of floating Bodies , and the Stability of Ships. 8g 
of gravity perpendicular to the planes of the square sections ; 
and this condition is insured by making the axis of sufficient 
length; for instance, if it is two or three times longer than 
one of the sides, the solid will not spontaneously revolve on 
any other axis. When the axis is diminished considerably, it 
is certain the body will be spontaneously moveable round 
some other axis ; but it is unnecessary to enter into a detail of 
multiplied instances, since the exposition of principles is the 
material object in disquisitions of this kind. 
The various positions which the square parallelopiped as- 
sumes when floating freely on a fluid's surface depending on 
its specific gravity, are brought under one point of view in the 
following abstract, the line IK denoting the surface of the 
fluid in the figures from fig. 11 to fig. 24. 
If the specific gravity of the solid should be between the li- 
mits o and d- — _L — (flg. 11? 12 , and 13.) that is, be- 
tween o and 0.211, the solid floats permanently on the fluid 
with a flat surface upward, and parallel to the horizon. 
If the specific gravity is between the limits .211 and .25 
(fig. 13, 14, and 15.), the solid floats permanently with a flat 
surface upward, but inclined to the horizon at sundry angles of 
which the limits are o°, corresponding to the specific gravity 
.211 and 26 s 34', corresponding to the specific gravity .25. 
If the specific gravity is between the liniits .25 = ^ and 
—> (Tab. IV. and Tab. V. fig. 15, 16, 17.) the solid floats with 
one angle only immersed under the fluid’s surface, the diagonal 
line being inclined to the vertical at various angles depending on 
the specific gravity, the limits of which angles are 18 0 2 6', cor- 
mdccxcvi. N 
