Ile gives the following formula :— wk Time of rotation= 1 Vficii+ where k is the radius of gyration about a longitudinal aids per pendicular to the plane of rotation through the centre of gravity, and o µ is the height of the metacentre above the centre of gravity. From which he deduces the following inferences, namely, the smaller the amount of a A, or the less the stability of the ship, the longer is the time of oscillation, and consequently the greater the easiness of the motion ; while such ease, however, may, as already observed, be beyond a certain`point a source of evident danger. Uneasy rolling may, more over, be partially corrected by removing weights nearer to the side of the ship, thus increasing the axis of rotation, or as some call it the radius of gyration. The questions of rolling and stability are of great moment to the shipbuilder, as what are called sea-going qualities pre eminently hinge on these. The well-known expression for comparison of stabilities its as follows, namely :— 2 a) D when/ y 3 x= the' automation of the functions of_ the cubes of the ordinates, d x being the differential of the length of the elementary prism, and n being the displacement. So that in fact the comparative
stabilities of ships may be said to be the comparative heights of their metacentres above the centres of gravity.
The rudder serves to govern the ship's motion ; for, on being turned so that its plane is in a position oblique to the plane of the masts and keel, the reaction of the water against it as the ship advances, being resolved in a direction perpendicular to the last-mentioned plane, becomes a force which causes the ship to turn upon a line passing through its centre of gravity. Thus by giving the rudder more or less inclination to the said plane, the ship may be made to move in any required direction, or may be made to avoid an object by which its safety might be endangered.
Certain highly interesting facts have been very lately under discus sion by the Institution of Naval Architects, aided by the opinions of naval officers of the greatest experience : these will be properly noticed under STEAM-VESSEL.