Dialing scales

Dialing scales are used to lay out the face of a sundial geometrically. They were proposed by Samuel Foster in 1638, and produced by George Serle and Anthony Thompson in 1658 on a ruler. There are two scales: the latitude scale and the hour scale. They can be used to draw all gnomonic dials – and reverse engineer existing dials to discover their original intended location.[1]


Dialing scales were first discussed by Samuel Foster in 1638. P. Pierre Bobynet, a Jesuit drew a scale in his book L'horographie ingenieuse contenant des Connoissances, & Curiositez Agréables dans la composition des Cadrans, in 1647.[2] It was however George Serles 1657 book, Dialling Universal, printed by R & W Leybourn that brought them to popular attention. These scales remained virtually unchanged for 250 years. E. C. Middleton, who had been engraving dialling scales from about 1895, supplied dialling scales accompanied by a typewritten instruction book from Birmingham in 1913– these were the scales calculated by Serle. The North American Sundial Society has printed facsimiles of both the Serle and Middleton books. The Middleton dial appeared without explanation in the 1994 Encyclopedia de Diderot et Alembert (French).[3] Further work has done on these rulers by F.W. Cousins, and by Fred W Sawyer from 1997–2009. [4] [5] [6]


The traditional scales (Foster Serle scales) are drawn on a ruler. The hour scale shows and the latitude scale shows . [7] The graduation of these rulers is independent of latitude, making them suitable for drawing all dials. The Foster Serle dial is randomly set for a value of 45°, and is more precise for latitudes below 45°. It is thus a special case in an infinite set of rulers.


A right-angle is drawn on the dial-face and the latitude scale is laid against the x-axis. The target latitude point is marked across on to the dial face. The hour scale is placed from this point to the noon line (conventionally, the zero point is on the noon line). Each of the hour points is copied over to the dial face, and this procedure is repeated, giving the hours both sides of noon. A straight edge is used to connect these points to the origin, thus drawing the hour lines for that location. A vertical line from the target latitude point, and a horizontal line through the noon point will bisect at the three-hour (9am–3pm) marker.

Serle scales method (1657)-(1)
Serle scales method (1657)-(2)
Serle scales method (1657)-(full)
Serle scales method (1657)-(result)

In the northern hemisphere the hours run clockwise. Symmetries about the noon line, the six-hour line and the three-hour marker can be detected – and these can be used to add additional lines.

The style will be at the same angle as the latitude. It can be simply drawn using the Line of Chords scale on the dialling ruler. A set of compasses is extended to the 60° point on the line of chords. A radius is drawn from the substyle. The compasses are set to the target latitude on the line of chords scale. This measurement is transferred along the radius. That angle represents the style height.

They can be used to draw all gnomonic dials – and reverse engineer existing dials to discover their original intended location. [1] [8]


  1. ^ a b Sawyer, Fred (1995). "Serle's Dialing Scales". Compendium. Glastonbury, CT,USA: North American Sundial Society. 2 (2): 5.
  2. ^ Bouchard, Andre E (1999). "Quelques exemples de règles à cadran". Gnomoniste. 42 Ave de la Brunante, Outremont, Québec, H3T 1R4, Canada: La Commission des Cadrans solaires du Québec. VI (2): 21.
  3. ^ Guicheteau, Claude (1999). "Des décourvertes en décourvertes". Gnomoniste. 42 Ave de la Brunante,Outremont, Québec, H3T 1R4, Canada: La Commission des Cadrans solaires du Québec. VI (2): 21.
  4. ^ Sawyer, Fred (1997). "Towards a general theory of Dialing Scales". Compendium. Glastonbury, CT,USA: North American Sundial Society. 4 (4): 14–20.
  5. ^ Sawyer, Fred (1998). "Vertical Decliner by Dialing Scales an Schema". Compendium. Glastonbury, CT,USA: North American Sundial Society. 5 (1): 5.
  6. ^ Sawyer, Fred (2009). "Differential Dialing Scales". Compendium. Glastonbury, CT,USA: North American Sundial Society. 16 (3): 36–38.
  7. ^ Sawyer, Fred (2003). "A Note on the origin of Dialing Scales". Compendium. Glastonbury, CT,USA: North American Sundial Society. 10 (1): 21.
  8. ^ Wall, Roderick (2007). "How a Sundial Works And Using Serle's Dialing to make your own Horizontal Sundial". Compendium. Glastonbury, CT,USA: North American Sundial Society. 14 (3): Digital Bonus.

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An hourglass (or sandglass, sand timer, sand clock or egg timer) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material (historically sand) from the upper bulb to the lower one. Factors affecting the time it measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty. Depictions of hourglasses in art survive in large numbers from antiquity to the present day, as a symbol for the passage of time. These were especially common sculpted as epitaphs on tombstones or other monuments, also in the form of the winged hourglass, a literal depiction of the well-known Latin epitaph tempus fugit ("time flies").

Outline of trigonometry

Trigonometry is a branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.

Scale of chords

A scale of chords may be used to set or read an angle in the absence of a protractor. To draw an angle, compasses describe an arc from origin with a radius taken from the 60 mark. The required angle is copied from the scale by the compasses, and an arc of this radius drawn from the sixty mark so it intersects the first arc. The line drawn from this point to the origin will be at the target angle.

Schema for horizontal dials

A schema for horizontal dials is a set of instructions used to construct horizontal sundials using compass and straightedge construction techniques, which were widely used in Europe from the late fifteenth century to the late nineteenth century. The common horizontal sundial is a geometric projection of an equatorial sundial onto a horizontal plane.

The special properties of the polar-pointing gnomon (axial gnomon) were first known to the Moorish astronomer Abdul Hassan Ali in the early thirteenth century and this led the way to the dial-plates, with which we are familiar, dial plates where the style and hour lines have a common root.

Through the centuries artisans have used different methods to markup the hour lines sundials using the methods that were familiar to them, in addition the topic has fascinated mathematicians and become a topic of study. Graphical projection was once commonly taught, though this has been superseded by trigonometry, logarithms, sliderules and computers which made arithmetical calculations increasingly trivial/ Graphical projection was once the mainstream method for laying out a sundial but has been sidelined and is now only of academic interest.

The first known document in English describing a schema for graphical projection was published in Scotland in 1440, leading to a series of distinct schema for horizontal dials each with characteristics that suited the target latitude and construction method of the time.

Term (time)

A term is a period of duration, time or occurrence, in relation to an event. To differentiate an interval or duration, common phrases are used to distinguish the observance of length are near-term or short-term, medium-term or mid-term and long-term.

It is also used as part of a calendar year, especially one of the three parts of an academic term and working year in the United Kingdom: Michaelmas term, Hilary term / Lent term or Trinity term / Easter term, the equivalent to the American semester. In America there is a midterm election held in the middle of the four-year presidential term, there are also academic midterm exams.

In economics, it is the period required for economic agents to reallocate resources, and generally reestablish equilibrium. The actual length of this period, usually numbered in years or decades, varies widely depending on circumstantial context. During the long term, all factors are variable.

In finance or financial operations of borrowing and investing, what is considered long-term is usually above 3 years, with medium-term usually between 1 and 3 years and short-term usually under 1 year. It is also used in some countries to indicate a fixed term investment such as a term deposit.

In law, the term of a contract is the duration for which it is to remain in effect (not to be confused with the meaning of "term" that denotes any provision of a contract). A fixed-term contract is one concluded for a pre-defined time.

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