I use a Suunto M-3DL Compass, which is simply the very best I have ever seen for hiking.
I have a couple of the ones with mirrors, like the K&R you reference. The guys who laid out the right of way for the underground power on my rural property used one of these and it seemed to be sufficient for a legal description of the ROW. OTOH, he laid out about 400 yards of ROW with several dog legs in 3 hours. Any of the mirrored compasses are more of hinderance for fast practical land navigation than a help.
For hiking I want to go a lot faster than 133 yards per hour. The Suunto M-3DL does not have the mirror, but it has the great advantage that it does not have to be perfectly level to be accurate, and it settles in a second or so.
If you can see several landmarks and want to determine your position on a map the mirrored compass will allow you to take accurate bearings and triangulate. But, if you have a topo map and know how to read it, you know where you are from the contours of the land.
But, a far more common use for a hiking compass is to use a map (or even better a GPS) to determine a heading to walk and then keep on that heading as you progress. Especially if you are in woods or brush — any kind of cover which reduces the distance you can see landmarks to less than a mile or so.
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How well defined are the trails you are following? Even a few people a day should make a trail which is easy to follow in almost any terrain.
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How good are you at determining how far you have walked from your starting point?
A trick I use is to count paces the way the Romans did. Every time your right foot touches the ground that is one pace. Most Americans count each step, but the Romans counted two steps as one pace. A mile is 1000 Roman paces for a man about 5’8”. This can be very useful.