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PIERHEADS, QUAYS, AND LANDING-STAGES. 215
the ballasting will become ; but, of course, there are limits of economy and
accessibility to be considered.
Before investigating the case of the ballasted pontoon, it is desirable to
reconsider the meaning to be attached to the term “centre of buoyancy”
which we have hitherto found an important and essential feature in the
statics of the unballasted pontoon.
After displacement through an angle, the forces tending to restore a
ballasted pontoon to its original position, or to move it further from that
position, are :—
(a) The weight of the displaced water, acting upwards through its
centre of gravity.
(6) The weight of the ballast water acting downwards through its centre
of gravity.
(c) The weight of the pontoon acting downwards through its centre of
gravity, which, in the case of a rectangular pontoon, is the centre of that
figure.
The resultant of the first two forces is a force equal in magnitude to the
third force, but opposite in direction, and acting through a point which may
be described as the centroid of the buoyancy area.
This resultant and the force (c) form the righting couple, and heuceforth
the term centre of buoyancy must be understood in the sense of centroid
Of the buoyancy area, which it really is. To avoid misconception on
the point, it will perhaps be as well to adopt the expression “centroid of
buoyancy.”
Resuming the investigation of the stability of the pontoon, it is, in the first
place, desirable to consider the alterations in position of the centroid of buoy-
ancy in a pontoon which is subdivided into compartments. Let fig. 191 repre-
sent such an arrangement, the number of compartments in this case being five.
Under a slight displacement, the pontoon takes the position shown with
reference to the inelined line in fig. 191. The buoyancy area has been
changed from a rectangle into a series of parallelograms. A little inspection
will, moreover, show that the portion of buoyancy area deducted from the
extreme left-hand compartment has been added to the compartment on the