What causes the small heading offset in a Sperry gyrocompass?

The small heading offset in a gyrocompass is caused by the vehicle's motion over the spherical Earth. When a vessel travels north or south, it acquires an angular velocity relative to inertial space that is perpendicular to the Earth's daily rotation.1

This motion causes the apparent [meridian]—the reference line relative to which stars appear to rise and set—to rotate about a vertical axis away from the true meridian. Specifically, the apparent meridian shifts westward for northerly velocity and eastward for southerly motion. To maintain an accurate reading of true north, the gyrocompass's indicating reference must be offset by the angle between these two meridians. This angle is a direct function of the vehicle's north-south speed, the Earth's rotation rate, and the latitude.1