Of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -**hV**/A, b 2 - **hV**/A, (I) h denoting the vertical height BG between C.G.

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.