des données astronomiques ou autres. Ils incluent souvent des éphémérides du Soleil et d'autres corps célestes, l'équation du temps, la déclinaison du soleil etc. Les almanachs sont soare sometimes inscribed on, or accompany, C16-18 dials.
Le "Nautical Almanac" (annuel), édité par le Royal Greenwich Observatory, continue la première version publiée en 1767 par l'Astronome Royal Nevil Maskelyne.

almucantarat: (pron. al-moo-can-tara) un cercle d'égale altitude sur la sphère céleste. Il s'agit d'un petit cercle sur la sphère céleste, parallèlele à l' horizon.

alidade: l'aiguille tournant sur un astrolabe permettant les observation des étoiles. Parfois utilisée sur les cadrans où un trou à une des extrémités de l'alidade forme une image du soleil sur un plateau portant une courbe en 8 (parfois appelée analemme).

altazimuth: {alt-azimuth} un système de monture d'instrument astronomique qui permet le réglage altitude et azimuth. Le terme est aussi employé pour décrire le système de coordonnées qui utilise ces deux paramètres.

altitude (du soleil): {élévation} [a, ALT] la distance angulaire du centre du disque solaire au dessus de l'horizon de l'observateur (une valeur negative indique que le Soleil est dessous l'horizon). Elle est mesurée sur le plan principal au centre du soleil et est le complément de la distance zénithale . C'est une valeur du système de coordonnées horizontales. Voir Equations. Noter que les aviateurs et d'autres utilisent le terme d'altitude pour la hauteur (distance) au dessus du sol.

anaphorique (horloge): une horloge avec une face de cadran comme un astrolabe, montrant les heures saisonnières.

ante meridiem (a.m.): avant midi.

analemme: (prononcer ana-lem-e) dans l'usage moderne c'est le tracé graphique avec l'Equation du Temps sur un axe et la déclinaison du soleil sur l'autre. Elle apparait comme une longue et étroite figure de huit. Les dates de différents points sont souvent indiqués autour de la courbe. L'ombre d'un point tombant sur un plan arbitraire à la même heure légale (clock time) chaque jour tracera sur celui-ci une analemme lors de sa course annuelle. On la voit normallement sur la ligne de midi d'un cadran, mais elle peut être tracée pour n'importe quelle ligne horaire .L'allure exacte de l'analemme dépendra du plan sur laquelle elle est projetée.

Figure 2. Les composants de l'analemme

le mot analemme a plusieurs significations dans l'histoire de l'astronomie et de la gnomonique. Au 1er siècle avant J.C. l'ingénieur romain Vitruve utilise le mot en faisant référence à un procédé de construction graphique équivalent à ce que nous appeloons aujourd'hui la projection orthographique . Au 2ième siècle après J.C. Ptolémée utilise le mot analemme pour un instrument jouant le rôle d'un nomographe pour définir les angles d'un cadran.
Cadran analemmatique: imaginé et publié par M. de Vaulezard en 1640 en utilisant la projection de l'analemme. L'usage du mot dans le sens moderne pour un cadran solaire date donc d'environ 1640, et le premier traité en anglais fut celui de Samuel Foster en 1654.

angle: (unité de mesure) peut être exprimé en degrés décimaux, en degrees, minutes d'arc et secondes d'arc; en radians (2 radians = 360º); ou (rarement, dans les équipements militaires anglo-saxons) en mils (6400 mils = 360º); ou (rarement également) en grade (1 grade=1/100 de l'angle droit). Les notations les meilleures sont: [dd.ddº or ddº mm' ss"]. Noter que les fonctions trigonométriques dans les feuilles de calcul des ordinateurs sont toujours définies en radians. La convention mathématique est que les angles sont mesurés positivement dans le sens contraire des aiguilles d'une montre, habituellement avec une origine angulaire dans la direction de 3heures suivant l'axe des x. (voir coordonnées cartésiennes). En gnomonique, il est plus courant de mesurer les angles dans le sens contraire des aiguilles de la montre à partir de midi bien que certains auteurs le mesure à partir de la ligne sous-stylaire.

Antarctic Circle: Cercle Antartique : la parallèle de latitude 66° 34' Sud. Noter qu'il delimite la région la plus au Nord autour du pôle Sud ayant au moins un jour sans nuit.

antisolar point: point anti-solaire: point de la sphère céleste directement opposé à la position du soleil.

aperture: ouverture: un petit trou transparent dans une surface opaque, conçu pour laisser passer un petit faisceau de lumière solaire sur un cadran ou une alidade c'est à dire pour les méridiennes, cadrans anneaux , héliochronomètres.

aphélie: le point où l'orbite terrestre est le plus loin du soleil. Ce phénomène se produit le 4 juillet.

apogee: (pron. apo-gee) le point de l'orbite de la Lune (ou d'un autre satellite) le plus loin de la Terre.

arc: une courbe partie d'une circonférence d'un cercle.

arc-minutes {or minutes d'arc}: une mesure angulaire égale à 1/60th d'un degré. La notation préférée est ' or arcmin.

arc-secondes {or secondes d'arc}: une mesure angulaire égale à 1/60th d'une minute d'arc. La notation préférée est" or arcsec.

Arctic Circle: Cercle Artique: parallèle de latitude 66° 34' Nord. Noter qu'il delimite la région la plus au sud autour du pôle Nord ayant au moins un jour sans nuit dans l'année.

Aries (first point of): Voir équinoxes.

armillary sphere: sphère armillaire: a skeleton model of the celestial sphere with rings representing the equator, tropics etc. Souvent finement fait en laiton, mais des versions en bois avec des échelles de papier sont courantes en France au 19ième siècle. C'est aussi la base du cadran armillaire - voir armillaire, dial (types de cadrans).

ascendant: se levant par rapport au zenith. Note: astrologues ont une définition différente.

astro compass: voir compas solairesolar compass.

astroide: (pron. as-troy-d) une courbe mathematque qui est formée par l'enveloppe d'une série de lignes droites, et qui a pour équation: x^2/3 + y^2/3 = 1. En gnomonique c'est la forme du gnomon utilisé dans le cadran astroide indépendant de la latiude. L' astroide est aussi la branche de la forme qui est tracée par un point de la circonférence d'un cercle lorsqu'il roule dans un cercle de rayon quadruple.

astrolabe: un instrument astronomique ancien de la forme d'un disque massif (la mère) qui est suspendue verticalement et qui comporte une échelle angulaire sur sa périphérie (le limbe). Un cercle coplanaire appelé klimata (ou tympan en français) et une alidade tournent autour du centre. Une fretted araignée donne la position des étoiles brillantes. Les différents composants sont tenus par le pivot central par une petite cale ou "cheval"; parfois appelée chien.

L'astrolabe planispherique represente la sphere céleste dans une projection stereographique, montrant la position du Soleil et des étoiles brillantes à différents jours et heures et à différentes latitudes. Un plateau est nécessaire pour chaque latitude. C'est probablement une invention grecque du second siècle avant J.C., mais il a été beaucoup développé par les cultures islamiques à partir du 9ième siècle près J.C. Il tomba en désuétude à la fin du 17ième siècjle en Occident.

L'astrolabe universel utilise des projections modifiées de la sphere céleste pour être indépendant de la latitude. Le type de Gemma Frisius (developpé en Occident au début du 16ième siècle) garde la projection stereographique but déplace le centre de projection au point 0° du Bélier. Le type de Rojas type (par J. de Rojas of Sarmiento, 1550) utilise une projection orthographique avec un point de projection à l'infini. Le type La Hire (fin du 17ième siècle) déplace le point de projection pour le rendre plus facile à lire.

L'astrolabe de marine est un instrument beaucoup plus simple conçu uniquement pour mesurer la hauteur du Soleil, Il uitilse un cadre ajouré et lesté en bas pour le rendre plus stable à bord des bateaux; c'est un precurseur du sextant.

Voir Appendix X pour une terminologie plus complète de l'astrolabe.

astronomical triangle: le triangle spherique de la sphère céleste dont les sommets sont le zénith, le pôle céleste, et la position su Soleil (ou d'un autre corps céleste).

atmospheric refraction (réfraction atmosphérique): voir refraction.

autumnal {or fall} equinox: voir équinoxes.

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 (du Soleil ou d'un astre): [A, AZ] l' angle du soleil, mesuré dans le plan horizontal et à partir du Sud. Les angles vers l'ouest sont positifs, ceux vers l'est négatifs. Celui de l'ouest est +90°, nord est ±180°, est -90°. C'est une partie du système de coordonnées horizontal. Voir Equations. Noter que les navigateurs (et quelques astronomes, mais pas Meeus) mesurent l'azimuth ou bearings dans lo sens des aiguilles d'une montre à partir du Nord.

