Resources / Celestial timing
The Sundial
A garden dial drawn for the place you give it. The latitude sets the angle of every hour line and the height of the style; the Sun's place in the sky at this moment throws the shadow. The dial reads the Sun's own time, and the page says how far that stands from your clock today and why.
Below the dial is its layout for your latitude, angle by angle, for anyone who wants to cut one in wood or stone.
Setting the dial for your time and place
The tradition
A stick and its shadow is the oldest clock there is. Herodotus says the Greeks learned the gnomon, and the twelve parts of the day, from the Babylonians; Vitruvius, writing for Roman builders, gives a whole book of his Architecture to dials and names the kinds then in use and the men said to have devised them. Those ancient dials read the tip of a shadow against a net of lines, and their hours were the unequal ones: twelve from sunrise to sunset, long in summer and short in winter.
The garden dial is a later thing. Its style, the edge that throws the shadow, is not upright but aimed at the pole of the sky, parallel to the Earth's axis. Then the whole edge of the shadow, not only its tip, falls along one line at a given hour on every day of the year, and the hours it marks are equal. The oldest dial of this kind still known is usually given as the one Ibn al-Shāṭir made for the Umayyad Mosque in Damascus in 1371; from the fifteenth century it spread through Europe with the mechanical clock, which kept the same equal hours and was set by it.
A dial tells the Sun's own time, and the Sun is not a steady clock. Ptolemy already treats the unevenness of solar days in the Almagest. Once pendulum clocks ran more evenly than the Sun, tables of the equation of time were printed so that a clock could be set from a dial; and once railways and telegraphs needed one time for many towns, clocks were set to the meridian of a zone and no longer to the town's own. Both differences are what this page works out.
Reading the instrument
- The plate is seen from above with north at the top. The gold stroke along the noon line is the style, and its foot is the dial's centre. Every hour line starts there. The dark wedge is the shadow of the gnomon; the edge of it that runs from the centre is the one that tells the time, and the ring where it crosses the numerals is the reading.
- The lines are drawn for the latitude you give: each stands from the noon line at the angle whose tangent is the sine of the latitude times the tangent of fifteen degrees for each hour from noon. Change the latitude and the fan of lines opens or closes; south of the equator the style leans south and the numerals run the other way round. A dial offers only the hours at which the Sun can be up at that place on some day of the year.
- The reading above the dial is local apparent solar time, taken from the Sun's hour angle at your longitude. The panel beside it splits the gap between that and your clock in two: the place's part, four minutes for every degree between you and the meridian your zone keeps, and the Sun's part, the equation of time.
- The table under the dial is a maker's layout: the angle of each hour line and of the style for your latitude, and how far a compass needle stands from true north where you are.
Where it descends from
- Herodotus, Histories 2.109
- The gnomon, the polos and the twelve parts of the day, which he says came to the Greeks from Babylon.
- Vitruvius, De Architectura, book IX
- The analemma from which dials were drawn, and the kinds of dial known to the Romans, with their reputed inventors.
- Ptolemy, Almagest III.9
- The inequality of solar days: the ancient account of what is now called the equation of time.
- Albert E. Waugh, Sundials: Their Theory and Construction (1973)
- The layout of the horizontal dial used here: tan θ = sin φ × tan H.
- Jean Meeus, Astronomical Algorithms (2nd ed., 1998)
- The Sun's place, from the VSOP87 series, sidereal time and refraction, from which the shadow and the equation of time are computed.
- World Magnetic Model 2025
- NOAA NCEI and the British Geological Survey, public domain: how far a compass needle stands from true north.
What this does not claim
The dial is drawn for a level plate, a style aimed exactly at the pole and a noon line on true north. The Sun's place is computed to a few seconds of arc, so the reading is good to about a second of time, far finer than a real shadow: the Sun's disc is half a degree wide, the shadow's edge is soft, and a real dial read to the minute is a good one. A dial set a degree off north or out of level is wrong by minutes. Near sunrise and sunset the air bends the light, and the shadow drawn there follows the Sun as it is seen under ordinary air. The zone and its summer time come from your browser.
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