In a diagram it is conducive to clearness to draw the ship in one position, and to incline the water-line; and the page can be turned if it is desired to bring the new water-line horizontal. Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is [sum]ydA tan[theta], so that there is no change of displacement if [sum]ydA = 0, that is, if the axis passes through the C.G. of the water-line area, which we denote by F and call the centre of flotation. The righting couple of the wedges of immersion and emersion will be [Sigma]wy dA tan [theta]·y = w tan [theta] [Sigma] y² dA = w tan [theta]·Ak² ft. tons, (4) w denoting the density of water in tons/ft.³, and W = wV, for a displacement of V ft.³ This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB1 = wAk² tan [theta], (5) BM = BB1 cot [theta] = Ak²/V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak² the moment of inertia of the water-line area about an axis through F, perpendicular to the plane of displacement. An inclining couple due to moving a weight about in a ship will heel the ship about an axis perpendicular to the plane of the couple, only when this axis is a principal axis at F of the momental ellipse of the water-line area A. For if the ship turns through a small angle [theta] about the line FF´, then b1, b2, the C·G. of the wedge of immersion and emersion, will be the C·P. with respect to FF´ of the two parts of the water-line area, so that b1b2 will be conjugate to FF´ with respect to the momental ellipse at F. The naval architect distinguishes between the _stability of form_, represented by the righting couple W.BM, and the _stability of ballasting_, represented by W.BG. Ballasted with G at B, the righting couple when the ship is heeled through [theta] is given by W.BM. tan[theta]; but if weights inside the ship are raised to bring G above B, the righting couple is diminished by W.BG.tan[theta], so that the resultant righting couple is W·GM·tan[theta]. Provided the ship is designed to float upright at the smallest draft with no load on board, the stability at any other draft of water can be arranged by the stowage of the weight, high or low.