Various descriptions of gyrocompasses that I can find (such as the Wikipedia article) claim that the compass will seek to align itself with the earth's rotational axis.
I think I can understand how that works if we place the compass on the ground, at rest with respect to the surface. Then the entire compass housing changes direction in space at a steady 15 degrees per hour, and it makes sense that one can use gyroscopic torques to sense the axis of that rotation and align a readout with it.
However, gyrocompasses are not usually employed at rest on the ground -- they're used on ships and aircraft. That's a moving, rolling, pitching, platform. Ships roll on the waves. Aircraft roll to maneuver, and pitch up and down to modulate lift -- all much more violently than the rate of the earth's rotation. How does a gyrocompass manage to pick out the slow overlaid rotation of the earth out from all that noise, accurately enough to be of any use for navigation?
In a (relatively slow-moving) ship I suppose you can put the compass close to the center of the rolling motion and use an outer set of weighted gimbals to keep one axis pointing straight down. But that won't work in an aircraft which moves so fast that the lateral accelerations while turning displace the direction of "down" (as measured by an onboard plumb line or accelerometer) by tens of degrees -- which again seems to drown out any hope of detecting the rotation of the earth.
The aircraft's orientation in space isn't even tied to the earth's rotation on average; you can fly it to the other side of the planet in about one planetary revolution's time.
Is there some additional effect at work here? Newtonian gravity and mechanics don't appear to offer anything the the moving compass could hang on to.