A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John D. Howard
Date: 2016 Aug 19, 14:26 -0700
From my readings over the years on observatories I think time could be measured to that precision. Clocks were avaible to a accuracy of 1/100 second at that time and the famous Riefler regulator clock came out just a little later in 1890.
The clock could not display time to that precision but the telescope could. A micrometer eyepiece was used with several wires in view and a star's passage over each of the several wires could be recorded to the millisecond. If I rember correctly the obsever would hit a button to record the exact moment.
Surveyors and especially astrometors could measure angles very precise - down to 1/10 second arc in the 1880's
Now, down near the antipod I don't know. :-)