In the case of an axial moment, the square root of the resulting mean square is called the radius of **gyration** of the system about the axis in question.

The automatic choice of the cut-off radius for RF is twice the radius of **gyration**.

The varying direction of the inclining couple Pc may be realized by swinging the weight P from a crane on the ship, in a circle of radius c. But if the weight P was lowered on the ship from a crane on shore, the vessel would sink bodily a distance P/wA if P was deposited over F; but deposited anywhere else, say over Q on the water-line area, the ship would turn about a line the antipolar of Q with respect to the confocal ellipse, parallel to FF', at a distance FK from F FK= (k2-hV/A)/FQ sin QFF' (2) through an angle 0 or a slope of one in m, given by P sin B= m wA FK - W'Ak 2V hV FQ sin QFF', (3) where k denotes the radius of **gyration** about FF' of the water-line area.

The formula (16) expresses that the squared radius of **gyration** about any axis (Ox) exceeds the squared radius of **gyration** about a parallel axis through G by the square of the distance between the two axes.

The squares of the radii of **gyration** about the principal axes at P may be denoted by k,i+k32, k,f + ki2, k12 + k,2 hence by (32) and (35), they are rfOi, r2Oi, r20s, respectively.