210 Mr . Atwood's Disquisition on 
CH : the area under water will now be COFAH, equal to the 
area BCOFA. 
Let the section WBCOFAH, and all the other vertical sec- 
tions intersecting the longer axis at right angles, be assumed 
similar and equal figures, projected on the plane WBOAH : in 
consequence, the area BOA will be to the area ASH, as the 
entire volume immersed is to the volume immersed by the 
vessel's inclination. Moreover, if E is the centre of gravity of 
the area BOA, that point will truly represent the centre of 
gravity of the volume immersed, when the vessel is upright : 
if the centre of gravity of the immersed area COFAH, when 
the vessel is inclined, should be situated at g, that point will 
also coincide with the centre of gravity of the corresponding 
displaced volume. For these reasons, the spaces BOA, ASH, 
COFAH, will be denominated, in the following pages, indif- 
ferently, areas or volumes. 
Let G be the centre of gravity of the vessel, by which term, 
the vessel and its contents, of every kind, are always under- 
stood to be implied. Through G, draw GU parallel to CH : 
and through g, draw gZ perpendicular to C H. When the 
ship is inclined round the longer axis, through the angle ASH, 
the fluid’s pressure acts in the direction of the vertical line 
gZ, with a force equal to the vessel’s weight ; and the sta- 
bility or effect of this force, to turn the vessel round an axis 
passing through G, perpendicular to the plane BOA, will be 
greater or less, according to the magnitude of the line G Z, 
or distance from the axis at which the force of pressure acts. 
In the same vessel, the weight not being altered, the stability, 
at different angles of inclination from the upright, will be truly 
measured by the line G Z ; and, in different vessels, or in the 
