Abstract: In a ribbon suspended meridian gyroscope in which the gyroscope restoring moment is compensated by a compensating moment, which compensating moment is measured, a North reference angle is determined from a number of different measurements taken in various azimuthal positions. In order to shorten the total measurement time required, for each current individual measurement, the degree of accuracy required for this current individual measurement is determined from the measurement results of the previous measurements in accordance with the magnitude of the effects caused by an error of the individual measurement upon the error in determining the direction of North. The current individual measurement is then carried out to this degree of accuracy. In this manner, each individual measurement is only carried out to the degree of accuracy which corresponds to the weight of this individual measurement in the total error-budget for the North-determination for the respective North reference angle.