the Stability of Ships. 285, 
The ordinates drawn in the several sections being set down, 
in regular order, the area of any horizontal section is to be 
found from the corresponding series of ordinates, by means of 
the Rules 11. and ill, and, by the same rules, from the areas of 
the horizontal section's so determined, the solid contents of the 
total volume immersed are to be inferred ; some allowance be- 
ing made for the irregular parts of the volume adjacent to the 
head and stern, if attention to these additional volumes should 
be thought necessary.. That part of the volume which is con- 
tained between the keel and the nearest horizontal area, is ob- 
tained by first finding the area of each vertical section between 
the keel and nearest ordinate : from, these areas, by means of 
the Rules ll and m. the solid contents of the volume between 
the keel and nearest horizontal section will be measured, and is 
to be added to the volume before found, which is contained be- 
tween the two extreme horizontal sections. 
Let the solid contents of the displaced, volume be denoted 
hy V.. 
From the areas of the horizontal sections, and the common in- 
terval between them, the distance DE, of the centre of gravity of 
the volume immersed, from the water-section, is to be obtained 
by means of the Rules 11. and in.; by finding the sum: of the 
products arising from multiplying each evanescent solid, of 
which the base is any horizontal section, and the thickness a 
small increment of the vertical axis, into that small increment, 
also into its distance from the water-sec.tion : the sum of these 
products, being divided by the solid contents of the volume dis- 
placed, will be the distance DE, of the water-section, from the 
centre of gravity of that volume. 
The- position of the vessel’s centre of gravity G, depends ; 