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

Bérosus (prêtre de Bel à Babylone vers 250 avant J.C. ayant vécu dans l'île grecque de Cos) on lui attribue le premier cadran solaire (à heures égales durant une journée) appelé hémisphérium. Auteur d'une histoire de la Chaldée, écrite en Grec, dédiée à Antiochus Soter (281-262 av. J.C.) comportant une chronologie établie sur les observations astronomiques poursuivies en Chaldée depuis des millénaires

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).

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.

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 ~.

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.

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.

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.

cycloide (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.

cylindre ~ (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.

déclinant ~: a cadran vertical qui ne fait face à aucun point cardinal . La sous-stylaire est décalé par rapport à la ligne de midi ligne de midi, bien although the latter will still lie vertically below the dial centre.

diamétrale ~ : un des cadran à projection équatoriale, décrit pour la première fois par Samuel Foster du Gresham College au 17ième siècle, C'est un cadran horizontal avec un style mobile et des points and horaires disposé sur une ligne droite Est-Ouest.

diffraction ~: un cadran inventé en 1999 par M. Catamo & C. Lucarini. Il n'a pas de gnomon, mais le disque du cadran consiste en un modèle de diffraction, qui forme une ligne brillante et multicolore pointant sur le soleil lorsqu'elle regarde which forms a bright, multicoloured diametrical line pointing at the Sun when viewed perpendicularly to the centre of the dial plate. Des versions horizontales, de hauteur and équinoxiales sont possible. Le plateau du cadran est habituellement réalisé à artir d'un CD (compact disc), d'où le terme "Cadran CD".

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) ~.

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.

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): [e_c, EC] a measure of the relative sizes of the major and minor axes of the Earth's elliptical orbit. e_c = 0.01671... in the year 2000 and is slowly decreasing. e_c = 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 [E_a,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).

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.

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: (prononcer no-mon) la structure physique du cadran qui projette une ombre (du grec gnômôn "indicateur"). Le gnomon aujourd'hui est le plus souvent polaire (appelé parfois "gnomon axial"), bien qu'il puisse être aussi horizontal ou vertical.

Diogène Laërce (début du 3ième siècle après J.C.) attribue à Anaximandre l'invention et l'utilisation ingénieuse du gnomon (à style vertical) pour connaitre les paramètres de latitude d'un lieu et l'obliquité de l'écliptique, alors que Hérodote (5ième siècle avant J.C.) le fait remonter aux chaldéens.

Les propriétés particulières du gnomon polaire étaient connues de l'astronome Marocain Abdul Hassan Ali du début du 13ième siècle après J.C., mais sa première utilisation est certainement plus ancienne. La distinction entre gnomon et style faite (et encouragée dans ce Glossaire) dans la littérature moderne gnomonique n'est pas utilisée dans les ouvrages anciens et les deux mots y sont parfois interchangeables. A l'origine (en Angleterre à partir de 1546), le gnomon désigne un bâton vertical qui projette une ombre indicatrice de temps. Voir Figure 1.

D'où le mot gnomonique: la science des cadrans solaires et gnomoniste (rarement utilisé): une personne qui practique la gnomonique.

Golden Number Nombre d'or: suite de nombre (1 à 19) utilisé pour décrire l'année dans le cycle de Metoni. Il est utilisé avec les lettres Dominicales , pou trouver Pâques, et on le rencontre souvent sur les cadrans portatifs.

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.

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.

Hérodote (Histoires II, 109) " pour l'usage du polos, du gnomon, et pour la division du jour en 112 parties, c'est des Babyloniens que les Grecs les apprirent "

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").

heure: habituellement désigne le 1/24 du mjour solaire moyen, à moins qu'il ne soit spécifié autre chose. Scientifiquement elle est définie comme 3600 secondes. Voir Heure (types) pour d'autres définitions. Le mot dérive du Latin Hora qui était synonyme de prière.

horaire 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.

antiques ~: identiques à heures inégales ou heures saisonières.

Babyloniennes ~: nombre d'heures écoulées depuis le Lever du Soleil, avec 24 heures égales par jour. L'origine de ce terme n'est pas clair mais peut être relié au fait que les ancioens babyloniens utilisaient la base 60 pour compter les angles, etc. Elles sont souvent écrites "horae ab ortu solis" ou H. AB ORT." sur les cadrans. Voir Equations pour la conversion des heures égales en heures babyloniennes.

bibliques ~: identiques à heures inégales ou heures saisonières.

Bohémiennes ~ : identiques à Babyloniennes ~.

Canoniales ~: les 7 temps de la journée (et non durées) utilisés pour définir les services ou offices divins dans l'église médiévale. Ces offices étaient basées sur la Règle du 6ième siècle de Saint Benoit. Voir Appendice IV pour des précisions.

Une autre définition des heures canoniales est parfois appliquée aux lignes des premiers cadrans Italiens: c'est le système introduisant des lignes horaires équi-angulaires autour de la base d'un gnomon horizontal fixé à un cadran vertical méridional.

communes ~: le système habituel de 2 x 12 d'heures égales, appelées aussi Allemandes ou Françaises~. En Latin "horae communes", elles sont souvent appelées "kleine uhr" (petites heures) sur les cadrans de Nuremberg.

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

égales ~: tout système d'heures où la durée de l'heure est indépendante de la date, et la même de jour et de nuit.

Françaises ~: un terme ancien pour le système de 2 x 12 heures par jour, commençant à midi et minuit. parfois écrit "Ultramontaines". Sometimes written "Oltramontane".

de la Révolution Française~: le système d'heures égales du Temps Révolutionnaire Français.

Grandes ~: un terme pour n'importe quel système d'heures inégales. Souvent désignées par "grosse uhr" sur les cadrans de Nuremberg.

Grecques ~: identiques à Babyloniennes ~.

Italiennes ~: {parfois italiques~} le nombre d'heures qui se sont écoulées depuis le dernier Coucher du Soleil (heure 0), avec 24 heures égales par jour. Elles furent utilisées dans de nombreux pays européens entre 1200 et 1600. Elles sont parfois écrites"horae ab occasu solis" or "H. AB OCC." sur les cadrans. Les deux termes (Italiennes et Italiques) sont souvent utilisés sans distinction dans les ouvrages modernes mais dans les ouvrages anciens les heures italiennes étaient comptées 30 minutes après le Coucher (avec l'Angélus du soir) . Voir Equations pour convertir les heures égales en heures italiennes.

modernes ~: le système d'heures égales utilisé dans les système de temps modernes. Elles sont parfois appelées heures communes, Européennes, Françaises, Allemandes ou vulgaires.

de Nuremberg ~: un système hybride d' heures égales. Les heures de jour étaient mesurées en utilisant le système babylonique commençant avec le Lever du Soleil, pendant que les heures de nuit étaient comptées avec le Coucher et utilisaient le système italique. En Latin, "horae norimbergenses".

octaval ~: un système de comptage du temps avec une période de jour divisée en huit heures. Probablement introduit par les Romains vers 250 avant J.C.. Voir Appendix III pour le nom des périodes du jour..

planétaires ~: une heure planétaire est le temps pour qu'un secteur de 15° de l'équateur céleste se lève au dessus de l'horizon en comptant à partir du Lever du soleil. Comme il y a toujours 180° de l'équateur au dessus de l'horizon il y a 12 heures planétaires du lever au coucher mais elles sont inégales non seulement d'un jour à l'autre mais d'une heure à l'autre.
Note: cette definition est basée sur les écrits de Sacrobosco, mais certains auteurs utilisent le terme "heures planétaires" simplement comme une autre forme de "heures saisonières", avec les heures associées aux planètes. Voir l' Appendix VIII pour les symboles des planètes et cette association.

Le programme Zonwvlak utilise la définition de l'universitaire allemand Joseph Drecker (1925) qui définit une heure planétaire comme le temps pour qu'un secteur angulaire de 15º de l'écliptique se lève au dessus de l'horzon (en comptant à partir du Lever du Soleil): elles sont donc très irrégulières.

saisonnières ~: une variété d'heures inégales, en général 12 heures de jour et 12 heures de nuit. Nommées ainsi parce que la durée d'une de ces heures varie avec les saisons .

temporales ~ or temporaires ~: un système d'heures inégales avec 12 heures du Lever au Coucher, et 12 heures (de durée différentes) du Coucher au Lever.

inégales ~: un système d'heures où la durée d'une heure dépend de la date et est différente de nuit et de jour (excepté aux équinoxes). Le nombre d'heures de jour est ordinairement 12 mais peut-être 8 voir 10 (c'est le cas sur certains cadrans canoniaux). Le décompte des heures de jour commence au Lever du soleil.

Welsch ~: c'est à dire étrangères. Identiques à Italiennes ~.

Fin de Heures (types d'~)

house: (astrologique) un segment de la sphère céleste. Différentes méthodes de division de la sphère en segments existent mais le plus utilisé est celui des signes du zodiaque, et des Maisons de Regiomontanus.

hyperbola: a conic section, its most common use in dialling is the shape of the declination lines on a dial.

