Why Is a Sundial Wrong? Two Corrections Between Shadow and Clock
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A correctly built sundial disagrees with a clock by up to a quarter of an hour, and the disagreement changes through the year in a fixed pattern. Two separate corrections account for it, and both are consequences of how Earth moves.
What the shadow actually shows
A sundial reads apparent solar time at the place where it stands, which is the time told by the actual position of the sun. A clock reads something different, being a uniform time for a whole zone, and the two differ for two independent reasons. The first is longitude, since the sun crosses the meridian at different moments at different places within the same zone and the clock does not care where in the zone you are. The second is that the sun itself is not a uniform timekeeper, because the length of a solar day varies through the year, so even a place exactly on the standard meridian will find the sundial ahead or behind the clock on most days. Adding daylight saving where it applies gives a third and entirely artificial offset.
The two real corrections
The difference between shadow and clock is built from parts that behave differently:
- •A longitude correction, fixed for a given location, of four minutes for each degree from the zone meridian
- •A varying correction from the sun's own irregularity, reaching about sixteen minutes in one direction and fourteen in the other
- •The varying part crosses zero four times a year and is different for each date
- •A daylight saving offset of a whole hour where and when it is in force
- •No correction at all for the observer's latitude, which affects the dial's construction rather than its reading
- •The combined correction is frequently engraved on the dial as a table or a figure-of-eight curve
Why the sun runs fast and slow
The varying correction has two causes that combine. The orbit is elliptical rather than circular, so Earth moves faster when nearer the sun in early January and slower when further away in early July, which makes the apparent motion of the sun along the sky faster at one time of year and slower at another. Separately, the axis is tilted, so the sun's apparent path is inclined to the celestial equator, and the component of its motion that actually advances the time of day varies through the year even at constant speed, being largest at the solstices and smallest at the equinoxes. The two effects have different periods, one annual and one half-yearly, and adding them produces a curve with two unequal maxima and two unequal minima, which is the familiar shape of the correction table.
Building one that reads correctly
A dial that tells the right time has to be built for its latitude, which is why a souvenir bought elsewhere is decorative rather than functional. The shadow-casting edge must point at the celestial pole, meaning it is set at an angle from the horizontal equal to the local latitude and aligned with true north rather than magnetic north, and getting either wrong throws the reading off badly. Given that, the hour lines on a horizontal dial are not evenly spaced and must be calculated for the latitude, while on a dial whose face is parallel to the equator they are evenly spaced at fifteen degrees, which is why that design is the simplest to make and the least common. A vertical dial on a wall needs the wall's orientation taken into account as well. Only after all that does the reading need the corrections at all.
The figure of eight in the sky
Photographing the sun from the same place at the same clock time on many days through a year produces a closed figure-of-eight path, which is the same information drawn geometrically. The vertical extent of the figure comes from the changing declination of the sun through the seasons, and the horizontal width comes from the correction, with the sun sitting east or west of where uniform time would place it. The asymmetry between the two lobes, with one larger than the other, reflects the unequal contributions of the two causes. Producing such an image requires a fixed camera and about a year of patience with clear skies, and the results are a recognisable genre of astronomical photography. The same figure is printed on old globes, where it served as a lookup table for converting between sundial and clock time.
The takeaway
A dial reads apparent solar time at its own location, while a clock reads uniform time for a whole zone, which produces a fixed longitude offset of four minutes per degree. A separate varying correction of up to about sixteen minutes comes from the elliptical orbit and the axial tilt combined. Photographing the sun at the same clock time through a year traces the same correction as a figure of eight.