Setting 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 plate.
The 3 essential things to get right are:
that the angle between the gnomon and the dial plate is the same as your latititude (see below if it is not)
that the top of the plinth is horizontal, as accurately as you can get it
that the gnomon is pointing to true North (not magneitc North)
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 North
Various methods are suggested in the literature, and are summarised here, with references to published sources if you need them.
Method 1 - Use a compass
This is not very accurate, but it will do for a small garden sundial.Remember that the compass points to magnetic north, and a correction must be made for magnetic deviation. (Magnetic deviation at Greenwich in the UK was 3º58 W, and decreasing by 0º08 annually, but in some areas of the world it is much higher, and there are also much more local variations)
Method 2 - Mark a shadow at the exact time of local noon.
The shadow must be cast by a true vertical object. You can use a plumb line, a pole aligned vertically with a spirit level, or a vertical corner of a building. You may need to experiment to get a good shadow, and to find a reliable method of marking the shadow at the instant of local noon.
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.
Method 3 - Use the method of equal altitudes
This requires a reliably sunny day, and an accurately level board with a true vertical nail or stick. In one variation, concentric circles are drawn around the base of the vertical stick. The position of the tip of the shadow is noted whenever it just touches each of the circles in the morning hours and in the evening hours. If one is lucky there will be two marks on the same circle. Join them with a line. Bisect this line, and draw a line from the bisection point to the base of the stick - this will be a true North- South line.
An alternative is to mark out points on the track of the tip of the shadow first, and then to connect them with a line. Then draw a circle to give the greatest possible distance between the two intersection points, and as before bisect the line, and draw a line from the bisection point to the base of the stick - this will be a true North-South line.
Checking and correcting the gnomon angle
Checking the angle of the gnomon
Since horizontal sundials are often mass-produced, they have to be made for just one latitude. Many are made in Birmingham, where the latitude is around 52½ deg.N, so the angle between the gnomon and the dial plate is also 52½ Quite often, people bring back a sundial when they have been on holiday, so the angle may be very different. For example, a sundial made for the south of Spain will have an angle around 37 deg. and will not tell the correct time if it is set up with the dial plate horizontal in Southern England where the latitude is 51 deg. Fortunately, this can be compensated for.
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.)
Compensating for an incorrect gnomon angle
Third, provide a wedge to bring the gnomon parallel to the earth's axis. For example, the holiday sundial brought back from Spain (lat 37ºN) to be set up in Southern England (lat 51ºN) would have to be wedged up by 14º, so that the gnomon is at 51º to the horizontal. You can either measure this angle with a protractor, or you can calculate the height of the wedge by multiplying the length of the dial plate by the sine of the correction angle. In this case, the wedge required for a square sundial with a side of 10 cm would be 2.4 cm.