Imbolic: an ancient Celtic festival held on the 2st of February, celebrating fertility. It is one of the cross- quarter days

inclination: [i, I] the angle between the back of the dial plane and the horizontal for inclining or reclining dials. Equivalently, it is the angle between the zenith and the positive z co-ordinate of the dial. i = 0º implies a horizontal dial. For an inclining dial, 0 < i < (the latitude of the place). For a reclining dial leaning away from the observer, i < 90º; whilst i > 90º implies a proclining dial leaning forward towards the observer. Beware: this convention is not followed by all authors.

inclinometer (or clinometer): an instrument for measuring the inclination or slope of a surface. Two types are common: simple devices with a plumb-line hanging across a protractor, or precision ones where a sensitive spirit level is moved to the horizontal position against an accurate scale. Note: the term inclinometer is also used to describe an instrument - also called a dip circle - for measuring the vertical component of the Earth's magnetic field.

index: besides its normal meaning of an alphabetical list, an ~ is a pointer on a scientific instrument, indicating a point on a graduated scale. The index arm of a sextant is the movable arm carrying the index mirror and the fiducial line.

inferior: refers to an event on the celestial sphere below the horizon. Opposite of superior.

inhiraf: the angle which the qibla line makes with the north ray of the meridian at any location.

International Date Line: the line from the N to S poles, approximately following the 180º line of longitude, through which the date alters by one day (positively if travelling from W to E). Variations from the 180º meridian are made to avoid political and geographic boundaries.

Islamic prayer lines: the lines on Islamic dials where the shadow of the nodus falls at the times when Muslims must pray. The times of the three most common lines are determined by a linear relationship to the noon shadow length of a vertical gnomon:

zuhr: noon shadow + 0.25 x gnomon height

asr-awwal: noon shadow + gnomon height

asr-tânî: noon shadow + 2 x gnomon height

isogonals: lines of equal magnetic deviation plotted on some navigational charts.

Jaipur: (pron. Ji-poor) a famous early 18th century solar astronomical centre in India, constructed by the Maharaja Jai Singh around 1724. It includes many monumental sundials, including a famous equatorial one with a gnomon 27 metres high.

Julian calendar: the calendar system introduced by Emperor Julius Caesar and devised by the Greek philosopher (and court astronomer of Egypt) Sosigenes. Widely used from 45BC to 1582AD. By this date, it was in error (compared to the Earth's orbit) by 10 days due to the imperfect use of leap years (i.e. it assumed the length of a year was 365.25 days).

Julian Day {sometimes Julian Ephemeris Day}: [JD] the astronomer's scale of date and time. Used in dialling, for example, for the accurate calculation of the EoT and sun's declination. Measured continuously in decimal days since noon GMT 1 Jan, 4713BC. By tradition, since midnight is difficult to define without an accurate clock, the JD begins at Greenwich Mean noon, that is, 12:00 UT. As an example, 9:36 GMT on 26 April 1977 is JD2,443,259.9. See Sources: Meeus for a full algorithm for converting modern date/time to JD. The Julian Day count was defined by John Herschel in 1849, based on the 4713 BC epoch used in 1583 by Joseph Scaliger (France). It is commonly stated (probably erroneously) that Scaliger named the system after his father.

kamál: an early Arabic navigational instrument for determining the Sun's altitude by means of a transom and a knotted cord.

Kepler's Laws (of planetary motion): three laws which describe the motion of the planets around the Sun, after Johannes Kepler (1571-1630). They are:

1. Planets travel in elliptical (rather than circular or epicyclic) orbits, with the Sun at one of the foci.
2. The line joining the Sun and the planet sweeps out equal areas of space in equal time intervals (so that the planet moves faster when it is nearer the Sun, and establishing the Sun as the main controller of the planets)
3. The link between the size of the planet's orbit and its period of rotation is described mathematically.

klimata: (pron. clim-arta) part of an astrolabe, it is a disk rotating on the mater with the north celestial pole in the centre and showing almucantar lines for the design location. After the Ancient Greek meaning "angle of the Sun's rays", and hence the modern word "climate".

Lambert's circles: circles of construction used when drawing sets of nested ellipses to represent analemmatic dials for different latitudes, these dials using a common scale for the (vertical) gnomon position. Such sets of dials are particularly useful for a solar compass, e.g. the Cole sun compass used in N. Africa during the Second World War. After the mathematician Lambert (b. 1728, Alsace).

Lammas ( or Lammas Day): one of the cross-quarter days. It is on 1st August, and was formerly observed as the harvest festival.

latitude (geographical, of a place): [ , PHI, Lat] Note: avoid LAT, since it implies local apparent time. It is the angular position of a place north or south of the equator. Positive values in the Northern hemisphere, negative in the South (i.e., the South Pole has = -90º). Part of the geographic co-ordinate system, the term comes from the Greek "latus" (breadth).

leap second: an extra second inserted into UTC at the end of some years between 24:00:00 Dec 31 and 00:00:00 Jan 1 to ensure that UTC remains in step with the Earth's diurnal rotation. It may also be added at the end of June. The addition is not predictable as it depends on many factors, such as the increased atmospheric drag on the Earth in El Niño years. The actual addition is performed by the Bureau International des Poids et Mesures near Paris. Leap seconds are gradually becoming more common as the rate of the Earth's rotation slows due to energy dissipation by the tides.

leap year: years in which an extra day (February 29) is introduced so that the (Gregorian) calendar keeps step with the Earth's orbit. The rule for leap years is that a year is a leap year if and only if the year number: is divisible by 4, except years divisible by 100 which are not leap years unless they are also divisible by 400. This corresponds to the length of the year being 365.2425 mean solar days. This can be compared to the 365.25 days in the earlier Julian calendar. (The Julian leap year doubled February 24.) The leap year system causes the EoT (and Sun's declination) on a particular day of the year to exhibit a small periodic variation.

lemniscate (curve): the term used in Latin countries for the analemma. From lemniscus, meaning ribbon. In English, the ~ is a mathematical curve which is similar to a spiral and is sometimes used in road design; it also looks similar to one lobe of the analemma.

libration (of the Moon): the periodic oscillation of the Moon from 'side to side' (and 'up and down') which allows an observer on the Earth to see somewhat more than half its surface.

limation: (rare) a term used by Flamsteed to mean the correction of a calculation or observation, having originally (1612) had the meaning 'filing or polishing'.

limb: part of an astrolabe, it is the circular ring with a scale of hours and degrees. Its first recorded English use was in 1593.

limb (of the Sun): the outer circumferential region of the Sun (or other celestial body). The term limb darkening indicates that the disk of the Sun does not have uniform brightness but is dimmer around the "edges" due to increased optical absorbtion by the photosphere.

local apparent time: [L.A.T.] solar time see LAT (types of). Hence local apparent noon, at the Sun's superior transit.

local hour angle (or just hour angle): [h, HA] Local Apparent Time expressed as the angular position of the Sun in its daily track. Measured from noon, it increases by 15º per hour with increasing time (i.e., morning hours are negative). Beware, this convention is not universal.

lodestone: a naturally occurring oxide of iron, mounted with two iron poles in a non-magnetic frame. Used for magnetising compass needles, small ones were made specially for portable dials.

longest day: a term in common parlance, defined as the day of the year with the greatest (astronomical) sunrise to sunset period. It is normally used synonymously with the summer solstice although, strictly, it can vary by a day depending on the exact time of the solstice and the relationship between the rate of change of the EoT and that of the local sunset/sunrise.

longitude (or geographic ~ to distinguish it from the ecliptic ~): [ , _t, LON] the angular location of a place on the Earth's surface measured east or west of the Prime meridian though Greenwich. Longitudes W are positive, E are negative. Part of the geographic co-ordinate system, the term comes from the Greek "longus" (length). See also Prime Meridian.

Longitude Act: a 1715 act of the British parliament which established a Board of Longitude to manage a prize of £20,000 for a practical method of finding longitude at sea.

longitude correction: the correction required to local apparent time to translate it to the L.A.T. for the central meridian of that time zone. The correction is +4.0 minutes for every 1º longitude W of the time zone meridian (and –4.0 minutes for E). Sometimes, this correction is built into the hour lines by calculating the local hour angle for times at the zone meridian.

lunar angle: the difference between the right ascensions of the Sun and the Moon. On a standard sundial used as a moon dial, the L.A.T. equals the time shown by the lunar shadow plus the lunar angle expressed in hours.

lunation: the time interval between successive New Moons. The mean interval is 29 days 12 hours 44 minutes 3 seconds (the synodic month) but, because of the perturbing action of the sun, the difference between the shortest and longest lunations in the 20th century is 5 hours 19 minutes.

