1816.] On the Stability of Vessels, 191 
gravity in both cases being at the water’s surface, and the maximum 
is at an angle of inclination of 20°; but when the centre of gravity is 
situated 2 an inch below the surface of the water, model lz has the 
advantage from 15° and upwards, as appeared from experiments; 
when the draft of water was decreased | inch more, being reduced 
to 1:5 inch, the stability was increased but little. It is therefcre 
probable that if the bottom of a boat be a semi-ellipsis, and the 
top sides, or the part above the water, be perpendicular to the 
horizon, or parallel to the plane of the masts, the maximum of 
stability, when the centre of gravity isat the load water line, is 
nearly 1. of the beam, From whence it appears that great advan- 
tage accrues by reducing the depth rather than increasing the 
breadth of boats designed for shoal water; as the latter, under the 
limits above-mentioned, are not only stiffer, but lighter, and of 
course more easily transported from place to place. But as vessels 
with a shallow draft of water, unless very Jong, are leewardly under 
sail, [ know of no contrivance to obviate this defect comparable to 
Admiral Schank’s ingenious invention of the sliding keels. 
Model 19 shows by experiments that if those parts of the vessel 
above the surface of the water incline inwards, the stability is 
diminished. In experiments with models tI, 12, and 13, the 
metacentre rises as the angle of inclination increases. In experi- 
ments with models 14, 15, 16, 17, 18, and 19, the metacentre 
lowers as the angle of inclination increases.. In experiments with 
models 20, 21, 22, and in the compound figure, model 23, the 
metacentre is.stationary. ~ 
From these experiments it is concluded that the draft of water 
should be 2 of the breadth, exclusive of the kee], if the centre of © 
gravity and the greatest breadth are at the surface of the water. 
This proportion would answer for men of war, for ships heavily 
rigged, or designed'to carry part of the cargo on the deck; but 
should a ship be designed to carry heavy materials, it should be 
' narrower and deeper, which would prevent its being laboursome at 
sea, and less likely to be dismasted; for broad and shallow vessels 
laden with heavy materials are liable to lose their masts, from the 
violent and jerking motion to which they must necessarily be ex- 
posed in agitated waters, as their centre of gravity is situated much 
beneath the surface of the water. If the greatest vertical section 
or midship-bend of a vessel be a parallelopipedon, it is evident, 
from experiments with model 9, that the draft of water, if the 
centre of gravity be at the surface of the water, must bear a less 
proportion than % to the breadth: and it is worthy of remark that 
a vessel of the last-mentioned shape, when the depth to which it is 
immersed is small, will be sufficiently stiff to a certain point, and 
overturns suddenly if the angle of inclination be increased, which 
was the case with model 8. Immersed 2} inches, and its centre 
of Bravity 44 inches, it had stability at 30°, but overset suddenly at 
35°. ‘The constructors of the Thames barges appear to be sensible 
of this, and make the vertical sections frystums of triangles, which 
