the Stability of Ships. 
213 
Through the points C and H, (fig. 1.) let the lines CF, 
WH, be drawn parallel to BA. The position of the points 
M and I, the magnitude of the line KL, and the areas or 
volumes ASH, BSC, being the same, whatever alteration 
may take place in the volume V, or the entire volume dis- 
placed, the quantity KL x area ASH or b A will remain 
the same : and, since the line ET= it will follow, that 
the zone WHFC, situated between wind and water, (ac- 
cording to a technical expression,) not being altered, ET will 
be in the inverse proportion of V, or the total volume dis- 
placed. If, therefore, the shape of the vessel under the line CF 
should be any how changed, so as to coincide with another 
figure, suppose C cfF, (fig. 2.) instead of COF, (fig. 1.) the 
volume C cf F being equal to the volume COF, the line ET 
will be the same in both cases. In consequence of this change 
of figure, the position of the point E, (fig. 1.) or centre of gra- 
vity of the volume BOA, may be situated higher or lower in 
the line OD ; yet, if the centre of gravity G is so adjusted by 
ballast, or other means, that the distance GE shall be the 
same, the stability of each vessel, BCOA (fig. 1.) and BC cf A 
(fig. 2.) will be perfectly the same, when inclined to the same 
angle ASH from the upright. It must also be observed, 
that since ET is always greater in the same proportion in 
which the volume immersed BOA is less, the zone WH CF 
being both in magnitude and form the same, having found 
by construction or calculation the value of the line E T cor- 
responding to any given volume displaced, suppose V = 
BCOA, (fig. 1.) the line E t corresponding to any other mag- 
nitude of volume displaced, suppose z> = BCV w l FA, (fig. a .) 
will he immediately inferred for, since V . v : : E t : E T, it 
