122 Mr. Atwood's Propositions determining the Positions 
will cause the vessel to overset : in this case, as the vessel is 
gradually inclined from the upright, the stability will first 
increase to a maximum, and afterwards decrease ; differing 
altogether from the variation of the stability in the preceding 
case, when the vessel was supposed to be of a cylindrical form. 
Although vessels are usually so constructed that during any 
inclination from o° to qo° they do not pass through a po- 
sition of equilibrium ; yet there seems reason to suppose 
that in some vessels the stability increases to a maximum, 
and afterwards decreases when the angle of inclination is 
farther augmented : whenever a vessel of this description 
should be inclined beyond the angle where the stability is 
greatest, the following consequence must necessarily ensue ; 
if the angular velocity should be considerable, the rolling of 
the ship will be extended to large angles of inclination, be- 
cause when the stability is more and more diminished as the 
angle of inclination is augmented, more time will be required 
for the diminished force to react against the ponderous mass 
of the vessel, in order to restore it to the upright. It is cer- 
tain that the angle, as well as the celerity or slowness of rolling, 
depend on other elements, as well as on the stability, particu- 
larly on the weight and extent of the masts and sails, and the 
position of the ballast and lading : but in comparing the vibra- 
tions of the same vessel through different arcs, those elements 
are the same, while the force of stability alters continually as 
' the angles of inclination are increased or diminished. 
These alternate vibrations of a ship in rolling have been 
deemed analogous to the oscillations of a pendulum ; and in 
order to reduce to some kind of measure so essential a quality 
of vessels, M. Bouguer and other writers propose to find a 
pendulum isochronal to the oscillations of a ship. This pro- 
