<Dd> T = 2 π ψ _̇ Ω I 2 I 1 sin ⁡ δ . (\ displaystyle T = (\ frac (2 \ pi) (\ sqrt ((\ dot (\ psi)) \ Omega))) \, (\ sqrt (\ frac (I_ (2)) (I_ (1) \ sin \ delta))) \, .) </Dd> <P> Therefore ω ~ (\ displaystyle (\ tilde (\ omega))) is proportional to the geometric mean of the Earth and spinning angular velocities . In order to have small oscillations we have required ψ _̇ <0 (\ displaystyle (\ dot (\ psi)) <0), so that the North is located along the right - hand - rule direction of the spinning axis, that is along the negative direction of the X 7 (\ displaystyle X_ (7)) - axis, the axis of symmetry . As a side result, on measuring T (\ displaystyle T) (and knowing ψ _̇ (\ displaystyle (\ dot (\ psi)))), one can deduce the local co-latitude δ (\ displaystyle \ delta). </P> <P> The first, not yet practical, form of gyrocompass was patented in 1885 by Marinus Gerardus van den Bos . A usable gyrocompass was invented in 1906 in Germany by Hermann Anschütz - Kaempfe, and after successful tests in 1908 became widely used in the German Imperial Navy . Hermann Anschütz - Kaempfe founded the company Anschütz & Co., which started in Kiel / Germany the mass production of gyro compasses . The company is today Raytheon Anschütz GmbH . The gyrocompass was an important invention for nautical navigation because it allowed accurate determination of a vessel's location at all times regardless of the vessel's motion, the weather and the amount of steel used in the construction of the ship . </P> <P> In the United States, Elmer Ambrose Sperry produced a workable gyrocompass system (1908: patent #1,242,065), and founded the Sperry Gyroscope Company . The unit was adopted by the U.S. Navy (1911), and played a major role in World War I . The Navy also began using Sperry's "Metal Mike": the first gyroscope - guided autopilot steering system . In the following decades, these and other Sperry devices were adopted by steamships such as the RMS Queen Mary, airplanes, and the warships of World War II . After his death in 1930, the Navy named the USS Sperry after him . </P>

What is the difference between magnetic and gyro compass