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Perhaps I can add a bit to Herbert Prinz's reply to Lisa Fiene's question..

You find variation by taking a compass bearing of any object of which the
azimuth is known. Simple as that. The discrepancy between them is the
variation.

For example, at apparent Noon, the azimuth of the Sun is known to be due
North or South, depending on your hemisphere, and its.

But (especially in the tropics) it's hard to take an accurate compass
bearing of the midday Sun, because it's so high in the sky. From where I
live (51d N), in Winter, the midday Sun is so low, it's easy.

It's best to use an object that's at, or near, the horizon. The amplitude
tables give the predicted azimuth at Sunrise and Sunset. Trouble is, the
uncertainties in refraction at very low altitudes make the moment of
Sunrise and Sunset rather indeterminate. In the tropics, that doesn't
matter too much, because the Sun is rising from, and falling to, the
horizon nearly vertically, so its azimuth changes only slowly. At high
latitudes, it emerges at a shallow angle, so uncertainties in refraction
make for big changes in azimuth. A good compromise is to calculate the
azimuth when the Sun's altitude is, say, 10degrees, using some form of
altitude-azimuth tables or calculation.

Lisa quotes Cook-

>"Found the Variation of the Compass by the Even'g and Morning Amplitudes
>and by 2 Azths to be West 20? 59'"

That raises another interesting question. How did Cook manage to take a
compass bearing of the Sun (or even the average of several) to sufficient
accuracy that he could quote the result to a minute of arc; to be 20deg
59', rather than 21deg? Compass bearings can't be taken to that accuracy
now, nor could they then. Cook was simply quoting the answer that his
calculations gave him. We have to take the 59' part of his measured
variation with a large pinch of salt.

George.

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