36 NAVAL SCIENCES. 



which brings the ship into the position ab. The force which produces this 

 inclination is represented by the line EH, and the force which tends to restore 

 the ship by the line EG. These forces, which act in opposite directions, pro- 

 duce the rolling, and the effect of the acting power is EH + EG. In regard 

 to the motion of the waves, the rolling must commence as soon as a wave 

 rises to one side of a ship and falls on the other. The inclination of the 

 side of a wave gradually increases from its horizontal position to its greatest 

 height, and conversely, thus gradually increasing the force which tends to 

 turn the ship around its horizontal axis ; and long before the roll has reached 

 its proper height, it is met by a wave from the opposite side, which destroys 

 its effect and prevents a further bending over of the ship. The axis of 

 rotation here spoken of has been thus far considered as at rest ; this, how- 

 ever, is far from being the case ; instead of remaining at the same height, 

 it rises or falls, or in fact, as often occurs, is at rest. It is found, for 

 instance, that when there is a tendency for a greater part of the ship's body 

 to sink on one side than to rise on the other, the axis of rotation must be 

 elevated during the motion. In this case rolling begins and the ship is 

 raised, while it lies on the side, and falls when it recovers itself The 

 opposite effect is produced when a smaller portion of the ship's body is 

 immersed than that which tends to rise on the other side. The occurrence 

 and the extent of this motion depend on the position of the centre of 

 gravity and on the form of the ship's sides between wind and water. Let 

 us investigate the case when the sides of the ship are parallel with the plane 

 of the masts. PL 7, figs. 20, 21, 22 : let AB be the water-line when the 

 ship is upright, ah the position of this line when the ship is inclined 10°, 

 and G the centre of gravity, which in the upright position is situated in 

 both lines, but above the surface of the water in fig. 22, and below it 

 in Jig. 21, then in the first position, when immersion and emersion are 

 equal, the ship in turning will neither rise nor fall ; in fig. 21, when the 

 immersion is greater than the emersion, it must rise, and in fig. 22, when 

 the reverse takes place, it must fall. But when the sides of the ship diverge 

 above the water-line, the axis of rotation (fig. 20), instead of being at rest, will 

 rise, as in this case the immersion is increased. In ^^.21, the immersion will 

 increase still more, and the axis, accordingly, will rise still more, and in fig. 22, 

 the immersion will also increase, and the ship will fall only in a slight degree. 

 But when, in the opposite case, the sides of the ship diverge under the 

 water-line, and above it are parallel with the plane of the mast, the ship 

 (fig. 20) will fall as it turns, the rising of the ship (fig. 21) will be corrected, 

 and the falling (fig. 22) increased. It hence appears that whenever the 

 equality between immersion and emersion is essentially impaired, the shock 

 to the ship in violent pitching must be great and dangerous. In order to 

 avoid this serious difficulty, the actual position of the centre of gravity of 

 the ship must be calculated, and such changes made in the ship's body that 

 when the ship turns on its axis, which passes through the centre of gravity, 

 the immersion and emersion may remain equal. The motions of rolling 

 will be free from all dangerous shocks whenever the ship's centre of gravity 

 lies in or near the plane of the water-level. 

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