A Treatise On The Principles And Practice Of Harbour Engineering

PIERHEADS, QUAYS, AND LANDING-STAGES. 205 Then, by the ordinary principles and operations of trigonometry and mechanics, we have 9 h^ = 2/qO = —L• Similarly, 2 Mi + h2g2 =-5- △, and the ratio area RFO _^FR.RO_ FR _ A area RHNT~ 2RO.RH “4RH-4D' Whence we obtain as values for the co-ordinates, 2. A AL ” 3L’4D 6D and 2/=3A-4D=6D- The equation of the locus accordingly is It is at once apparent that, L and D being fixed quantities, y varies directly as a:2; that is, the locus of B is the curve of a parabola whose longitudinal axis is QBls and vertex, Br These equations for a: and y hold good up to the point where A becomes equal to D. Giving A the value ?, we obtain L D and, giving it the value D, L D This brings us to the diagonal HOP, at which inclination the side GP commences to be immersed and the side GH is entirely out of water. It will simplify matters now if we regard the pontoon as undergoing disturbance from an initial position in which the vertical axis is RT, and the surface level KQ, for that is the position towards which the pontoon is tending in the continuation of its revolution. The calculations for the locus of B in reference to the new axis will equally give a parabolic curve, having its vertex at Z, where OZ=^- Accordingly, the locus of B resolves itself into a curve consisting of four parabolic arcs touching at the diagonals, HP and GN, of the parallelogram. A moiety of the curve is traced in fig. 179. Now, to find the metacentre corresponding to any assigned centre of