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 special properties of the polar-pointing gnomon (axial gnomon) were first known to the Moorish astronomer Abdul Hassan Ali in the early thirteenth century[1] 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.
Graphical projection was once commonly taught, though this has been superseded by trigonometry, logarithms, sliderules and computers which made arithmetical calculations increasingly trivial/ Graphical projection was once the mainstream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.
The art of sundial design is to produce a dial that accurately displays local time.
Modern dialling started in the tenth century when Arab astronomers made the great discovery that a gnomon parallel to the Earth's axis will produce sundials whose hour lines show equal hours or legal hours on any day of the year: the dial of Ibn al-Shatir in the Umayyad Mosque in Damascus is the oldest dial of this type.
If the latitude is known the dial plate can be laid out using geometrical construction techniques which rely on projection geometry, or by calculation using the known formulas and trigonometric tables usually using logarithms, or slide rules or more recently computers or mobile phones.
A sundial schema uses a compass and a straight edge to firstly to derive the essential angles for that latitude, then to use this to draw the hourlines on the dial plate.
His book which describes this method was De gnomonum umbrarumque solarium usu published in 1574.
Two construction are made: a parallel horizontal line that defines the tan h distances, and a gnomonic polar line GT which represents sin φ. Benedetti included instructions for drawing a point gnomon so unequal hours could be plotted.
It views the horizontal and the perpendicular plane to the polar axis as two rectangles hinged around the top edge of both dials.
[7] [5] The Jesuit Mario Bettini penned a method which was posthumously published in the book Recreationum Mathematicarum Apiaria Novissima 1660.
His description relies heavily on the term line of chords, for which a modern diallist substitutes a protractor.
The line of chords was a scale found on the sector which was used in conjunction with a set of dividers or compasses.
[e] This method requires a far smaller piece of paper,[5] a great advantage for higher latitudes.
