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222   NAVIGATIONAL COMPASSES

the reversible motor to rotate in one direction when one plunger is pushed in, and in the reverse direction when the other plunger is pushed in. If the ship is headed in the direction of the spinaxle, the air-blast strikes the two plungers equally and no electric contact is made. As soon as the ship begins to turn, the supporting frame F turns relative to the sensitive element, thereby moving the two plungers relative to the air-blast nozzle B. One plunger is pushed more strongly than the other, the reversible motor starts and rotates the follow-up gear till the two plungers are pushed equally. The angle through which the follow-up gearring has been rotated is the angle the ship's head is turned from the north-south line. The follow-up gear is electrically connected to step-by-step motors which rotate the cards of the repeaters through the same angle that the follow-up gear has been rotated.

133. The Ballistic Deflection Error. - The resting position of the spin-axle of a compass depends upon the latitude and the meridian component of the velocity of the ship (Art. 111). When the velocity of the ship changes either in direction or in magnitude, the spin-axle is deflected from its resting position and oscillates about a new resting position. The magnitude of the so-called ballistic deflection depends upon the latitude, the meridian component of the linear acceleration of the ship's velocity, and upon the period of vibration of the gyro-axle back and forth across the meridian plane.

In Art. 113, it is shown that if the period of vibration of the sensitive element is of the proper value, the ballistic deflection error will be zero and the spin-axle will move without oscillation into the resting position proper for the new velocity of the ship. As so much sailing is done at latitudes about 40°, it is common practice to adjust the period of the Brown compass for zero ballistic deflection error at this latitude.

134. Prevention of the Quadrantal or Rolling Error. - While a ship is rolling or pitching, a jerk is imparted to the pendulous system at the end of each roll or pitch. It is shown in Art. 115 that these jerks produce zero deflection of the gyro-axle when the ship is headed on a cardinal course, north, east, south, or west, but that an error is produced when the ship is on an intercardinal or quadrantal course, unless means be taken to prevent it. Any error in the indication of a gyro-compass that might be produced by these jerks can be avoided by delaying the action of the jerks on the sensitive element till the axis of suspension is vertical.

THE BROWN GYRO-COMPASS   223

In the Brown gyro-compass this result is produced by motion of the oil in the control bottles.

Owing to the rotation of the earth, the spin-axle of the compass tilts out of the horizontal plane. Oil is forced into the control bottle on the upper side of the gyro-case. As the earth rotates on its axis so very slowly, the flow of oil due to this cause ceases as soon as the tilting of the gyro-axle ceases.

When the ship rolls, the gyro-compass is forced into oscillation about the fore-and-aft axis of the ship with a period equal to that of the roll. The mean angular velocity of the compass relative to the spin-axle is some two thousand times the mean angular velocity of the earth about its axis. Now, the velocity of oil from one control bottle to the other is so great that the kinetic energy of the oil causes the flow to continue after the tilting of the spin-axle has ceased. Hence, the oscillation of the oil from one control bottle to the other lags behind the oscillation of the compass and behind the oscillation of the ship. The lag is made such that, when the ship is at its maximum inclination to the vertical, the oil is at the same level in the two control bottles; when the ship is upright and the air-blast is equally divided at the two compartments of the air-box, the oil is at its maximum height in the control bottle on the side of the gyro-wheel from which the ship has just righted itself. Thus, the jerks imparted to the compass at the end of a roll do not affect the gyro-wheel till the ship is on even keel, a quarter period later.

If the ship is heading on a quadrantal course, Fig. 149, the jerks imparted to the compass when the ship is at the end of a roll are not received by the sensitive element of the Brown gyro-compass till the axle of the vertical supporting ring is vertical. Hence, the linear motion of the north-seeking end of the spin-axle produced by these jerks can have no vertical component. There will be zero deflection from the meridian due to the rolling (Art. 117, a).

If the moment of inertia of an oscillating pendulous system is not the same with respect to all horizontal axes through the point of support, the system will tend to rotate about a vertical axis till the moment of inertia of the system is maximum with respect to the axis about which it is oscillating (Art. 14). A gyro-compass having unequal moments of inertia with respect to different horizontal axes through the point of support would exhibit quadrantal error. The moment of inertia of the Brown gyro-compass is made of the same value with respect to all horizontal axes through