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How to set up a horizontal sundial
A horizontal sundial consists of the dial plate, marked off in hours, and the
gnomon which sits on the noon line and projects out from the dial
In order to tell the correct local time the gnomon must be parallel with the earths axis, or, in other words, that it should point towards the celestial pole. In the northern hemisphere, this means, for practical purposes, that the gnomon should point at the Pole Star. One should first check whether or not the sundial is correctly made for the place at which it is to be set up. If it is not, the base plate of the dial must be corrected so that the gnomon is pointing correctly true north, towards the celestial pole.
Finding the direction of true NorthVarious methods are suggested in the literature, and are summarised here, with references to published sources if you need them
Remember that the sun travels 15º westwards in one hour, and thus travels 1º westwards every four minutes. (In the latitude of London, this is equivalent to 950 feet per second). The time on your watch must be corrected for this. For example, at Lowestoft (which is the easternmost point of England at 1º45E, local noon is exactly 7 minutes earlier than noon in Greenwich. Penzance in the far West of England is at 5º33W, and local noon there is 22 minutes and 12 seconds later than at Greenwich.
Remember too that the sun appears to be fast or slow compared to watches by an amount discussed under the Equation of Time The sun is "fast" between 16 April and 14 June, and again between 2 September and Christmas and "slow" at other times of year. "Fast" means that, if you are on the standard meridian for your time zone, the sun will be directly overhead ("sun noon") not at 12:00:00 by your watch, but a few minutes earlier. When you are setting up your horizontal sundial, you want to know the time the sun is directly overhead. So you mentally add the Equation of Time to your watch time, or advance your watch by the amount of the Equation of Time so that, at the instant when your watch says 12:00:00, everyone else's watches will be saying it is actually a few minutes earlier than that, and it will indeed be "sun noon" The same thing, of course, applies if you are not on the standard meridian for your time zone, but you have already taken account of this with the calculation in the preceding paragraph.
First, measure the angle of the gnomon with a protractor.
Second, you can if you wish cross-check this measurement and check that the hour lines have been laid out correctly, by "back-calculating the gnomon angle from the angles of the hour lines. (The book by Waugh gives an example of this calculation on p.48, and also a table showing the correct angles of the hour lines for each degree of latitude. For example, the angle of the 9am and 3pm hour lines from the noon line is 26º24 at 30ºN, 29º50 at 35ºN, 32º44 at 40ºN, 35º16 at 45ºN, 37º27 at 50ºN, and 39º20 at 55ºN.)
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