NATURAL ERRORS 185
(c) Push the gyroscope in the direction S-N with constant velocity and then suddenly move it toward either the right or left. Note that, during the change in the direction of the velocity, the spin-axle precesses in the same direction as in case (b) when the motion in the direction S-N was decelerated.
(d) Now accelerate the motion of the gyro-frame in either the direction E-W or W-E, that is, perpendicular to the spin-axis. No change in the direction of the spin-axis is produced.
Question. Suppose that we have a non-pendulous mercury ballistic gyrocompass with the spin of the gyro in the direction opposite that considered above. Find the direction of the deflection of the spin-axle that would be
produced if the instrument were to be accelerated in each of the ways considered above.
So long as the velocity of a ship is constant, the spin-axle of the gyro-compass will have a resting position at a small angle from the meridian of a magnitude depending upon the velocity and latitude of the ship (Arts. 110 and 111). If the velocity of the ship is changing while the ship is on any heading except perpendicular to the spin-axle of the gyro-compass, then during the time the velocity is changing, the spin-axle will be deflected from the resting position which the spin-axle had when the ship was moving with its first velocity. This deflection will be constant while the acceleration remains constant. The deflection of the spin-axle from its resting position, produced by an acceleration of the meridian component of the ship's velocity, is called the ballistic deflection.
A diminution of velocity in the meridian is produced not only by diminishing the speed in the meridian but also by changing the heading either eastward or westward. In every case, the ballistic deflection produced by any acceleration of the ship's velocity is in the same direction as the change in the direction of the resting position of the gyro-axle, on account of the changing meridiansteaming error.
Consider a ship steaming north at 10 knots. Because of the meridian-steaming error, the resting position of the spin-axle will be at an angle NOX, west of the meridian, Fig. 144. Suppose that now the speed on the same heading be increased to 20 knots. The resting position of the spin-axle corresponding to the new velocity is shifted to YO. Suppose that during the time the speed was changing from 10 knots to 20 knots, the ballistic torque acting on the gyro-frame caused the gyro-axle to precess into the position