Mach bands: (pron. mak) subjective light and dark bands which an observer sees when looking at a black-white edge. They are produced by the brain's visual processing (i.e. they are not real) and have the effect of sharpening up edges. First described by the German physicist Ernst Mach (1838-1916).

magnetic variation {magnetic declination, magnetic deviation}: Note, the use of the term magnetic declination is best avoided because of confusion with the other types of declination. It is the angle between the true N pole and the magnetic N pole. At present in the UK, the magnetic pole is very approximately 3º W of true north, and decreasing by about 12' annually. See Appendix IX for more detailed and historical values. There can be large local variations to the general values, some of which can be found mapped on navigational charts. The use of a magnetic compass for aligning a permanent dial is not recommended, even if due corrections are made, as the presence of steel or magnetic rocks will cause very local variations.

manaeus: (pron. man-ay-us) the circle of months which formed part of the ancient orthographic spherical projection used by late Middle age diallists. It establishes the sun's declination.

maquette: a sculptor's small preliminary model. The term is used to describe small mock-ups of three-dimensional dials.

Martinmas: St Martin's day, on 11th November. It is one of the cross-quarter days.

mass dial: see Dial types (mass dial).

mater: the heavy disk which forms the base of an astrolabe.

mean solar day: the time between successive transits of the fictitious mean Sun (i.e. an imaginary sun which appears to circle around the celestial equator at a constant rate equal to the average rate of the Earth's real rotation). The basis of civil time keeping.

mean time: see Time (types of).

mean local time (or local mean time) : see Time (types of).

Mercator projection: the most common projection used to produce a 2-D map of the globe. Developed by Gerardus Mercator in Belgium, 1586. It has straight meridians and parallels of latitude that intersect them at right angles. Scale is true at the equator or at two standard parallels equidistant from the equator. The Transverse Mercator projection is obtained by projecting the sphere onto an enclosing cylinder tangent to a central meridian. This is the projection used for Ordnance Survey maps of the UK.

merkhet: a transit instrument from ancient Egypt, consisting of a horizontal "L" shaped stone with a plumb-bob supported from the short vertical arm. It was used in conjunction with a bay.

meridian: the great circle (or, more usually, half of a great circle) passing through the N and S poles. The same as a line of longitude. The term is sometimes used to mean the meridian line passing through the observer's location, or its representation on the dial face.

meridional: south-facing (e.g. a direct-south dial). In more general usage, it generally means of, or from, the south.

meridian line: see Dial Types (noon line) for the lines inscribed in the floors of Renaissance cathedrals, etc.

metonic cycle: a cycle of 19 years (or 235 lunar months) over which the Sun and the Moon return to the same relative positions amongst the constellations. It was discovered by the Greek astronomer Meton c.433 BC and determines the epact number and the Golden Number. Actually, the moon runs 1½ hours slow over this period, or one day over 312.7 years. This fact has to be included in the calculations for Easter.

midnight: strictly, the time when the Sun achieves its most negative altitude (or, equivalently, when its azimuth is ±180º). More loosely defined as half-way between sunset and sunrise or, with even less accuracy, 12 hours after local noon.

midsummer, midwinter (~ day): the same as summer or winter solstice. Note that Midsummer (with capital M) is a legal term for the Quarter Day on June 24.

mil: unit of angular measurement used in some military equipment, e.g. rangefinders, theodolites. 6400 mils = 360º. Beware possible confusion with use as a linear measurement of 1/1000 inch used by engineers (particularly in the USA).

mileways: an obsolete term for an hour angle of 5º, equivalent to 20 minutes of time. So called because this is the approximate time that it takes to walk one mile.

minute of arc: see arc minute.

minute (of time): is now defined as 60 seconds. Historically, the definition was 1/60th hour, where the hour was derived from the rotational period of the Earth.

month: an interval of time related to one revolution of the Moon around the Earth (a "moonth"). The calendar month derives from the synodic month (full-moon to full-moon) which averages 29.53 days. The anomalistic month (perigee to perigee) averages 27.53 days.

Moon: the natural satellite of the Earth. It has a mean distance from the Earth of 384.4 x 10³ km and a semi-diameter at mean distance of 15' 33". The inclination of its orbit to the ecliptic is 5º 8' 43". Note: "moon", without an initial capital letter, is sometimes used to refer to moons of planets other than the Earth.

moondial (cadran lunaire): voir cadrans (types de).

moonlight: rays of light which reach the observer directly from the Moon, having originally been sunlight reflected by the Moon's surface. There is usually sufficient light to cast a shadow only between the 1st and 3rd quarters of the Moon. Since the angular size of the Moon is approximately the same as that of the sun, the ratio of umbra to penumbra of a moon shadow is also the same as for a sun shadow.

motto (devise): une sentence, phrase ou vers écrite sur le cadran exprimant divers sentiments. Les devises apparaissent sur les cadrans à la fin du 16ième siècle mais furent particulmièrement populaires au 19ième siècle.

nadir: the point on the celestial sphere that is diametrically opposite the observer's zenith.

nautical mile: a distance (6080 feet or 1853 metres) determined as 1 arc-minute of longitude at the equator.

night (or night-time): the period of darkness between sunset and sunrise.

nocturnal: (noun) a fixed or, more usually, portable instrument used to tell time by the apparent revolution of the stars on the celestial sphere. The stars most often used on these instruments are either the "guards" of the Little Bear (Ursa Minor) or the "pointers" of the Great Bear or Plough (Ursa Major). These are known as the Little Dipper and Big Dipper, respectively, in the USA. Most nocturnals have inscriptions "GB" and "LB" on their scales. The term ~ can also be used as an adjective, meaning "of the night".

nodus: a point which casts a shadow to indicate the time and/or date on a dial face. It may take the form of a small sphere or a notch on a polar-pointing gnomon, or it may be the tip of a gnomon with an arbitrary (usually horizontal or vertical) orientation. See Figure 1.

nodus height: [N, NH] the height (distance) of a nodus perpendicular to the dial plane. It is also the same as a vertical style height.

nomogram (sometimes nomograph): a system of graphs showing relationships between three or more variables. From the Greek "nomos" (law).

nonius: a device similar to a vernier for interpolating readings on an angular scale, but using a large number of concentric scales rather than a single movable one. Named after the 16th century Portuguese mathematician Pedro Nõnes.

noon: the time of the sun's transit each day. Equivalently, the time that the Sun reaches its largest altitude for that day. Note that noon is specific to the observer's location, unlike 12:00 o'clock with which it is often confused.

The word ~ originates from the Latin 'nonus' or ninth, indicating the ninth hour of the day counting from sunrise. By 1420 it meant the hour or ecclesiastical office of Nones, so noon gradually became associated with the beginning of this office.

noon cross: a cross shape often seen instead of XII on the noon line of dials. It can have many forms, many of which look like an Iron or Maltese cross. The nearest heraldic term is the cross patty.

noon gap (or gnomon gap or split noon ): the gap in the hour scale of a dial to account for the finite thickness of the gnomon. It is positioned on the dial plate where the Sun is in the same plane as the gnomon, i.e. at noon for horizontal or direct S dials. A gnomon gap is occasionally seen on the sub-style of a declining dial. See Figure 1.

noon line (on a dial): simply the hour line corresponding to noon, it is the most important line from which the others are usually calculated. It is the line which most often carries an analemma.

noon marker: a single mark or stone in the ground (or on a wall) set to show noon when crossed by the shadow of a convenient vertical; for example, a stick or edge of a wall. Sometimes also called a shepherd's dial.

North: the intersection of the local meridian with the horizon, in the direction of the north celestial pole.

North Pole: the point on the Earth's surface and its axis with a latitude of +90º . It lies in the direction of the North celestial pole, from which the Earth is seen to rotate anti-clockwise.

numerals: The numerals on dials are usually either Arabic (the usual 0-9 used in English) or, especially on older dials, Roman numerals (I, II,..XII etc.). Note that it is common to find IIII in place of the later IV on some dials. A convention sometimes used on dials with more than one hour ring is to use Roman numerals for Local Apparent Time, and Arabic ones for civil time (often BST etc.). Many other forms of numerals (e.g. Chinese, Turkish) are used world-wide.

nutation: a small periodic (principal time constant of 18 years 220 days) oscillation of the rotational axis of the Earth about its mean position. Discovered by James Bradley (1693-1762), the third Astronomer Royal, in 1748. The disturbance of the idealised orbit of the Earth (as a two-body system) is due to the gravitational attraction of the Moon and, to a lesser extent, the other planets. Nutation introduces small changes, typically 7 arcseconds annually, to the precession of the equinoxes.

obelisk: a tall tapering shaft of stone, usually monolithic with a square or rectangular section ending with a pyramidal apex. Prominent in Ancient Egypt as a solar symbol, often at the entrance to tombs or as a cult object in shrines to the sun.

