Abstract
Simpson's rules may be used to find the areas and volumes of irregular figures. The rules are based on the assumption that the boundaries of such figures are curves which follow a definite mathematical law. There are three Simpson's rules. Simpson's first rule assumes that the curve is a parabola of the second order, second rule assumes that the equation of the curve is of the third order, and the third rule is used to find the area between two consecutive ordinates when three consecutive ordinates are known. The chapter uses extensions of Simpson's rules to find the areas of water-planes and similar figures. It also provides some examples to calculate areas. It further explains how to calculate the volume of ship shapes and similar figures, and centre of flotation. The centre of flotation is the centre of gravity or centroid of the water-plane area, and is the point about which a ship heels and trims.
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