A siderial watch measures siderial (star) time. A star (or other celestrical object) transits the upper part of a meridian every 23 hours, 56 minuites and four seconds, so a siderial day is shorter than a normal day measured by a normal watch. Knowing the siderial time was important for surveyors for the determination of longitude and azimuth.
The Society has two sidereal watches in its collection.
Watch, Sidereal
Watch, Sidereal, Waltham