FLOATING bodies, are those which swim on the surface of a fluid, the most interesting of which are ships and vessels employed in war and commerce. It is known to every seaman, of what vast mo ment it is to ascertain the stability of such vessels, and the positions they assume when they float freely on the surface of the water. To be able to accomplish this, it is necessary to understand the princi ples on which that stability and these po sitions depend. A floating body is press ed downwards by its own weight in a ver tical line passing through its centre of gravity ; and it is supported by the upward pressure of a fluid, which acts in a vertical line that passes through the centre of gra vity of the part which is under the water ; and without a coincidence between these two lines, in such a manner as that both centres of gravity may be in the same vertical line, the solid will turn on an axis, till it gains a position in which the equili brium of floating will be permament. From this it is obviously necessary to find what proportion the part immersed bears to the whole, to do which the specific gravity of the floating body must be known ; after which it must be found by geometrical method, in what positions the solid can be placed on the surface of the fluid, so that both centres of gravity may be in the same vertical line, when any given part of the solid is immersed under the surface. These things being determined, something is still wanting, for positions may be assumed in which the circumstances now mentioned con cur, and yet the solid will assume some other position, wherein it will perma nently float. However operose and dif ficult (says an able mechanic) the calcu lations necessary to determine the stabi lity of nautical vessels may, in some cases, be, yet they all depend upon the four fol lowing simple and obvious theorems, ac companied with other well known stereo metrical and statical principles.
Theorem 1. Every floating body dis places a quantity of the fluid in which it floats, equal to its own weight ; and con sequently, the specific gravity of the fluid will be to that of the floating body, as the magnitude of the whole is to that of the part immersed.
Theorem 2. Every floating body is im pelled downward by its own essential power, acting in the direction of a verti cal line passing through the centre of gravity of the whole ; and is impelled upward by the re-action of the fluid which supports it, acting in the direction of a vertical line passing through the cen tre of gravity of the part immersed ; therefore, unless these two lines are co incident, the floating body thus impelled must revolve round an axis, either in mo tion or at rest, until the equilibrium is restored.
Theorem 3. If by any power whatever a vessel be deflected from an upright po sition, the perpendicular distance be tween two vertical lines passing through the centres of gravity of the whole, and of the part immersed respectively, will be as the stability of the vessel, and which will be positive, nothing, or negative, ac as the metacentre is above, coin cident with, or below the centre of gra vity of the vessel, Theorem 4. The common centre of gravity of any system of bodies being given in position, if any one of these bo dies be moved from one part of the sys tem to another, the corresponding motion of the common centre of gravity, esti= mated in any given direction, will be to that of the aforesaid body, estimated in the same direction, as the weight of the body moved is to that of the whole sys tem. From whence it is evident, that in order to ascertain the stability of any ves sel, the position of the centres of gravity of the whole, and of that part immersed, must be determined ; with which, and the dimensions of the vessel, the line of floa tation, and angle of deflection, the stabi lity or power either to right itself or over turn, may be fbund.