what is the name and function of this apparatus
Looks a bit like a simple gyrocompass.
Oh! I almost made one of those one day.
It apparently has many names: Dip Circle, Dip Needle, Inclination Compass..., there may be more.
https://en.wikipedia.org/wiki/Dip_circle; [Broken] "Dip circles (also dip needles) are used to measure the angle between the horizon and the Earth's magnetic field (the dip angle)."
Separate names with a comma.