What is the Schuler period in a gyrocompass?

The Schuler period is a specific period of oscillation for a gyrocompass defined by the formula $2\pi \sqrt{R/g}$, where $R$ is the radius of the Earth and $g$ is the acceleration due to gravity.1

Named after Max Schuler, this period is critical for the instrument's accuracy in an accelerated vehicle. When a gyrocompass is tuned to this period, the heading precession of the gyroscope spin-axis caused by vehicle acceleration perfectly matches the rate of change of the angle between the apparent and true meridians as seen from the moving vehicle. This allows the instrument to maintain an accurate reading of true north despite the vehicle's motion.1