the Stability of Ships . 25 1 
point Z : GZ is the measure of the vessel's stability. For, since 
O is the centre of gravity of the volume immersed, when the 
vessel is inclined, and the line MF is drawn through it, per- 
pendicular to the water’s surface CH, QM will be the direction 
in which the pressure of the fluid acts, to turn the vessel round 
an a^is passing through G ; and GZ, being the perpendicular 
distance of this line from the centre of gravity, will be the 
measure of the vessel’s stability. 
Let the sine of the angle of the vessel’s inclination ASH, or 
OMF, be represented by the letter s to radius = 1 : by the 
2DA 3 
BA 3 
12 xarea BOA 
if, 
f> 
12 xarea BOA 
and ET 
properties of the circle ME = ■ „ „ A 
* r 3 Xarea BOA 
therefore, BA be made = t, ME 
t 3 5 
“ 12 x area BOA * 
The area representing the volume displaced is here con- 
sidered as entirely circular : but if it should be of that form 
only to the extent of the sides *AH, BC, the remaining part of 
the area being of any other figure, and the whole area un- 
der water should be denoted by V, the line ET will be 
t 3 s 
area BOA 
X 
or ET 
t 3 s 
Let GE be denoted 
12 xarea BOA ~ V ’ ~ 12V’ 
by d ; then ER = ds, and RT, or the measure of the vessel’s 
t 3 s 
stability -('GZ 
12V 
— ds. 
* Proposition and observations in pages 213, 214. 
t tn this expression for the measure of stability, s is the sine of the angle of the 
vessel s inclination, whatever be its magnitude : this value, for the stability of vessels 
which have a circular form, is the same with that which M. Bouguer gives for ves- 
sels of any form, when the angles of inclination are evanescent, the breadths at the 
water-line being — t, and the other conditions the same ; from which circumstance, 
the following remarkable conclusion is inferred : if the measure of stability should be 
calculated for finite angles of inclination, by the rule M. Bouguer has given for the 
Kk 2 
