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The dial is designed to tell local apparent time so the longitude is not important.
That instant is local apparent noon: 12:00 local apparent time.
The difference between local mean time and local apparent time is the equation of time.
Since local apparent time could be determined with some ease, the problem centred on finding a means of determining the time at a known place.
For example, at 10:30 AM local apparent time the hour angle is -22.5 (15 per hour times 1.5 hours before noon).
This is a precise sundial which tells not only local apparent time but also local mean time using a scale on it.
Nevertheless, up to the Second World War, the old practice of keeping local apparent time prevailed on many independent merchant ships.
It is a fine example of a precision sundial telling local apparent time with a scale to convert this to local mean time.
Time indicated by the sun, referred to as local apparent time, differs by about one minute for every 12 miles east or west one travels.
Local mean time is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude.
When the sun has covered exactly 15 degrees (1/24 of a circle, both angles being measured in a plane perpendicular to the earth's axis), local apparent time is 13:00 exactly; after 15 more degrees it will be 14:00 exactly.
Having found the (absolute) Greenwich time, the navigator either compares it with the observed local apparent time (a separate observation) to find longitude or compares it with the Greenwich time on a chronometer if one is available.
Prior to 1920, all ships kept local apparent time on the high seas by setting their clocks at night or at the morning sight so that, given the ship's speed and direction, it would be 12 o'clock when the sun crossed the ship's meridian.