In Fig. 142, the two angular velocities ews and mwe are represented by the lines OX and O Y, respectively. The resultant angular velocity of the ship with respect to a horizontal axis in the meridian plane, .ws, is represented by OR. The spin-axle of the gyro-compass sets itself parallel to the axis of the resultant angular velocity of the ship. In this figure
tan S, = -e = Ryw os X
This deflection, S,, called the meridian or north-steaming error, is westerly for a northern course, and easterly for a southern course. It is independent of the construction of the compass. In Art. 113 it will be shown how the appropriate meridian-steaming deflection can be produced, without oscillation, just as soon as any change occurs in either the speed or the course of the ship.
If the linear speed of the ship be expressed as v knots, then
vs = 6080 v ft. per hour. R = 20,925,000 ft.
pwe = 1 rev. per day = 24 radian per hour = 0.26 rad. per hour. Hence,
6080 feet per hour v cos 0 tan S, _ (20,925,000 ft.) (0.26 rad. per hr.) cos X
Neglecting the small difference between 5, and tan S,, and remembering that 1 radian = 57.3 degrees, we have the value of the meridian-steaming error:
S, = 0.0011 co sA radians = 0.063 co sA degrees (119)