214 Mr. Atwood's Disquisition on 
follows that E t = ET - X -— , or because E T = by substitu- 
tion, Et = — . For these reasons, the determination of sta- 
bility does not require that the form of the entire volume 
displaced should be given, but the form only of the zone 
W C H F, (fig. i. and 2.) including the angle of the vessel's 
inclination ASH; these conditions, together with the mag- 
nitude of the immersed volume, and the distance between the 
two centres of gravity G and E, are sufficient for finding 
the measure of stability, at any given angle of inclination 
from the upright. 
CASE I. 
The sides of a vessel are parallel to the plane of the masts, 
both above and beneath the water-line. 
QBCOAH (fig. 3 ) coincides with the vertical section of 
a vessel when it floats upright and quiescent, and is inter- 
sected by the water's surface in the line B A ; the sides Q C, 
HD, are parallel to each other, and to the plane of the masts 
WO, and are therefore perpendicular to BA. G is the centre 
of gravity of the vessel ; V represents the magnitude of the 
volume immersed under the water ; the centre of gravity of 
this volume is situated at E. Suppose the vessel to be in- 
clined from its quiescent position through any given angle, 
it is required to express, by geometrical construction, the mea- 
sure of the vessel's stability, when thus inclined. Bisect B A 
in the point S, and through S draw C SH, inclined to BA, at 
the given angle of the vessel's inclination from the upright. 
Bisect BC in F, and AH in N ; and join SF and SN. In the 
line SF take SI to SF as 2 to 3 ; also, in the line SN, take 
