offloating Bodies, and the Stability of Ships. 51 
1st.* The equilibrium of stability, in which the solid floats 
permanently in a given position. 
2dly. The equilibrium of instability, in which case the solid, 
although its centre of gravity and that of the part immersed 
are in the same vertical line, spontaneously oversets, unless 
sustained by external force. This kind of equilibrium is si- 
milar to that which subsists when a needle, or other sharp- 
pointed body, is placed vertically on a smooth horizontal sur- 
face. 
3dly. The third species, being a limit between the two 
former, is called the equilibrium of indifference, or the insen- 
sible equilibrium, in which the solid rests on the fluid indif- 
ferent to motion, without tendency to right itself when in- 
clined, or to incline itself further. 
These different kinds of equilibrium may perhaps be more 
clearly perceived, by referring to the instance in which a cy- 
linder was supposed to be placed on the surface of a fluid with 
the axis vertical. If the axis is assumed double the diameter 
of the base, the solid oversets, the equilibrium of position being 
that of instability : but if the length of the axis is only half 
the diameter of the base, the solid floats permanently with the 
axis vertical. It seems evident, therefore, that there must be 
some intermediate proportion between the cylinder’s axis and 
the diameter of the base r greater than 1 to 2, and: less than 2 
to 1, which will correspond to the case intermediate, where 
stability ceases, and' instability begins : this is the precise pro- 
portion when the equilibrium is of the species called the equi- 
librium of indifference, or the insensible equilibrium. 
When a solid body floats permanently on the surface of a 
* Euler. Tbe'orie complette de la.Co)istrtiction et M anoeuvre des Vaiszeaux, chap. iv. 
FI 2 