obliquity (of the ecliptic): {sometimes the slant} [ , EPS] is the angle between the Earth's equatorial plane and the ecliptic. The current mean value of the obliquity (i.e. ignoring its nutation) is 23º 26' 21", decreasing by 23" over the next 50 years. Note that this figure sets the position of the tropics.

obtuse angle: an angle of greater than 90º and less than 180º.

occidental: west-facing (e.g. a direct-west dial). In more general usage, it generally means of, or from, the west.

orbit (of the Earth): the path of the Earth around the sun. For dialling purposes, this is taken as elliptical, with a very small eccentricity, i.e., it ignores the small perturbations due to the effects of the Moon and other planets.

origin: the (0,0) point (or (0,0,0) in three dimensions) of a co-ordinate system used to describe a dial plane. It is usual to place this point at the centre of the dial (if it exists), but it is sometimes placed at the sub-nodus point.

oriental: east-facing (e.g. a direct-east dial). In more general usage, it generally means of, or from, the east.

orrery (pron. or-rer-re): (sometimes called a planetarium): a physical model of the solar system, used for demonstration purposes. Named after Charles Boyle, 4th Earl of Orrery, who had an early example built by John Rowley in 1712. Sometimes powered by clockwork to provide the correct relative orbital periods of the planets. Early examples are very valuable. See also tellurian.

orthography: the art of drawing anything without perspective, as though viewed from infinity. In dialling, the sphere so drawn consists of circles, straight lines and ellipses. Hence orthographic (or orthogonal) projection, which is used in the universal astrolabe.

ortho-style: a style which is perpendicular to the dial plate. It was used in many ancient dials.

parabola: a mathematical term for the conic section obtained by cutting a cone with a plane parallel to its generator (or "edge"). A parabolic surface, obtained by rotating a parabola about its own axis, is much used for mirrors as it has the property of focusing parallel rays of light to a point focus.

parallactic angle: [ ] the angle of the polar triangle between the directions to the pole and to the zenith at the celestial object. Hence it is the angle between the vertical and the hour circle, of use in calculating the effects of astronomical refraction.

parallax: the effect whereby the apparent position or direction of an object changes with the observation point. See solar parallax for its affect on solar parameters. The effect can affect the accuracy of reading scales.

paschal moon: (pron. pas-kal) the first full moon following the Spring equinox. Important for the determination of Easter.

patina: Coloured, metallic compounds (usually oxides and sulphides) which form on metal surfaces left exposed to the atmosphere. The actual colour depends principally on the metal, but also on the impurities in the atmosphere resulting from pollution or proximity to the sea. Typically, copper-containing alloys develop a greenish colour.

pedestal: the supporting structure for a dial, particularly horizontals. Usually of stone, it may comprise several different pieces and brings the dial to a convenient viewing position. See Appendix VII for more details of architectural terms.

pelorus: an instrument for finding the solar azimuth, consisting of a magnetic compass and an alidade, with some means (e.g. mirrors, prisms, shades) of viewing the Sun and the compass needle.

penumbra: the area of partial shadow surrounding the central umbra. It is due to the finite size of the sun. An observer standing in the penumbra would observe only part of the sun's disk.

perigee: (pron. pe-ri-gee) the point in the Moon's (or other satellite's) orbit when it comes closest to the Earth.

perihelion: (pron. perry-he-le-on) the point in the Earth's orbit when it comes closest to the sun. It occurs during the first week of January.

perpetual calendar: a device, usually in the form of a circular plate with one or two rotating engraved disks, for finding the day of the week for any date (over a wide range of years). They are often combined with portable dials as part of a compendium. More sophisticated versions have extra tables for Saint's Days and similar data.

phase (or age) of the Moon: the approximately monthly variation of the angular separation of the Sun and the Moon, leading to the sequence of new, waxing, full and waning moons. The age (as seen, for example, in tables associated with moon dials) is measured in days since the last new moon. Astronomically, the phase of the Moon is defined as the angle between the Sun and the Moon measured from the Earth (the lunar angle). The mean length of the synodic (i.e., lunar) month is 29.53059 days (usually approximated to 29½ days in the lunar mechanisms of clocks).

photosphere: the outer envelope of the Sun which produces the visible light by which it is seen.

pinnules: sighting pinholes (usually in pairs) in an alignment device, e.g. an alidade.

planet: astronomically, a celestial body in orbit around a star. The five planets of the solar system known to the ancients were Mercury, Venus, Mars, Jupiter and Saturn. In addition, they often counted the Sun and the Moon as planets; for example, in the planetary hours system. See Appendix VIII for symbols.

planetarium: see orrery.

planisphere: a map of part of the celestial sphere, formed by a stereographic projection of the sphere onto a flat plane and showing (or adjustable for) the positions of the stars at a particular time and location.

plinth: the base part of a pedestal, normally resting on the ground. Note that some authors use ~ to refer to the whole of the pedestal. See Appendix VII for more details of architectural terms.

plumb-line: a freely suspended line with a weight (or plumb-bob) at its lower end, used for defining the vertical.

plummet: the form of plumb-line incorporated in a portable dial and used for levelling it. It usually consisting of a solid elongated cylinder suspended, by a joint with free movement in the horizontal axes, above a datum point.

pobble: the bead on the plumb-line of a card dial.

polar axis: see axis.

polar co-ordinates: see co-ordinates.

polar distance: the distance (as an angle) of the Sun from the elevated celestial pole; the complement of the declination.

polarised light: light in which the electromagnetic waves have a single plane of vibration in a direction perpendicular to the direction of propagation. Polarising filters allow the transmission of light rays with only a selected plane of polarisation. Discovered by Christiaan Huygens (1635-1703). Sunlight is randomly polarised, but skylight is partially plane polarised, with the direction of polarisation at any point in the sky being perpendicular to the plane containing the point, the Sun and the observer. The proportion of the skylight which is polarised is a maximum in the principal plane and at 90º to the sun. The proportion is always less than 75%, and substantially less in slightly hazy conditions.

Polaris (or Pole Star): actually Ursae Minoris, it is the star which appears quite close to the N celestial pole and is frequently used for finding north by navigators. It currently appears to rotate daily around a circle of radius 1º, so it requires some knowledge if it is to be used for aligning a sundial. The size of this circle varies over the centuries with the precession of the equinoxes.

polar plane: any plane which is parallel to the Earth's axis.

polar triangle: the spherical triangle on the celestial sphere whose vertices are at the pole, the zenith, and a celestial body, with respective angles of the hour angle, the azimuth, and the parallactic angle. The arcs joining these are the co-latitude, the north polar distance (90º - ) and the zenith distance. The polar triangle is fundamental to the operation of most types of sundial, whose function it is to derive the hour angle, and hence the time, given any three of the other quantities.

poles (N and S of the Earth): the locations on the Earth's sphere with latitudes of +90º (N) and –90º (S).

polos: an old term for a polar-pointing style.

post meridiem (p.m.): the portion of the day between noon and midnight.

precession (of the equinoxes): the slow westward progression of the equinoxes on the ecliptic. It is caused by the drift of the Earth's axis in space, as in a precessing spinning top. The position of Polaris turns around the pole of the celestial pole once in about 26,000 years. As a consequence, the vernal equinox regresses by about 50 arcseconds per year along the ecliptic. It is caused predominantly by the gravitational force of the Sun and the Moon on the Earth's equatorial bulge. Secondary effects, due to the other planets, give a rotation of the ecliptic plane of 47 arc-seconds per century.

La première mesure de précession fut effectuée par Hipparque en 129 avant J.C..

précision (d'un cadran): une combinaison de la résolution et de l'exactitude d'un cadran, elle donne une mesure de combien le cadran gives a measure of how exactly (and correctly) it indicates n'importe quelle heure.

Premier meridien: la ligne méridinne définie comme l'origine des longitudes. Maintenant synonyme de meridien de Greenwich, Avant 1884 de nombreux pays définissait leur propre origine.Les premiers grecs utilisaient Rhodes ou AlexandrieThe early Greeks used Rhodes or Alexandria. Ptolemée utilisait les îles Fortunées, que les savants de la Renaissance pensaient être Ferro aux îles Canaries. Nuremberg était fréquent pour les cadrans qui y étaient fabriqués et jusqu'à des dates récentes de nombreuses nations maritimes avaient leur propre lieu; Paris en particulier continua à être utilisé après 1884.
Noter que la ligne de longitude 0° utilisée par le système GPS est actuellement une valeur moyenne, périodiquement recalculée pour tenir compte de la dérive des continents et se situe actuellement à environ 38 m (80 feet) à l'est de la ligne méridienne de l'Observatoire de Greenwich.

Premier vertical: le cercle vertical perpendiculaire au meridian. Il passe par les points Est et Ouest de l'horizon.

