NavList:

It's a reflecting circle.  Just as you say, it looks like a sextant, and it has the same operating principle.  The advantage is that it's self-calibrating, because the circular scale can be arbitrarily rotated and redundant measurements taken, permitting the target angle and the scale errors to be jointly estimated.  It's bulkier for a given radius, though, and I guess somewhat more expensive too.

"Reflecting circle" on images.google.com pulls up a number of nice examples.  I think the name of Borda is associated with the device, but I'm sure others here know more of the history.

Cheers,

Peter