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remery said..
Today I learned that, because the earth is not flat, compass needles are weighted differently for northern and southern hemispheres to avoid the "needle dip".
I am not sure that effect is solely linked to a non-flat earth surface.
If you put a magnet under a flat piece of paper you would get different dip angles in different locations across the flat paper. Didn't you do this in skool with iron filings ?.
I'd assume you could measure the dip angle across the earth's surface to determine the curavature of the surface you were on, but managing compasses for needle dip would also be required on a flat earth, assuming that flat earth was entirely within a magnetic field. It is more to do with the magnetic field characteristics than the surface you are stood on when you measure that field.