You would not be able to tell the time accurately, for you will have to estimate degrees across the sky. AND you'll need to know whether you have daylight saving or not; and also the magnetic variation of the magnetic field at your location. And of course which hemisphere you are in. BUT don't forget, this was the basis of telling the time used by the ancients before the compass (and watches) were invented, for they knew the direction in which the sun was highest in the sky.
Start. For this exercise, we'll assume that you're in a location where you can make marks on the ground, And that you have an undamaged compass. You'll also need a small branch with two tips with you can draw a circle on the ground.
First. Determine the direction of true north. Correct the direction pointed by the compass needle for the magnetic variation at your site. This variation will be + or - from the needle indication, and may have a magnitude of several tens of degrees. Mark this direction on the ground with a line. This direction is true north. [For a +ve variation, subtract the number from the compass scale. For a -ve variation, add the number to the compass scale.]
Second. Using the pair of tips of your branch as a pair of compasses [this is the drawing instrument we refer to, and that's its proper name.] draw a circle on the ground, and in this circle, proceed to draw one of those six-pointed propellers. You will have played around doing this with your drawing set at some time. Thus the angle between any adjacent pair of 'propeller tip' is 60o (degrees). It will be helpful to mark the 30o and the 15o positions as well between one of the pairs of adjacent 'propeller tips'.
Now you know that the sun appears to revolve around the earth 360o degrees in 24 hours, so the sun moves across the sky by 15o per hour. [360 divided by 24].
Third. Mark on the ground a line in the direction of the sun and intersecting your 'true north' line above. This your Sun Line. Using our 'propeller diagram' estimate the degrees between your true north line, and your Sun Line. Remember the sun moves 15o each hour. You should be able now to determine the time. This time will be the true time for that longitude.
BUT. In some countries, the accepted time zones span many degrees of longitude; China and Russia come to mind; so local time as given by the time zone may well be out by several hours when compared with the true time! And daylight saving also has its effect. [And my country has a permanent 30 minute offset as well for reasons convenient to us.]
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