Stability may be defined to be the resistance which a ship offers to being inclined from the upright position, and tends to restore her, if inclined, whether that inclination be transverse or longitudinal.

The degree in which a vessel may derive this property (from form) will depend upon three points, viz. her length; her breadth; and the height of the centre of gravity of displacement.

Centre of gravity of displacement :-The centre of the immersed portion of a ship is called the centre of gravity of displacement; and the force of the water in supporting her, and in resisting heeling, may be considered as centered there. A ship is supported by a number of pressures in different directions, but the effect of their sum is a pressure passing through that centre, and perpendicular to the surface of the water; for this reason if a vessel be free and at rest, its centre of gravity must be in the mean direction, or resultant of the force of the water which supports it.

When a ship heels, the effort of this water should be to right her, or restore her to the position in which she was when at rest.

Let E, fig. 1, Plate I, be the centre of gravity of displacement of a ship; A D B, a vertical section passing through the point E; A B the water-line when the ship is upright; let G D be a perpendicular to the waterline passing through the point E.

Position of the centre of gravity :-As the resultant of the force of the water supporting the ship, is in the line G D, it follows necessarily, that the centre of gravity of the ship must also be in the same line; let C be the centre of gravity, situated in the load water-line. When a ship is inclined, a prism is immersed on the

one side, and an equal one is emerged on the other side, as in fig. 2, Plate I.

A B being the water-line, when upright and a c b the water-line when inclined: now suppose a ship cut in the middle, and suppose that B D A, fig. 1, shews a vertical transverse section C Bb and CA a being sections of the aforesaid prisms, N and M being their respective centres of gravity.

Now, suppose the vessel inclined and a b the waterline then a C A is immersed, and B C b is emerged, or practically a quantity equal to B Cb is transferred from one side to the other, the effect of which is, to carry the centre of gravity of displacement towards the part to which the prism has been transferred; let F be its new position, draw from the point F a perpendicular to the water-line a b; it will meet the line D G in some point G; G is the meta-centre.

Stability

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Displacement CO:-If the centre of gravity were above this point, the vessel would upset, if it were at E, the weight of the ship would act at the whole distance E F, (E F being perpendicular to F G) to right the ship, but being at C it will act only through the distance CO, which is the perpendicular distance of C, from the vertical line F G, the centre of gravity and centre of gravity of displacement remaining constant, the distance CO will vary with dimensions of the transferred prism.

Stability varies as the cube of the breadth.-Now, it is easily seen, that if the breadth of the vessel be increased, that the dimensions of these prisms will also be increased, and very much more so by each additional foot, and as their volume may be considered as collected at their centres, so with each additional foot the centres will be carried out, and the moments thus increased, so

that if the breadth be doubled, (the length remaining the same) the stability would be increased as the cube of 2 (the double) or eight times; the volume increases as the square, but the moment of the increased volume being double of that of the less volume the stability is increased as the cube.

Stability varies as the length :—But it may also be seen that if the length of the vessel be increased (the breadth remaining the same) the dimensions of the prisms will be increased only as the length, and their centres of gravity will remain at the same distance from the vertical line, therefore C O will not be increased, but only the force which acts through C O, consequently the stability varies only as the length, while it varies as the cube of the breadth. Thus for instance, the Trafalgar, though she has seven tons more armament than the St. Vincent (which must tend to increase the apparent stability) appears to have much more stability than her-and this is in accordance with the above reasoning for she has one foot more beam, and their stabilities ought to be as 157 St. Vincent to

166 Trafalgar.

Stability may not vary as the cube of the breadth and as the length :-But as this section may not, and seldom can represent, all the sections, those both before and abaft being smaller, and the more small the shorter the vessel is, then in calculating the stability at a given angle of inclination, the volume of all these sections of both prisms must be estimated together with the distance of their respective centres of gravity from the vertical line.

The effect of the sections afore and abaft being greater or smaller is such, that a vessel with less extreme beam than another, may have greater stability,

because of having a greater mean breadth; this is the case in the Espiègle as compared with the Flying-fish, and her greatest inclination was 12" while that of the Flying Fish was 14.

In confirmation of this I may quote Captain Corry, who says in his public letter, "I must state that I could not help remarking the extreme stiffness of the Espiègle when compared with the other vessels, which must give her a great advantage when firing her guns."

Stability less when the centre of gravity of displacement is low than when higher :-Now, suppose sections of two vessels of equal displacement, whose centres of gravity of displacement are respectively E and E', fig. 3, Plate I., and when inclined F and F1, F1 lower.

The consequence of this would be that C O1, the perpendicular distance of C from the vertical F1 G1, would be less than CO, the perpendicular of the vertical F G ; in the other case therefore the stability of the vessel which has the centre of gravity of displacement lowest, would be less by the difference of this leverage, nor could the difference be compensated for by the position of the ballast.

Professor Inman has shewn, in his notes on Chapman, that Clairbois was wrong in supposing that a ship having greater displacement at the floor, (if ballast be placed there) will have greater stability than a ship having greater displacement at the load water-line, each having the same total displacement.

The difference in the height of the centre of gravity of displacement of the Espiègle and Flying-fish was another reason why the former manifested greater stability, even though she carried her guns several inches higher!

The parliamentary returns shew 5 inches, but it

must have been more unless the Flying-fish had broken her sheer. If we assume that the weight of these two vessels above water was 100 tons, and the centres of gravity of this weight in each to be at the "height of port" their moments of inertia would be

to the latter, as tending to make her roll by decreasing her practical stability.

It is because thes tability depends upon the volume of these prisms of immersion and emersion, and upon the height of the centre of gravity of displacement that Chapman recommends rising floors, and a full waterline.

From this recommendation of Chapman's, many have approved of the peg-top shape, which is essentially different from that recommended by Chapman.

Unreasonableness of comparing a small ship with a larger. As it has been seen that stability, (cæteris paribus,) increases in a faster ratio than the dimensions, so it may be seen how unreasonable it is to expect a small ship to sail equally well with a larger, and more unreasonable if the small ship has a larger armament, and still more unreasonable if the smaller in dimensions has under those dimensions an equal, or more so, greater displacement—because the power of carrying a larger armament, and her sails well, must depend in a great measure upon her stability.

The inclining power of the sail varies only as the cube, while the stability or power to resist inclination varies as the fourth power of the dimensions. As the nominal tonnage depends upon the length and breadth