48 Mr. Atwood's Propositions determining the Positions 
with this observation, positions may be assigned, in which a 
solid is immersed in a fluid to the true depth according to its 
specific gravity, and the centre of gravity of the solid and 
that of the part immersed are in the same vertical line, yet 
the solid does not rest in any of these positions, but assumes 
some other in which it will continue permanently to float. 
To make this evident, a very obvious instance may be referred 
to. Suppose a cylinder, the specific gravity of which is to 
that of a fluid on which it floats as 3 to 4; and let the axis of 
the cylinder be to the diameter of the base as 2 to 1 : if this 
cylinder is placed on the fluid with its axis vertical, it will 
sink to a depth equal to a diameter and a half of the base ; and 
as long as the axis is sustained in a vertical position by ex- 
ternal force, the centre of gravity of the solid, and the centre 
of the immersed part, will be situated in the same vertical 
line : but the solid will not float permanently in that posi- 
tion ; for as soon as external support is removed, it falls from 
its upright position, and remains floating with the axis hori- 
zontal. If the axis of the cylinder is made only \ instead of 
twice the diameter of the base, the solid being placed with its 
axis vertical, will sink to the depth of -f of a diameter, and 
will float permanently in that position. Even if the axis 
should be placed not exactly coincident with the vertical, but 
in a direction somewhat inclined to that line, the solid will 
change its position until it settles permanently with the axis 
perpendicular to the horizon. 
The cylinder here instanced is caused either to float per- 
manently with its axis vertical, or to overset, according to the 
different proportions between the length of the axis and the 
diameter of the base : although an exact estimate of the effects 
