Bisect the angle between the hour hand and the 12 o'clock mark to find South

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This is the tricky part. Find the middle point of the angle between your hour hand and the 12 o'clock mark on your watch

Before noon, you'll have to measure clockwise from your hour hand to the 12 o'clock marking, while afternoon, you'll have to measure counterclockwise from your hour hand to the 12 o'clock marking. The middle point between the two marks South, while the point directly across from it marks North.
For example, if it's exactly 5 o'clock in the afternoon and you've lined up your hour hand with the sun, South is the direction exactly between the 2 and 3 o'clock marks and North is the spot across from this point (exactly spacebar clicker between 8 and 9).
Note that during Daylight Saving Time, your watch is most likely one hour "off" from the "real" time. If this is the case, substitute 1 o'clock for 12 o'clock before finding your North-South line.

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