Primum Mobile: (pron. pree-mum mo-be-lay) un terme ancien pour la supposée sphère cristaline portant les étoiles dans leurs orbites autour de la Terre.

plan principal {or plan vertical}: le plan obtenu en faisant varier l'altitude du soleil à azimuth constant. Perpendiculaire à l'almucantarat.

prosthaphaeretical arc: a term introduced by Samuel Foster to describe an arc on the surface of the earth between the location of an inclining/declining dial and the position where it would be identical to a horizontal dial (i.e. the complementary dial). In astronomy, prosthaphaerisis is the adding of a small amount to an observed value.

Ptolémée: (85 à 165 après J.C.) d’ Alexandrie, auteur de
« Synthèse mathématique » de 13 livres appelée "Almageste par les Arabes"
Tables de cordes
" Comment la durée du jour le plus long permet de déterminer la hauteur du pôle et réciproquement"

Ptolemy's rulers: an interconnected set of three linear scales used to measure the angular positions of stars, used particularly by Regiomontanus and the Nuremberg group in the 1460s.

Qibla line: parfois trouvé sur les cadrans musulmans, c'est la ligne d'azimuth sur la surface du cadran partant du centre and pointant la Mecque.

quadrant: a term used for a large genus of astronomical and navigational instruments. In the form of a quarter-circle, it incorporates a sun or star sighting device along one of its radial edges and a plumb-bob hanging from the centre of the circle. The old quadrans vetus was originally an Islamic invention which provides seasonal hours but is only truly accurate for an observer on the equator. The quadrans novus, invented by Profatius in 1288) was more accurate, incorporating the circular scale of the astrolabe folded into a quadrant but it was difficult to read. The 1438 horary quadrant of von Gmunden was one of several attempts to improve on this. The Gunter ~ (after Edward Gunter, Gresham College, 1623) is latitude dependent and employs a stereographic projection. The navigational ~ is actually an octant (eighth of a circle) with two reflecting mirrors replacing the plumb-bob. For the Davis ~, see back-staff.

Quarter days: the first or last days of each quarter of the year on which rent or interest is due. These dates are occasionally used instead of the zodiac signs for declination lines on dials. See Appendix XII for their names and dates.

quincunx: five dots arranged as on dice. It sometimes appears on mass dials at noon or service times.

radian: [rad] the primary unit of angular measurement, it is the central angle subtended by an arc of a circle equal in length to its radius. 2 radians = 360ºor 1 rad 57.3º.

ray: a single line or narrow beam of light.

reclination: a term sometimes used for the angle by which a reclining dial leans away from the observer (i.e. the complement of the inclination). It is more consistent, however, to translate this into the equivalent inclination.

rectificatory: an old term for a right-angled triangle where the other two angles are the latitude and co-latitude. Used particularly in the graphical construction of dials.

reflex angle: an angle of greater than 180º.

refraction: the "bending" of light at the interface of two materials of different refractive indices. It accounts for the focusing action of lenses. In dialling, use is made of ~ in dials which use a clear liquid in a solid cup to compress the hour lines, or which use a cylindrical lens to focus sunlight onto a curved dial plate. Atmospheric refraction (due to the curve of the Earth's surface and the variation of atmospheric density with height, in turn dependent on meteorological conditions) is the effect which makes the Sun (or other celestial body) look slightly higher in the sky than its true astronomical position. It is only significant when the Sun is within a few degrees of the horizon. At 0º altitude, the bending is equivalent to approximately 34 arc-minutes, so that it is possible to see the Sun when it has actually just sunk below the horizon. See Equations. This effect is not generally included in normal sundials but it must be allowed for when calculating solar parameters from observations using meridian lines.

The refractive index [ , MU] of a medium (or its index of refraction), needed to calculate these effects, is defined as the ratio of the speed of light in a vacuum to its speed in the medium.

Regiomontanus houses: an astrological division of the celestial sphere into 12 segments or houses. The division is performed in equal segments around the celestial equator, rather than around the ecliptic as is done for the normal signs of the zodiac. The houses are numbered I to XII, beginning at the east point of the horizon and are, confusingly, associated with the standard zodiac signs with I corresponding to Aries. Only the last 6 of the signs appear above the horizon. They are shown as domifying circles on some old dials.

resolution (of a dial): the smallest time increment to which the scale on a dial can be read. Contrast with accuracy. See also precision.

rete: {or net or spider} (usually pron. ree-tee) part of an astrolabe, it is the fretted disc containing a number of star pointers, and which can be turned on the limb until the star's pointer crosses the altitude circle on the stereographic projection, allowing the time to be read off (assuming the date is known). The term ~ has sometimes (first reference in 1677) been used as a graduated scale fixed to an astronomical telescope.

reticule: fine lines or scales on an optical element in a sighting device (e.g. a telescope) to aid in alignment or measurement of an object.

revolve: (astronomical) to orbit around another body, e.g. the Earth revolves around the Sun. Contrast to rotate.

right ascension: [, RA] a co-ordinate used by astronomers, as part of the equatorial co-ordinate system, (together with declination) to define the position of a celestial body. It is the angular distance measured along the celestial equator (positive to the east) from the vernal equinox to the intersection of the celestial equator to with the hour circle through the point in question. Usually measured from 0 to 24 hours, but sometimes 0º to 360º.

root (of a gnomon): The fixing between the gnomon and the dial plate. See Figure 1

rotate: (astronomical) to spin on its own axis, e.g. the Earth rotates on its polar axis. Contrast to revolve..

Samhain: an ancient Celtic festival held on the 1st of November. It is one of the cross-quarter days.

saros cycle: a cycle of 18 years 11 days 8 hours (223 lunations) between repetitions of eclipses.

scales: see dialling scales.

Scaphe (mot grec féminin): nom générique de tous les cadrans creux (concave)

sciagraphy: {skiagraphy} the art or science of shading and shadows. From sciaterics or scioterics - the name for gnomonics in ancient Greece.

seasons (saisons): the saisons sont définies astronomiquement comme suit:

Printemps: de l'équinoxe de printemps (soleil au point gamma dans l'H.Nord)) au solstice d'été

Eté: du solstice d'été à l'équinoxe d'automne.

Automne: de l'équinoxe d'automne au solstice d'hiver

Winter: from the winter solstice to the vernal equinox


Dans hémisphere nord les saisons comprise the following months:

Printemps    20 (ou 21) mars à 21 ou (22) juin

Eté    20 ou 21 juin à 22 ou 23 septembre

Automne    22 ou 23 à 21 ou 22 décembre

Hiver     21 ou 22 décembre à 20 ou 21 mars

Les signes du signes of the zodiaque pour les saisons sont donnés dans l'Appendix I.

second (of angle): see arc-second.

second (of time): the fundamental unit of time. The accepted scientific definition of the second is now 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels in the ground state of caesium 133. This definition was adopted in 1967, and replaced the earlier (since 1955) ephemeris second which was defined in terms of a fraction of the mean tropical year in 1900. The above frequency was chosen because it gives a close approximation to the number of seconds in a day (86,400). Fluctuations in the Earth's rotational rate since about 1969 have been such that the day is between 1 and 3 ms longer than this number of seconds. These variations are totally insignificant to even the best sundial. The word ~ derives from the Latin "secunda minuta" or second minute.

semidiameter (of the sun): [s, S] half the angular size of the Sun (or, more correctly, its photosphere). As the distance from the Earth to the Sun varies during its orbit, the semi-diameter varies from 15.76 arc-minutes in July to 16.29 arc-minutes in January. In dialling, it is usual to take the sun's full diameter as ½º .

septentrional: a term now rarely used for "of the north" and sometimes applied to north-facing dials.

shadow sharpener: any of the various devices for sharpening the edge of a shadow, allowing more accurate time readings to be made. Usually a physical addition to the gnomon or nodus, it casts a secondary shadow, with its own penumbra, in which the primary shadow can be located more accurately (although it may have less contrast). The term is sometimes also used to refer to a movable lens which produces an image of the shadow edge.

shadow square (carré des ombres): une échelle carrée (ou rectangulaire) souvent trouvée sur lesquadrants et astrolabes qui permet de trouver la tangente ou la cotangente de la of the hauteur (altitude) d'un corps céleste.

Jour le plus court: dans le langage commun, le jour avec la plus petite durée entre lever (sunrise) astronomique du soleil et son coucher. Il est utilisé comme synonyme de solstice d'hiver, bien que le solstice d'hiver soit un instant ayant lieu le 21 ou 22 décembre à une heure de Temps Universel bien définie. Pour certains lieux la date du solstice d'hiver ne correspondra pas à la date du jour le plus court. Voir Equation du Temps (EoT) et Lever local/Coucher local.

sidereal time, sidereal day Temps sidéral, jour sidéral: voir temps (types de).

signes du zodiaque: voir Zodiaque.

