of floating Bodies, and the Stability of Ships. 
.785, the number of those positions will be sixteen ; of which 
eight will be positions of permanent, and the remaining eight 
positions of unstable equilibrium ; these different species of 
equilibrium succeeding each other alternately while the solid 
revolves round its axis. If the specific gravity should be of 
any value not included within these limits, the solid in revolv- 
ing through 360° will pass through 8 positions of equilibrium 
only ; of which four are positions of permanent, and four of 
unstable equilibrium. 
In the investigations which have preceded, the solid is sup- 
posed to be of uniform figure in respect to the axis of motion, 
so as to make all the vertical sections drawn perpendicular to 
the axis equal. But when the floating body is of such a form 
that the sections drawn through it perpendicular to the axis at 
various points thereof are unequal, a different process, depend- 
ing however on the same principles, will be necessary ; both 
for determining whether the solid will float permanently or 
overset, and for ascertaining the several positions in which it 
will float on the surface of a fluid. 
Let EFCD (dig. 23.) represent a cylinder* placed on 
the surface of a fluid with the axis NP vertical. Sup- 
pose the specific gravity to be such as causes the solid 
to sink to the depth QP ; let it be required to determine 
in what cases, depending on the dimensions and specific 
gravity of the cylinder, it will float permanently in that 
position, and in what cases it will overset. Put the radius 
QA = r ; the specific gravity of the solid = n, that of 
* In this and the following propositions, the plane surfaces which terminate the 
solid are always understood to be perpendicular to the axis. 
N 2 
