Hello mister and misses so-and-so, and team NASA,
If the earth is a sphere, the compass always shows the point “in the earth”, except north. But it usually shows the North on the horizontal way. But the world is a flat so your compass always shows the North on the horizontal!
So the earth is a flat.
I have a counter-theory. You observe that "the compass...shows the North on the horizontal way", but you perhaps are not aware that compass needles are weighted on one end to achieve this 'horizontal' display. Were they not, compass needles in the northern hemisphere WOULD point down to the north, and in the southern hemisphere they would point down to the south. For example, compass makers
Suunto imply this in passing when they mention having a two-zone balancing system, with a northern hemisphere zone and a southern hemisphere zone available. Same thing from a marine compass manufacturer,
Amee & Company, but made more explicit. Here is
another discussion, this time related to aviation. The point being: the effect you think does NOT exist, in fact DOES exist, is well known, and is compensated for.
The effect is most extreme at the magnetic poles (opposite of the "...except north" portion of your statement) where an unrestrained compass needle would point straight up and down. In fact, a device designed for exactly that motion was used to identify the geographic location of the magnetic north pole, called a
Dip Circle or a
Dip Needle.
The effect was discovered in 1544 by a German mathematician and instrument maker named
Georg Hartmann, and his immediate reaction was to try and compensate for it in the compasses he made. Anybody here who wants to experiment with it will be better served to suspend a magnetized needle from a fine thread, rather than using a camping-style compass, since that compass will be at least partly compensated by weight on one end of the needle. Or, if you have some money to spend, you could buy a
Dip Needle demonstrator.
Bottom line: the phenomenon you state WOULD exist, IF only the earth was round? It in fact DOES exist. Draw from that what conclusion you will.
(Should I add "Proud mister so-and-so, team NASA" to my signature? I think I should!)