212 
Mr . Atwood's Disquisition on 
principally inferred from the general theorem for ascertaining 
the stability of floating bodies ; which is here subjoined, to 
avoid the necessity of future references, as well as for the 
purpose of stating more distinctly the observations which fol- 
low it. 
Let M (fig. 1.) be the centre of gravity of the volume ASH, 
which has been immersed under water, and let I be the centre 
of gravity of the volume BSC, which has emerged above the 
water's surface, in consequence of the vessel's inclination ; 
through the points M and I, draw the lines ML, IK, per- 
pendicular to the line CH, which coincides with the water's 
surface when the vessel is inclined : through E, the centre of 
gravity of the displaced volume BOA, draw EV parallel and 
equal to KL, and through G draw GU parallel and GR perpen- 
dicular to CH ; according to the theorem, the line ET will be 
determined by the following proportion. As the total volume 
displaced BOA is to SAH, the volume immersed in consequence 
of the inclination, so is KL or EV to ET ; and, since the angle 
EGR is equal to the vessel's inclination ASH, and the dis- 
tance GE is supposed to be given, the line ER will be known ; 
because ER is to GE as the sine of the angle EGR to radius; 
ER being subtracted from ET will leave RT or GZ, equal 
to the measure of the vessel’s stability. 
Suppose the line K L to be denoted by the letter b : let 
the volume ASH be represented by A, and the volume BOA 
by V. Then, according to the theorem, since V : A : : : : b : 
ET, it follows that ET = ^, and if GE is put = d, an ds 
— the sine of the angle to which the vessel is inclined, radius 
being = 1, E R will be = ds ; and the measure of the ves- 
sel's stability RT or GZ = j — d s* 