Sirius: (the Dog star) the brightest star in the night sky, used by the Egyptians as a means of determining the beginning of the Nile floods. See heliacal rising.

skylight: light which reaches the observer from the general (blue) sky. It is sunlight which has undergone multiple scattering events with the molecules of the Earth's atmosphere (i.e. Rayleigh scattering) or with clouds or other aerosols in the atmosphere. High levels of skylight reduce the contrast of a shadow. It also tends to be polarised.

slant: see obliquity.

small circle (petit cercle de la sphère): un cercle à la surface de la sphère dont kle centre ne coïncide pas avec le centre de la sphère (et donc a toujours un plus petit diamètre).

solarium: terme latin pour cadran solaire. Il peut aussi être interprété comme "place ensolleillée".

solar compass: an instrument for direction finding which uses dialling principles. The most common are modified versions on an analemmatic dial with a vertical gnomon. Sometimes called an astro-compass, although these latter more properly use sightings of the fixed stars.

solar longitude: the ecliptic longitude of the Sun, it varies from 0º (at the vernal equinox) to 360º during the year. By Kepler's Second Law, the rate of change of the solar longitude is such that the Earth sweeps out equal areas on the ecliptic plane in equal times.

solar parallax: the difference between the Sun's altitude as observed from the Earth's surface and its true astronomical value from the centre of the Earth./

solar time: voir temps (types de).

solstices: (Eté ~, Hiver ~) littérallement, "Le soleil s'arrête". Dans l'hémisphère Nord, ils représentent le début de l'été (20 ou 21 juin) et le début de l'hiver (21 ou 22 déccembre). Ils sont habituellement identifiés (usually) comme étant le jour le plus long et le plus court, respectivement. Astronomiquement ils sont parfaitement définis comme étant les instants où la longitude écliptique du soleil vaut 90º ou 270º, respectivement, et correspondent aux valeurs extrêmes de declinaison. Voir Figure 1.

sous stylaire : projection du style perpendiculairement à la surface du cadran

South: one of the cardinal points of the compass, it is the direction opposite north, in the direction of the south celestial pole. It is also the direction of the Sun at local noon (in the northern hemisphere).

southing: another term for a southern transit.

South Pole: the location on the Earth's surface where it intersects the axis, and opposite the North Pole. It has a latitude of -90º.

spherical angle: the angle whose vertex is at the intersection of two great circles of the celestial sphere. Spherical trigonometry deals with spherical angles and triangles.

spherical triangle: the figure formed on the surface of a sphere by three intersecting great circles. The fundamental (or nautical) triangle is the special case of a spherical triangle on the celestial sphere with vertices at the zenith, North celestial pole and the Sun.

split noon: see noon gap.

standard time zone: [TZ] a geographical region which uses the same civil time. These are approximately regions between two lines of longitude, set 15º apart, and hence with 1 hour time difference between adjacent zones. The standard time for each zone is the mean solar time at the central or standard meridian for the zone. For the UK, which is in Zone 0, the standard meridian is the Prime Meridian at Greenwich, and the zone nominally extends from 7½º W to 7½º E. For political reasons, other time zones have their boundaries adjusted to follow country borders or other features. The zones were defined at the same international conference in 1884 that set Greenwich as the Prime meridian.

steradian: (pron. ster-ade-e-on) unit of solid angle. It is the central solid angle of a sphere subtended by a surface area equal to the square of its radius. The whole sphere supports an angle of 4 steradians around its centre.

stereography: (hence stereographic projection) a drawing method in which a sphere is projected from a point on its surface to a plane which is tangent to it. Its main property is that circles on the celestial sphere are projected as circles or straight lines on the plane. It is fundamental to the construction of planispheres and astrolabes as the rete is a stereographic projection. Its use is difficult in the construction of sundials due to the vast length of some of the radii required (although this can be overcome by calculating in cartesian coordinates and then converting). Its use was advocated by 17th century diallists.

string gnomon: a gnomon in the form of a flexible cord which is pulled tight when the dial, typically in diptych form, is opened.

style {stile}: la ligne d'espace qui génère le coin d'ombre utilisé pour indiquer le temps sur la face de lecture du cadran. Noter qu'un gnomon avec une épaisseur finie aura deux styles (un sur chacun des angles supérieurs) dont chacun sera utilisé une partie de la journée. Si le gnomon a la forme d'une longue tige le style sera la ligne virtuielle passant par le centre de la tige et on lit sur le cadran en estimant la position du le centre de l'ombre. Noter: cette moderne distinction entre gnomon et style n'est pas faite dans la littérature ancienne où à partir de 1577) le mot style était utilisé pour indiquer un gnomon polaire (un polos) ou plus rarement un noeud. D'où stylaire: relatif au style ou au gnomon d'un cadranl (utilisé pour la première fois en 1688). Voir Figure 1.

style height: [SH] of a polar style is the angle that the style makes with the sub-style line. Note that this is an unusual use of the word "height", and style angle could be regarded as a better term. For a style which is perpendicular to the dial plane, style height is simply the distance from its top to the foot. See Figure 1.

sub-nodus (point): the point on the dial plane that lies perpendicularly below (or behind for a vertical dial) a nodus. The distance from this point to the nodus is sometimes called the ortho-style distance.

sub-style angle: [SD] the angle that the sub-style makes with the noon line, measured positively clockwise (towards the p.m. hours for a south-facing vertical dial).

sub-style (line): the line lying in the dial plane which is perpendicularly below (or behind for a vertical dial) the style. See Figure 1.

sub-style triangle: the right angled triangle formed with the polar style as the hypotenuse, with the other sides lying along the sub-style and the ortho-style distance.

summer solstice; see solstices.

Sun: the star at the centre of our solar system. The mean distance to the Earth (designated the Astronomical Unit or AU) is 149.6 x 10⁶ km. It has a surface temperature of about 5800 º K. The solar spectral irradiance reaching the Earth's surface (at AM1 - air mass 1 - i.e. looking through a standard atmosphere with the Sun at the zenith) ranges from about 250 nm to 2000 nm, with the main peak at 490 nm. See semi-diameter for the apparent size of the Sun.

sun clock: see Dial types.

sun compass: see solar compass

sundial: an instrument for telling the time and/or date from the position of the Sun. More generally, it can give any function of the Sun's co-ordinates. See dial for the origins of the term, and Dial (types of) for types.

sunlight: light reaching the observer directly from the Sun. Contrast with skylight. Note that the Sun's rays reaching the Earth are always taken as parallel, but coming from an extended source (see semi-diameter).

sunrise, sunset: the first (last) appearance of the Sun above the horizon each day. This occurs when the sun's altitude reaches -0º 50'. Note that astronomers define the rising of an object as an altitude of 0º. The difference is due to the combined effects of the Sun's mean semi-diameter (16 arcmin) and atmospheric refraction (34 arcmin). See Equations for expressions to calculate sunrise and sunset.

sunshine recorder: a meteorological instrument for recording the hours in which the Sun shines. The most interesting type is the Campbell-Stokes ~, which uses a spherical lens to focus bright sunlight onto a paper chart, burning a track along it.

superior: refers to an event on the celestial sphere above the horizon. Opposite of inferior.

synodic: pertaining to the successive conjunctions of a planet (or moon) with the Sun.

tellurian: a demonstration model, similar to an orrery, but showing the Earth-Sun system, or the Earth-Sun-Moon system. This latter is sometimes referred to as a lunarium. Note: the tellurian is sometimes called a tellurium but this term is best avoided as it is the name of the 52nd element in the periodic table.

terminator: the edge of the shadow cast by a self-shadowing object, such as the edge of the illuminated part of the Moon.

terrella: from the Latin for "little globe". See globe dials.

tide(s): the divisions of a day used in the Anglo-Saxon period. The time from sunrise to sunset was divided into four tides or time periods. See Appendix II for the names of the tides. Lines showing the tides are found on Anglo-Saxon and some mass dials. Some dials also have lines denoting the half-tide. Note that this use of the word has no connection with the marine tides.

Apparent solar ~: the measure of time based on the diurnal motion of the true sun.

British Summer Time: [BST] civil time in the UK during the "summer", one hour ahead of GMT. Invented by William Willett and first introduced in 1916. A sundial showing BST in Petts Wood, near Chislehurst, Kent, is his memorial. BST usually begins on the last Sunday in March, and ends on the last Sunday in October. These dates are now co-ordinated with Summer Time in the rest of the EU.

civil ~: the legally-accepted time scale in a particular country or region. It is based on the standard time for that standard time zone, but may have fixed differences (eg BST). Measured in modern hours from the most recent midnight, with either a 24 hour or 2 x 12 hour format.

clock ~: simply the times shown by a clock, usually civil time. Hence the appendage "o'clock" to some times.

