How can north-south acceleration make a gyrocompass wander from north?

A gyrocompass relies on its pendulosity—the same property that allows it to seek north—to function. Because this mechanism responds to accelerations in addition to gravity, north-south vehicle accelerations exert torques on the gyroscope spin-axis.1

These torques cause the instrument to wander about north, which would normally render it useless for navigation. To mitigate this, the system is designed with a specific period of oscillation—known as the Schuler period—which ensures that the heading precession caused by acceleration matches the rate of change of the angle between the true and apparent meridians experienced by a moving vehicle. By offsetting the indicating reference by this calculated angle, the gyrocompass can maintain an accurate reading of true north despite the vehicle's motion.1