In the Vernon, and other ships which were built according to the de signs of the late Sir William Symonds, the form of a transverse section paneling vertically through the hull differs from that which had been before given to ships, in exhibiting an increase of breadth above the plane of floatation (a horizontal plane passing through the ship when she floats upright, and coinciding with the surface of the water). This construction produces, without any diminution of velocity, an increase of stability not only when the ship is afloat, but also when, on lying aground, she is subject to the force of waves against her side. It may however be said to be attended by the disadvantages of too great stability ; that is, it may cause the ship to be considerably strained, and the masts to be carried away by a sudden impulse of the wind.
The lateral action of the wind against the sails, and of the waves of the sea against the bull of a ship, are the causes that the plane passing through its masts is made to decline from the vertical position which it has when the ship is at rest; and the ship is then prevented from being overturned only by the reaction of the water against the bottom and sides. The momentum of this reaction is that which is called the stability of the ship. The axis of the rotation has been placed by different writers in different situations, but both Bouguer and Euler have proved that, if the ship has not at the same time a pitching motion, it should be considered as a horizontal line passing through the centre of gravity of the ship. In order to find approximatively the
dependence of a ship's stability on its length and breadth, let it be supposed that the ship is a homogeneous solid in the form of a prism or segment of a cylinder its axis in a horizontal position ; and, the vessel being supposed to float upright, let A B C (fig. 1) be a transverse section through the immersed part in a vertical plane passing through c and g, which are respectively the centres of gravity of the whole solid and of that part (A n) coinciding with the surface of the water : let also A' 13' c' be the position of the same section when the vessel is inclined. Now, while the weight of the ship remains the same, the volume of the immersed part is the same whether the ship be upright or inclined, and the volume raised above the water by the inclination on one side is equal to the volume depressed below it on the other ; therefore the area M e' N may be considered as equal to A c and A' 13 31 to D N. Next let p and q be the centres of gravity of the trilateral spaces last mentioned; then, by mechanics, the centre of gravity of ar D will be at some point, as r in p g produced, the displacement of g by the inclination being supposed to be very small ; and the centre of gravity of II N (the section immersed when the solid is inclined) will be at some point ft in q r : also— A'B'C' : Ass : : pr : yr, and