A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Geoffrey Kolbe
Date: 2020 Jan 26, 22:54 -0800
The sighting of zenith stars is the basis of the Talcott-Horrebrow method, as used with geodetic theodolites to find latitude. The accuracy of latitudes determined this way is of the same order as a GPS device - a fraction of an arc-second. The advantage of using (near) zenith stars is that refraction corrections can be neglected.
The star will, of course, not be exactly on the zenith. But errors in measuring the zenith angle due to the theodolite not being exactly level are essentially cancelled out by turning the theodolite through 180° and measuring the zenith angle again on "the other face".