page thirty

The Gnomon

Twenty-nine rooms, and every one of them took the time from the clock in the corner of your screen. This one takes it from the sun, and then has to argue with the clock about it. The day's number picks a town, puts it on a latitude, and sets a sundial in it with the hour lines cut for that latitude and no other. The sun that lights it is the real sun for the real date. Read the shadow. Then work out why the clock on the town hall disagrees with it, and by how much.

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The dial

Seen from above, with north at the top. The bar is the gnomon, and the shadow of its sloping edge falls on the hour line for the sun's time, the time a sundial keeps. The hour lines are not evenly spaced; they bunch around noon by exactly as much as this latitude asks. The dot at the tip of the shadow walks the green line today. The dashed lines are the tip's path at midsummer, the equinoxes and midwinter. The gold figure of eight is where it falls at noon by the clock, through the year.

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Town hall clock

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Mode
Town
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P lets the day run, and the left and right arrow keys walk to other days. Every day is a different town, and the sun moves on with the date.

Why the sun keeps bad time

The sun is not a good clock. Earth's orbit is an ellipse, so it moves faster in January than in July, and its axis is tilted, so the sun's eastward drift along the sky is foreshortened near the equinoxes. Put the two together and a sundial runs up to sixteen minutes ahead of a clock in early November and fourteen behind in February. That difference is the equation of time. Dials used to carry a table of it engraved on the plate.

Date
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Latitude
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Longitude
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Sun's declination
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Equation of time
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Sun due south
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Sunrise – sunset
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Summer time
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What is real here and what is not

The sun, the geometry and the arithmetic are real. The town is not, and nor is its dial. Nobody should go looking for either.

  1. 01

    The hour lines are real

    A horizontal dial's style has to point at the celestial pole, so it leans at the latitude. The hour line for an hour angle H then sits at an angle θ from the noon line with tan θ = sin(latitude) × tan H. That is why a dial is only right in one latitude, and why the lines crowd round noon. Every line and every ten-minute tick on this dial comes from that formula.

  2. 02

    The sun is real

    The sun's declination and the equation of time come from the NOAA solar equations for the real date, good to a few seconds, and the shadow is cast by projecting the tip of the gnomon along the sun's direction onto the plate. The curves the tip draws through the year are real conic sections, and the figure of eight is the analemma a dial maker would cut for a noon mark.

  3. 03

    The corrections are real

    A dial keeps local sun time. The clock keeps the mean time of a meridian that is a whole number of hours from Greenwich, so a town west of it sees the sun late, four minutes for every degree. Add the equation of time, then the hour for summer time, which here follows the European rule of the last Sundays in March and October. That sum is the whole argument between dial and clock.

  4. 04

    The mottos are real

    Horas non numero nisi serenas, Umbra sumus, Sine sole sileo, Ultima latet: all of them are cut into real dials across Europe, many of them hundreds of times over. Sundial mottos have mostly been about death, which you might expect of an instrument that goes quiet every evening.

  5. 05

    The rest is invented

    The town, its coordinates, the dial's maker and the year it was made are all the day's number. Every town sits in the northern hemisphere. Refraction is left out of the shadow, which only matters when the sun is very low. A real dial is also only as good as the mason who levelled it and turned it to true north, and that is usually a few minutes' worth of error that no table corrects.

Thirty rooms, and one number doing all the work. Today it builds a town, puts a stone in its square with a bar of bronze on top, and then lets the sun, which nobody can seed, do the rest.