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The Gnomon - Sundial

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Author Topic: The Gnomon - Sundial  (Read 14732 times)
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« Reply #15 on: December 16, 2007, 08:11:34 am »

house: (astrological) a segment of the celestial sphere. Several methods of dividing the sphere into segments exist, the most common of which produce the signs of the zodiac, and the Regiomontanus houses.

hyperbola: a conic section, its most common use in dialling is the shape of the declination lines on a dial.
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« Reply #16 on: December 16, 2007, 08:12:53 am »


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 = 0 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 < 90; whilst i > 90 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 180 line of longitude, through which the date alters by one day (positively if travelling from W to E). Variations from the 180 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-tn: noon shadow + 2 x gnomon height

isogonals: lines of equal magnetic deviation plotted on some navigational charts.
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« Reply #17 on: December 16, 2007, 08:13:58 am »


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.
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« Reply #18 on: December 16, 2007, 08:15:09 am »


kaml: 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:

Planets travel in elliptical (rather than circular or epicyclic) orbits, with the Sun at one of the foci.
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)
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".
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« Reply #19 on: December 16, 2007, 08:16:17 am »


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  = -90). 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 Nio 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 15 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 1 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.
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« Reply #20 on: December 16, 2007, 08:17:25 am »


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 3 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 1 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 180). 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 = 360. 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 5, 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 5 8' 43". Note: "moon", without an initial capital letter, is sometimes used to refer to moons of planets other than the Earth.

moondial: see Dials (types of).

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: a sentence, phrase or verse inscribed on a dial expressing an appropriate sentiment. Mottoes started appearing on dials in the late 16th century but were particularly popular in the 19th century.
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« Reply #21 on: December 16, 2007, 08:18:40 am »


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 Nnes.

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 +90 . 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.
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« Reply #22 on: December 16, 2007, 08:19:43 am »


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 23 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 90 and less than 180.

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.
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« Reply #23 on: December 16, 2007, 08:20:49 am »


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 29 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 90 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 1, 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 (90 - ) 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 +90 (N) and 90 (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.

The first measurement of precession was made by Hipparchus in 129 BC.

precision (of a dial): a combination of the resolution and accuracy of a dial, it gives a measure of how exactly (and correctly) it indicates any time.

Prime meridian: the meridian line defined as the origin for longitudes. Now synonymous with the Greenwich meridian, before 1884 various countries defined their own origin. The early Greeks used Rhodes or Alexandria. Ptolemy used the Fortunate Islands, assumed to be Ferro in the Canary Islands by scholars in the Renaissance. Nuremberg was common for dials made there, and in relatively modern times many maritime nations had their own locations; Paris in particular continued to be used even post-1884. Note that the 0 longitude line used by the GPS system is actually a mean value, periodically recalculated to allow for tectonic drift etc. and currently lies approximately 38 m (80 feet) east of the Greenwich line.

Prime vertical: the vertical circle perpendicular to the meridian. It passes through the E and W points.

Primum Mobile: (pron. pree-mum mo-be-lay) an old term for the supposed crystal sphere carrying the stars in their orbits around the earth.

principal plane {or vertical plane}: the plane obtained by varying the Sun's altitude whilst its azimuth is constant. Perpendicular to the almucantar.

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.

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.
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« Reply #24 on: December 16, 2007, 08:21:50 am »


Qibla line: sometimes found on Arabic dials, it is an azimuth line on the dial plate starting at the centre and pointing to Mecca.

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.
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« Reply #25 on: December 16, 2007, 08:23:00 am »


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 = 360or 1 rad  57.3.

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 180.

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 0 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 0 to 360.

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..
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« Reply #26 on: December 16, 2007, 08:24:21 am »


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.

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

seasons: the seasons are defined astronomically as follows:

Spring: from the vernal equinox to the summer solstice

Summer: from the summer solstice to the autumnal equinox

Autumn: from the autumnal equinox to the winter solstice

Winter: from the winter solstice to the vernal equinox

In popular parlance, the seasons of the northern hemisphere comprise the following months:

Spring    March, April, May

Summer    June, July, August

Autumn    September, October, November

Winter    December, January, February
The signs of the zodiac for the seasons are given in 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 .

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: a square (or rectangular) scale often found on quadrants and astrolabes which allows the tangent or cotangent of the altitude of a celestial body to be found.

shortest day: a term in common parlance, defined as the day of the year with the least (astronomical) sunrise to sunset period. It is normally used synonymously with the winter 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.

sidereal time, sidereal day: see time (types of).

signs of the zodiac: see Zodiac.

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: a circle on the surface of a sphere whose centre does not coincide with that of the sphere (and hence it must always have a smaller diameter).

solarium: Latin for sundial. Beware, it can also be interpreted as "sunning place".

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 0 (at the vernal equinox) to 360 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: see time(types of).

solstices: (Summer ~, Winter ~) literally, "Sun stands still". In the Northern hemisphere, they represent the beginning of summer (on or around 21 June) and the beginning of winter (on or around 21 December). They are (usually) the same as the longest and shortest days, respectively. Astronomically, they are the occasions when the Sun's ecliptic longitude is 90 or 270, respectively, and correspond to the extreme values of declination. See Figure 1.

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 -90.

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 15 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 7 W to 7 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}: the line in space which generates the shadow edge used to indicate the time on the dial plate. Note that a gnomon with finite thickness will have two styles (one along each of the upper edges) which will each be operational for parts of every day. If the gnomon is in the form of a long rod, the style will be the virtual line running along the centre of the rod and the dial is read by estimating the centre of the shadow. Note: this modern distinction between gnomon and style is not the one found in earlier literature where (from 1577) the word style was used to indicate a polar-pointing gnomon (a polos) or, more rarely, a nodus. Hence stylar: pertaining to the style or gnomon of a dial (first used 1688). See 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 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 -0 50'. Note that astronomers define the rising of an object as an altitude of 0. 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.
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« Reply #27 on: December 16, 2007, 08:25:21 am »


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.
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« Reply #28 on: December 16, 2007, 08:26:20 am »

Time, (types of):

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.

- End of Time (types of) -
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« Reply #29 on: December 16, 2007, 08:28:19 am »

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 120 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 23 26' N (tropic of Cancer) or to 23 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: -0 50' and -6

nautical twilight: -6 and -12

astronomical twilight: -12 and -18
These values reflect the need for decreasing light levels for various activities.
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