130   THE GYROSCOPIC PENDULUM

Angles in azimuth can be laid off relative to the N-S line of a gyro-compass, and angles in elevation with respect to a gyrovertical or gyro-horizontal forming part of the apparatus. An electric circuit through the gun, gyro-compass and firing mechanism may be closed automatically at the instant the gun axis makes the proper angle to the N-S line of the gyro-compass, and the proper angle of elevation relative to a gyro-pendulum forming part of the firing mechanism.*

* U. S. Patents. Schneider, No. 1507209, 1924; Radford, No. 1531132

1925; Ford, No. 1597031, 1926; Crouse, No. 1689327, 1928.

CHAPTER IV
GYROSCOPIC ANTI-ROLL DEVICES FOR SHIPS
§1. The Oscillation of a Ship in a Seaway

82. The Rolling of a Ship Due to Waves. - From Archimedes' Principle, a body either wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced. The weight of a body acts at a point called the center of gravity of the body. The buoyant force acts at a point called the center of buoyancy. The center of buoyancy is at the center of mass of the fluid displaced.

If the center of gravity of a completely immersed body is below the center of buoyancy, the body is statically stable, that is if this body be tilted and then released it will recover its former position. If the center of gravity of a completely immersed body is above the center of buoyancy, the body is unstable; that is if this body be tilted and then released, it will not recover its former position but will turn over till the center of gravity is below the center of buoyancy.

A floating body, however, may be statically stable when the center of gravity is above the center of buoyancy. Figure 101 represents a ship standing upright in still water with the center of gravity of the vessel at G and the center of buoyancy at B. Suppose that a wave moves under the ship from the left to the right. At the instant represented in Fig. 102, the center of buoyancy has moved to the left of the line of action of the weight Fs. The weight Fg and the buoyant force Fb now constitute a couple having a lever arm x. This couple causes the ship to " heel " or roll, in the clockwise direction. If the water surface is again level when the ship has rolled into the position shown in Fig. 103, the center of buoyancy is to the right of the line of action of the weight. Now the couple tends to roll the ship back into the upright position. The advancing wave emerging from under the ship adds a couple in the same direction.

The angular amplitude of vibration of a ship produced by a single wave is always small. If, however, a series of waves pass under

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