s8i 
the Stability of Ships. 
lace, intersecting the vessel in a plane passing through the line 
CH, when the vessel is inclined, will so divide the areas of the 
several sections, that although the area ASH/6 may not be equal 
to the area BSCc, in any of the vertical sections, yet the volume 
immersed, corresponding to, and included between, the areas of 
the figures ASH/6, taken from the head to the stern of the ship 
shall be equal to the emerged volume which is included between 
the areas BSCc, in the several sections. Suppose the breadth 
of any section at the water-line* to be denoted by BA, and to 
be bisected in the point D. A vertical plane passing through 
the vessel s longer axis and the centre of gravity G,-f* and divi- 
ding the ship into two parts perfectly similar and equal, will 
pass through the points D, in all the sections : this plane may 
be termed the plane of the masts. It is easily shewn, that at 
whatever distance DS, from the middle point D, the plane of 
the water’s surface, passing through the lines CH, intersects 
the line DA in any one section, when the vessel is inclined 
through the angle ASH, it will intersect the line DA at the 
same distance from the middle point D in all the other sec- 
tions; that is, the distance DS will be the same in all the 
sections : for, by the supposition, the vessel is inclined round 
the longer axis, and consequently, the intersection of the two 
planes, passing through the lines BA and CH, will be parallel 
The same letters which are used to denote the several lines, in this vertical section, 
must be understood to represent the lines similarly drawn in each of the other sections. 
In the present instance, BA does not represent the breadth at the water’s surface, of the 
principal, or any other individual vertical section, but represents generally that breadth, 
in any of the sections that may be referred to. 
f Represented by the point G projected on the plane BOA. The centre of gravity 
h is, in like manner, here represented by projection on the same plane. 
MDCCXC VIII. O O 
