stability is generally spoken of in connection with her heeling or rolling, it will be best to illustrate it in connection with these transverse motions.

Fig. 6 is a representation of a transverse section of a vessel supposed to be heeled to, say 20°. E is her centre of buoyancy in her upright position, and F her centre of gravity. Upon being heeled or inclined, the centre of buoyancy, owing to the irregular shape of the vessel, shifts to some point, E2. As the centre of buoyancy has been shifted to E2, the resultant of the water pressure no longer acts through E, but through E2; and it must be remembered that this resultant always acts vertically, or at

right angles to the water-level. The resultant of the force represented by the weight of the ship continues to act vertically downwards through her centre of gravity F, that being the point it would act through if the vessel had not been heeled; it is of course assumed that no part of the weight of the ship has been shifted, so as to cause her centre of gravity to shift.

Thus we have the weight of the ship acting downwards through the centre of gravity F, in a direction F H, and the weight of the water displaced acting upwards through the centre of buoyancy E3, in the

direction E2 M; and the point M, where E2 M cuts what is the middle line of the upright position of the ship, is the meta-centre. The length of the righting couple is the horizontal distance between F H and E2 M, represented in Fig. 6 by F K or æ G.

The wedge-shaped piece of the hull A B O is called the wedge of immersion; and the wedge-shape piece O C D the wedge of emersion. By naval architects they are usually referred to as the "in" and the “out” wedges. By the wedge of immersion, or the part that is put into the water, being largely in excess of the wedge of emersion, or the part that is taken out, the centre of buoyancy is made to shift very rapidly over to leeward as the vessel is inclined, and so the couple x G lengthens very fast. In all broad and shallow vessels the wedge of immersion, even at small inclination, is much in excess of that of emersion, and so they have considerable stability at small angles of heel-which may be conveniently referred to as initial stability-which stability, however, rapidly vanishes as the deck becomes immersed.

In saying that the wedge put into the water is larger than the one taken out, it must not be supposed that the displacement is increased in proportion to the excess. The displacement always remains exactly the same as the weight of the vessel; but if the volume of the wedge of immersion be in excess of the volume taken out, then the vessel shifts or rises bodily in the water, to an extent which is dependent upon the area of the new load water-plane and the excess in the volume of immersion.

The righting moment or power is computed by multiplying the weight of the ship, or displacement in tons, by the length of the righting couple a G (Fig. 6). That is, if the weight of the ship or her displacement be 40 tons, and the length of the righting couple at 20° inclination be 2ft., then her righting power or moment of stability at that inclination will be 40 × 280 foot-tons. If the righting moment of a yacht at 20° inclination be equal to 80 foot-tons, as described, then it will require a steady force equal to 80 foot-tons upon her canvas to maintain her at that inclination.

If a vessel with such a section as that portrayed in Fig. 7 were filled out in the garboards at O O just above the keel, it is plain that the centre of buoyancy (B) would be lowered, and the point M would be brought nearer the centre of gravity (G); therefore the arm of the righting lever G Z would be shortened. But in the case of a yacht the added displacement about O O would be utilised for the stowage of additional ballast; and by this means the centre of gravity (G) would be brought lower; so that it is quite possible that the original distance between G and Z would be maintained.

The effect of increasing the height of the centre of buoyancy relative

to the surface of the water can be illustrated in this way. Assume that the displacement, or rather the hull, is cut away at the garboards as shown at P P, and added to the hull near the load water-line as at R R, then the centre of buoyancy would be higher, and upon inclination of the vessel would shift out farther to leeward than shown by B', so that the distance G Z would be increased, always supposing that G was kept in its original position by shifting the weights lower, such as could be done by putting additional weight on the keel. If the centre of gravity could be brought to K, and, with the centre of buoyancy at B, the length of the righting lever would be K L. As a matter of fact, however, we know of but

few instances where the centre of gravity has been found below the centre of buoyancy.

It is obvious that the weight of a vessel has largely to do with her stability; thus, if the length of righting lever at 20° inclination be 2ft., and the weight of the vessel, instead of being 40 tons (see page 10), is only 35 tons, then it is plain that the righting moment at 20° inclination will only be 70 foot-tons instead of 80 foot-tons. Therefore, in considering stability, the problem that exercises the naval architect in designing is how to attain a given maximum righting moment; that is, shall he increase the beam and diminish the displacement, and thereby lengthen out the righting couple represented by G Z (Fig. 7)? or shall

he contract the beam and add to the displacement at O O, and thereby largely add to the weight that will act on the couple? Of course, by adding to the beam and decreasing the displacement better lines for speed can generally be obtained; but, on the other hand, the longer and fuller bodied vessel will most likely be the better or more easy sea boat, and will have a greater range of stability.

It is quite a common thing to hear a person say that this, that, or the other vessel has "great artificial, but very little natural or structural stability," as if there were various kinds of stability. This confused way of regarding stability is very likely to prevent a clear understanding of the conditions on which stability depends, and it must be understood that there are no such things as no such things as "artificial stability" or "natural stability" or "structural stability" or "stability of form as distinct qualities. In "Yacht Designing" in reference to stability we find the following:

There is no such thing as stability of form per se, although it is sometimes convenient to speak of form as if it had absolute stability independent of the position of the centre of gravity of the vessel. For instance, let it be conceived that a body of no weight be placed in a perfect fluid, then it would rest as well in one position as another, whatever its form; so that when stability of form is referred to it must always mean the influence that form has on stability in relation to the centre of gravity of the body and its metacentric height.

Or it may be assumed that a homogeneous substance is placed in a fluid, or that a portion of a fluid is turned into a solid, maintaining its inherent bulk, weight, and uniform specific gravity; then such a substance or solid would float in whatever position it were placed. Let A be such a

substance or solid; then its centre of buoyancy and centre of gravity must necessarily be at the same point, k; and, as the resultant of these two forces acts in the vertical line a a, the body will be in equilibrium if placed in the position-which may be assumed as its natural one-A. But A will be in equilibrium in any other position; for instance, in that shown by B, as the two forces still act in the same vertical line through k, as

shown by bb. It is thus evident that such a substance or solid has no stability whatever.

Now the equilibrium can be made stable by shifting the point through which the centre of gravity acts. Assume that the specific gravity of the solid, B, is made unequal, so that it becomes denser or heavier about p (see C); it is apparent that on such a change the centre of gravity would be shifted to some point, g, and the forces would no longer be acting in the same vertical line. The resultant of the buoyant pressure of the water would act upwards in the line a a through k; and the resultant of the weight of the body would act downwards in the line b b through g. The horizontal distance between the two lines a a and b b would be the couple upon which the two forces acted, until the solid got into the position D, where the two forces would act in the same vertical line, a a. The equilibrium of a solid such as D floating would be stable, if, upon being inclined from its original position until in the position C, it had the power to regain the position D.

It has been proved that "form" of itself has no stability, and it remains to be shown how the variableness of form in a partially immersed body can bring about a stable condition of equilibrium. Let it be assumed that the solid A has an addition made to it, as illustrated in E by w x y z. The bulk will be increased, but the weight is to remain exactly the same,

with the centre of gravity still at k. The body will rise in the water until in the position F, so that a part remains immersed equal in bulk to A. Owing to the altered form of the immersed part of the solid, the centre of buoyancy has shifted to some point m, but the centre of gravity remains at k. Now the resultant or buoyant pressure of the water in the line a a no longer acts through k, but through m, whilst the weight of the solid still acts through its centre of gravity, k, in the line b b. It is quite plain that the solid could not remain in the position F, but would take the original position of A, as shown by G, with the forces of buoyancy and gravity acting in the same vertical line a a.