Ill 
of floating Bodies, and the Stability of Ships. 
tained by having recourse to the theorem demonstrated in 
page 59, where it is shewn, that the stability of a vessel is 
truly measured by its weight, and the distance between the 
two vertical lines which pass through the centres of gravity of 
the vessel and the centre of gravity of the immersed volume ; 
or if s be put to represent the sine of the angle of inclination 
from the perpendicular, V = the total displacement or volume 
immersed ; A — the volume immersed in consequence of the 
inclination ; b — the horizontal line be ; d — the line GO, 
(fig. 2.) and W = the weight of the vessel, the measure of the 
vessel's stability appears by this theorem to be W x GZ = 
ds x W. In applying this expression to any case in 
practice, it is supposed that the position of the centre of gra- 
vity of the ship, and the position of the centre of gravity of 
the immersed volume, when the ship floats in an upright posi- 
tion, are both known, and consequently the distance of those 
points, represented by the line GO — d, is a given or ascer- 
tained quantity. The total displacement is supposed to have 
been determined by previous measurements, which quantity is 
denoted by the letter V ; and consequently the weight of a 
quantity of water, the volume of which is V, will be = W, or 
the vessel's weight, s, the sine of the angle of inclination 
from the upright position, is necessarily given from the nature 
of the case, and may be of any magnitude. The only quan- 
tity which remains to be determined, for ascertaining the mea- 
sure of the vessel's stability, is bA. To facilitate this determi- 
nation the following observations are premised. If a line be 
conceived to pass through the centre of gravity parallel to 
the horizon from the head to the stern, when the ship floats 
in an upright position, that line is termed the longer axis, to 
distinguish it from another line, also horizontal, which passes 