Daylight Saving Time: [DST] civil time during the summer in much of the USA (and some other countries) obtained by advancing clock time one hour from local standard time. Equivalent to BST in the UK.

dynamical ~: [or Terrestrial Dynamical Time, TDT] "scientific time" – it superseded ephemeris time in 1984, and is based on a uniform scale of time derived from atomic clocks (i.e. not subject to fluctuations in the Earth's rate of rotation). Now usually called international atomic time (TAI).

ephemeris ~: [ET] "scientific time" - used between 1960 and 1983, this uniform timescale was based on the ephemeris second, itself derived from the period of rotation of the Earth at a particular date. It was succeeded by dynamical time when the second was redefined in 1984.

French revolution ~: a decimal timescale (10 equal hours or decidays per day) devised in 1790 by the French Academy after the French Revolution. Each hour was divided into 100 millidays (of 86.4 seconds) and each milliday into 1000 microdays (0.0864 seconds each). The decimal timescale, which had been used previously in ancient Egypt and China, was never fully implemented and was quickly dropped, with the result that sundials so calibrated are extremely rare.

Greenwich Mean Time: [GMT] the basis for civil time standards worldwide, it is the time at Greenwich as given by the fictitious mean sun. It is derived from UT, but GMT is measured from midnight.

Local Apparent Time: [L.A.T. - the use of the full-stops is encouraged to avoid confusion with the common contraction of "latitude"] this is solar time, as derived from the real Sun at any particular location. It is the hour angle of the Sun + 12 hours. Some authors (non-UK) may refer to it a Local True Time.

local mean ~ {mean ~}: [LMT] this is solar time which has been corrected for the EoT but not for longitude, so it is still location specific. English towns used this form of time prior to the coming of national railways and the telegraph, e.g. Oxford time.

Mean Solar Time: the authoritative (by the National Physical Laboratory) definition is: a measure of time based conceptually on the diurnal motion of the fictitious mean Sun, under the assumption that the Earth's rate of rotation is constant.

railway ~: (or London time) a colloquial term used for Greenwich time as it began to replace local time with the introduction, in the mid-1800s, of railways and the resulting need for unified timetables.

sidereal ~: [, SDT] "astronomical or star time". This is timekeeping based on the sidereal day, and hence it runs ahead significantly with respect to solar-based time. Local sidereal time is equal to the hour angle of the first point of Aries and is, to a first approximation, sidereal time with a longitude correction.

solar ~: the same as Local Apparent Time.

Summer time: a generic term for BST, DST etc.

standard ~: [ST] is mean solar time at the central meridian of a given time zone.

universal ~ :[UT or UTC] this is the basis for terrestrial and civil timekeeping, and was adopted in January 1972. It is tied to the rotation of the Earth, and hence has to be periodically adjusted by the addition of leap seconds to account for the gradual slowing of the Earth, and the vagaries of its rotation. UT is by definition measured from the superior transit of the fictitious mean sun (i.e. mean noon at Greenwich), and hence is 12 hours behind GMT (although this difference only tends to be recognised by astronomical calculations). UT measurement is based on standard seconds. The version referred to as UTC (Universal Time, Co-ordinated) simply means the value averaged over a number of atomic clocks world-wide. In aviation, it is referred to as Z or zulu.

zonal solar time: sometimes used to denote solar time at a time zone meridian. Thus it is local apparent time with a longitude correction but without EoT. In the UK, it would be denoted Greenwich Solar Time.

time zone: see standard time zone.

torquetum: (pron. tor-kwet-um) an early (known to be before 1326 AD) astronomical instrument capable of fixing star positions and producing conversions between equatorial and ecliptical co-ordinates. Some forms may have been used to help delineate dials, and torquetum-style dials for solar and sidereal time were made in the late 17th century. Most famously, it features amongst the instruments in Holbein's 1533 painting "The Ambassadors" (National Gallery).

transit: the meridian passage of a celestial body. For the sun, this occurs when it is directly south of the observer. It can also refer to the time of this occurrence. Transits may be either superior or inferior.

transom: a crosspiece of fixed length, as on a cross-staff. Sometimes called a vane.

triangle (fundamental or nautical): see spherical triangle.

triens: an extended quadrant, with a 120º arc. It can usually tell the time in both equal and unequal hours.

trigon: in dialling, a mechanical aid to drawing lines of declination on dial plates. It consists of an instrument which is fitted to, and can swivel around, the nodus on a polar-pointing gnomon, and can be set at an angle equal to the sun's declination angle to the gnomon. Often used with an associated auxiliary dial. Trigon is also an archaic term for a triangle. From the Greek "trigonon" or three-cornered.

triptych: (pron. trip-tich) literally "three leaves", it refers to a set or compendium of three instruments, including at least one dial. Other instruments often include a compass and perpetual calendar.

tropical year: see year.

tropics: geographical bands of the Earth's surface, extending from the equator to latitude 23º 26' N (tropic of Cancer) or to 23º 26' S (tropic of Capricorn). The terms are also used to refer to these specific latitudes. Note that they represent the extremes of the region where the Sun can reach the zenith when the sun's declination is at its extreme values.

twilight: the interval after sunset or before sunrise when the Sun illuminates the upper atmosphere and hence it is not completely dark. It is determined by the sun's altitude falling within a given range, as follows:

civil twilight: -0º 50' and -6º

nautical twilight: -6º and -12º

astronomical twilight: -12º and -18º

These values reflect the need for decreasing light levels for various activities.

umbra: the central, darkest portion of a shadow, i.e. the region which does not receive direct rays from any part of a distributed light source (e.g. the Sun).

umbra recta: Latin for "upright shadow", it is the label often found on the cotangent scale of altitudes < 45º on a shadow square.

umbra versa: Latin for "reverse shadow", it is the label often found on the tangent scale of altitudes > 45º on a shadow square.

Universal Time (UT): see time (types of).

vernal {spring} equinox: see equinoxes.

verdigris: (pron. ver-de-gree) the green patination found on weathered brass and copper.

vernier: a small moveable scale for obtaining fractional parts of the subdivisions of a fixed scale. Invented by Pierre Vernier in 1631 (published Brussels, 1638). For circular scales, a Type A vernier has a central zero. After about 1780, sextants commonly had a Type B vernier with the zero on the right of the scale. European instruments often have the very similar nonius.

vertical angle: the angle from the zenith to the horarius circle passing through the sun, measured along the prime vertical (the E-W vertical circle). It is one of the ptolematic co-ordinates.

vertical plane: see principal plane.

Vitruve : architecte romain du 1er siècle avant J.C. On suppose qu'il participa à la guerre de Gaule avec Jules César pour lequel il aurait construit machines de guerre, fortifications … Dans son ouvrage "de architectura" dédié à Auguste il traite des cadrans solaires (Livre IX)

volvelle: (pron. vol-vel) an old device consisting of one or more movable circles surrounded by other graduated or figured circles. It is used for showing the rising and setting times of the Sun and Moon, the state of the (marine) tides etc. A ~ has sometimes been included around the rod-gnomon of equiangular dials.

wedging out: (or canting out) placing wedges between a dial plate and its mounting surface. (a) for a horizontal dial: to compensate for moving a dial to a different latitude from the one it was designed for, (b) for a vertical dial: to ensure that it faces a cardinal point of the compass (usually S).

West: the point on the horizon 90º (measured anti-clockwise) from the north point. The Sun appears to set at the west point at the equinoxes.

winter solstice: see solstices.

year: the time that it takes the Earth to make one orbit of the sun. The tropical year is the interval in which the mean ecliptic longitude of the Sun increases by 360º. This is the version of the year used in normal calendars and has a length of 365.24219 days. Other versions of a year (e.g. the sidereal, anomalistic and Julian years) have differences of about a hundredth of a day to this figure.

Yule: an ancient Celtic festival held on or around the 21st of December, celebrating the winter solstice. It is one of the cross-quarter days, and has now become synonymous with Christmas.

zenith: (astronomical) the point on the celestial sphere vertically above the observer. In everyday parlance, ~ usually implies the highest point. This gives rise to confusion as the mid-day Sun is often described as its ~, irrespective of the latitude.

zenith distance (or zenith angle): [z] the complement of the altitude i.e. (90º - a)

zodiac: an imaginary band, centred on the ecliptic, across the celestial sphere and about 16º wide, in which the Sun, Moon and the planets Mercury, Venus, Mars, Jupiter and Saturn are always located. The band is divided in 12 intervals of 30º , each named (the Signs of the Zodiac) after the constellation of stars which it contains. The sun's ecliptic longitude may be measured against this scale. The names (and/or signs) of the constellations are given in Appendix I and are often used in sundials, instead of the date, to specify declination lines etc. Because of the effects of precession over the period of 2,300 years since the constellations were first named, the signs of the zodiac have slipped by a whole sign, i.e. at the vernal equinox (defined as the first point of Aries), the Sun is actually in the constellation of Pisces.

Zonwvlak: a major suite of computer programs for calculating sundial lines. Written by Fer de Vries (Netherlands) it is available at www/iaehv.nl/users/ferdv. The name is short for zonnewijzer (sundial) vlak (plane).