So you've decided to adjust your compass, and you need to point your boat north. The problem is that you usually use your compass to do that. And your compass may be wrong -- that's what you're trying to fix.
Fortunately, there's hope. The sun travels across the sky in a
known course; if you stood and pointed at the sun and then lowered
your arm straight down until it points at the horizon (this is easy to
do near sunrise or sunset, hard to do near noon), you'd end up
pointing at some spot on the horizon. If it's early morning, that spot
is somewehere in the east, about 90 degrees away from true north. The
exact amount away from true north is called the
If you think about it, the shadow cast by the sun will point in exactly the opposite direction from its azimuth. If the sun's azimuth is 82 degrees, shadows will point in the direction 262 degrees (82 + 180). If the sun's azimuth is 240 degrees, shadows will point in the direction 60 degrees. Of course, these bearings are relative to true north, rather than magnetic north. To keep things clear, I'll henceforth write everything bearing in the form "241 T" (relative to true north) or "87 M" (relative to magnetic north).
So if you knew the sun's azimuth at 8 AM today, at your boat's home port) was 97 degrees, you could point your boat (at 8 AM !) straight towards the sun and know that you were headed ... almost (true) east. If you could point it 7 degrees to the north of that, you'd be headed due (true) east. But who can guess how much 7 degrees is, by eye? The solution is a simple one: you make a compass rose, like the one I made a program to generate, stick it on a piece of cardboard, put a pin through the cardboard (absolutely perpendicular, please!), and set this "dumbcompass" on deck, with "0" pointed at the bow. You now steer the boat so that it's pointed with the sun 7 degrees to starboard, so that the shadow of the sun will be 7 degrees to port of 180...i.e. at 187. At that moment, you're headed due east (true).
Unfortunately, to calibrate your compass, you want to be able to head to due east MAGNETIC. If your magnetic variation (printed on every NOAA chart) is, say, 18 degrees west, then when you are pointing to TRUE north, your compass will read 18 degrees east. That means that when you're headed true east, your compass will read 108 degrees (if it's completely adjusted and has no error). You want to point towards MAGNETIC east, so you need to head 18 degrees below where you had planned: you point your boat not so the sun bears NOT at 187, but at 169 (187 - 18). If your variation is east, you have to add it to the direction you planned to head...
You can record what your magnetic compass says at that moment (you hope it says "90", but it probably says something like "88"), and now you know how far wrong it is when you're headed due east.
Now you head due west (magnetic). How? Let's suppose it's still 8 AM. You turn the boat so that the shadow of the pin on the "dumbcompass" is at 349 degrees (7 degrees, minus the 18 degrees for the variation). And you record the magnetic compass reading. Let's suppose it was "271".
Now you do the same for due north and due south. How do you find the right shadow points for the pin on the dumbcompass? Add or subtract 90 from the headings for due east or due wast...that makes 259 degrees and 79 degrees. (Of course, all this assumes you're working impossibly fast...that it's still 8 AM and so the sun hasn't moved much at all.)
Your compass read 2 degrees too low when headed due east, and 1 degrees too high when headed due west. You can't fix these both by adjusting the E/W screw, but you can balance out the error: you adjust the screw to make the reading 1.5 degrees low headed east, and 1.5 degrees high headed west. If both readings had been "low" -- for example it was 6 degrees and 4 degrees low for east and west respectively, you could adjust things by 5 degrees, and make it 1 degree low and 1 degree high, for east and west respectively.
If the derivation of the "adjustments" above wasn't obvious to you, try this: if the reading for east is 3 degrees low, write down "-3"; if the reading is 5 degrees high, write down "+5". Using this notation, write down both the east and the west readings, add them, divide the result by two, and change the sign. In our case, we would write down -2 and +1; we add them to get -1; we divide by 2 to get -0.5; and we change the sign to get +0.5
Add this amount to either the east or the west reading to get the "final result" for that direction. For east, we have -2 + 0.5 = -1.5; for west, we have +1 + 0.5 = 1.5. This tells us that we shoul adjust the "E/W screw" to make the reading, when we're headed east, be 1.5 degrees low (i.e., 87.5 degrees), and when we're headed west, it should be 1.5 degrees high (i.e., 271.5)
Do the same for the N/S reading: while heading N or S, adjust the screw until the N/S readings are "off by the right amount."
Now take your boat and head towards magnetic north (you should know how to do this by now), and record what your compass says. Then head 10 degrees east of north, and record the reading. Continue around until you're headed 10 degrees west of north. The record of your readings is a "deviation table;" by reading backwards, you can take any compass course and convert it into a "real" magnetic course.
The details of compass adjusting can be found in lots of places -- I think that "Chapman's" has it, for example. But the details of finding true north via the sun, and using a dumbcompass are not everywhere, so I've included them here.
How does one determine the sun's azimuth at a particular time, for a particular place? (The sun's azimuth depends on where you are, and it depends on that in a big way.) I'll give two ways to compute the Sun's azimuth: