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 con sidering 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 0 0, 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 " 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 con venient 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 b b. 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 in, 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.