a torque L', which, in turn, produces a precessional motion wp. As a result, the north-seeking end of the spin-axle precesses westward.
It has now been shown that a pendulous gyro-compass on a rolling ship headed either north-west or south-east is deflected toward the west. In the same manner it can be shown that a pendulous compass on a ship headed either north-east or southwest will be deflected toward the east when the ship rolls. The spin-axle of a pendulous gyro-compass on a rolling ship steaming on any intercardinal course is deflected in the direction to make it more nearly parallel to the keel of the ship. The deflection due to pitching is in the direction opposite that due to rolling for a heading in any direction.
116. Quadrantal Deflection Due to Lack of Symmetry of the Sensitive Element. - It has been shown that, if the mass of a swinging pendulum bob is not distributed symmetrically with respect to the pendulum axis, the bob will tend to set itself in the position in which its moment of inertia with respect to the vibration axis is maximum (Art. 14).
In the case of all gyro-compasses having a sensitive element consisting of a single gyro, inert masses must be added to the sensitive element in order that the moment of inertia of the suspended system with respect to every horizontal axis through the center of mass may be equal. The mass, however, of a sensitive element comprising two or more gyros can be distributed symmetrically about the line through the center of mass and the center of oscillation. Neither a compass consisting of a single gyro with properly adjusted balancing masses nor a compass consisting of two or more properly placed gyros is subject to deflections due to centripetal forces developed during rolling and pitching of the ship.
117. The Suppression of the Quadrantal Error. - No feature of the gyro-compass has so taxed the ingenuity of physicists and designers as the avoidance or elimination of the quadrantal error. In Art. 115 it has been shown that the quadrantal error is due to the cumulative effect of vertical components of the precession of the spin-axle produced by the swinging of the compass system from side to side as the ship rolls or pitches. The quadrantal error would be avoided: (a) if the suspended compass system remained vertical however the ship rolls or pitches; (b) if the impulses imparted to the swinging gyro-frame by the rolling and pitching of the ship were applied only when the line through the center of the