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202
HARBOUR ENGINEERING.
The calculations necessary for the purpose are much simpler in regard to
pontoons than they are in regard to ships and other navigable craft, since the
former are generally constructed to some regular geometrical figure which
permits of the easy determination of its centre of gravity and also of the
centre of buoyancy. The calculation of the weight of an ordinary ship
and the point at which it may be assumed to be concentrated, as also
of the displacement and its geometrical centre, are matters of great com-
plexity and difficulty, calling for the exercise of no little patience, ingenuity,
and skill.
Pontoons, on the other hand, are generally, if not universally, either
rectangular, cylindrical, or spherical in form, with centres of gravity and
displacement readily determinable by simple geometrical construction.
Thus, in fig. 175 a rectangular pontoon is shown partly immersed
in water. The disposition of the principal resultant forces is that shown
by the arrows, and the primary condition of equilibrium is manifestly
fulfilled.
Now, suppose such a body to have acquired a slight displacement,
with the result that it has taken up the position shown in fig 176. The
centre of gravity (G) remains unchanged, but the centre of buoyancy (B)
has been removed to a point which does not lie vertically below the centre
of gravity. Obviously there now exists a couple, the moment of which,
Wx, is the weight of the body (W) into the horizontal distance (x) between
the two centres. The moment is a righting moment, and tends to bring the
pontoon back to its original position.
Suppose, however, the pontoon to float on its narrower side or end as
shown in fig. 177. In the upright condition the primary condition of
equilibrium obtains as before. But when a slight displacement takes place
(fig. 178), the moment (Wæ) called into existence is an overturning one
instead of a righting one, and the pontoon has every tendency to capsize. We
see, then, that a different state of things has been produced, and it becomes
necessary, therefore, to investigate the relative positions of the centres of
gravity and buoyancy a little more closely.
In each of the figures, let the vertical line drawn through the centre of
gravity when the pontoon is in its initial position, and also that through the
centre of buoyancy in the displaced condition, be continued until they inter-