297 
the Stability of Ships. 
from the axis; which force is equivalent to a weight or pressure* 
of 241 tons, acting at a distance of 21.58, or half the breadth 
at the water-line from the axis. 
In this computation, the distance GE, between the centres of 
gravity G and E, has been assumed without considering the 
absolute position of these points, in respect to the water-section 
or keel. But the distance DE, or OE, ought to be known, since 
the point E being fixed in the same vessel, when the weight is 
given, and the centre of gravity G being within certain limits 
moveable, the adjustment of this centre, by means of the lading 
and ballast, will be better regulated, if the position of the point 
E be first ascertained: the distance DE will be found from 
having given the areas of the 12 horizontal sections, and the 
contents of the volume between the section 1 and the keel. 
Suppose the areas of 12 horizontal sections of the vessel to 
be given, as they are expressed in page 294 ; let the displaced 
volume be conceived divided into laminae, or very thin solids, 
of which the bases are the areas of the successive horizontal sec- 
tions, and the thickness a small increment of the vertical 
axis. The sum of the products arising from multiplying each 
of these segments into its perpendicular distance from the sec- 
tion 12, also a similar sum of products for the solid contents 
adjacent to the keel, will be found from the computation 
subjoined. 
* This equivalent weight is not here supposed to be counterbalanced by the wind, 
which probably never acts with sufficient force to keep a vessel of this weight inclined 
permanently from the upright to so great an angle. But the measure of force which 
acts to turn the vessel round the longer axis, when inclined to this angle of 30°, is 
precisely that which is here stated, according to the given conditions. 
Qq 
MDCCXCVIII, 
