the Stability of Ships. 283 
computing according to the Rules 11. and in.; suppose this 
volume to be denoted by the letter P, and the volume contained 
between the planes DB, DN, and the side of the vessel, found 
by similar operations, to be denoted by the letter Q. Let the 
area* of the section of the vessel passing through the lines 
NDW be measured, from having given the lines NW in all 
the sections from the head to the stern, and let this area be 
put — R. If the volumes P and Q should be unequal, P being 
the greatest, in the line DA, set off, in each section, a line DS 
= R x ■ aBw • If a plane CSH be drawn passing through all 
the points S, and inclined to the plane BA at the given angle of 
the vessel’s inclination, the solid contents of the volume between 
the planes SA, SH, and the intercepted side of the vessel, will 
approximate to equality with the volume contained between the 
planes SB, SC, and the intercepted side of the vessel. Since, 
therefore, the water’s surface coincides with the plane BA when 
the vessel is upright, when it is inclined round the longer axis, 
through the given angle ASH, the water’s surface will inter- 
sect the vessel in the direction of a plane passing through the 
lines CH, in all the sections. 
Let the solid contents of the volume immersed, or emerged, 
by the inclination, be denoted by the letter A. 
In the section QBOAW, let M be the centre of gravity 
of the triangle ASH, and let h be the centre of gravity of the 
curvilinear area AHZ>; also, let I be the centre of gravity of 
the triangle BSC, and let c be the centre of gravity of the 
curvilinear area BCc; through these points, draw the lines 
• That is, the area of the section coinciding with the water’s surface, when the ves- 
sel is inclined to the giyen angle. 
Oo 2 
