The fundamental system connected with n quadratic forms consists of (i.) the n forms themselves f i, f2,ï¿½ï¿½ fn, (ii.) the (2) functional determinants (f i, f k) 1, (iii.) the (n 2 1) in variants (f l, fk) 2, (iv.) the (3) forms (f i, (f k, f ni)) 2, each such form remaining unaltered for any permutations of i, k, m.
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.
Of span, consider a small interval Fk =Am on which the load is wLm.