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Those ultimately cheap compasses are easily remagnetized in the opposite
direction with two magnets of very modest strength. Bring either pole of
one magnet up to the case so that one end of the compass needle is
strongly attracted to it. Now bring *the same pole* of *another* magnet up
to the other end of the compass needle. (You should find that the needle
stays in its original orientation.) Remove the first magnet and, finally,
remove the second magnet. The compass needle will now be magnetized in
the opposite direction.
You can even do this with one magnet if you kind of sneak up on the
compass needle from below, trapping it frictionally in the case while
maneuvering the magnet so that its south (or north) pole is next to the
needle's south (or north) pole. In fact, this is so easy to do
accidentally that I suspect it is the primary reason for the commonly
observed lack of any statistically significant correlation between the
needle markings and the directions in which they point.
John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm