Do compasses work in caves

Yes, they do, although in a few areas ferruginous igneous rocks or magnetic iron-ore close to the cave can introduce errors.

Until the recent invention of range-finding and position-locating instruments like the "Disto" (t.m.) the three measurement instruments for surveying caves were a builder's tape-measure for distances, a clinometer for slope angles and a magnetic compass for bearings. The latter two are types calibrated and read to 0.5º.

In high-grade cave-surveying the lengths and angle measurements from the above were, or are, then usually converted to (x,y,z) co-ordinates for plotting.