Note on the Stability of the Equilibrium of a Circular Cylinder floating in a Liquid

Abstract

§6. In this paper, the stability of the equilibrium of a uniform circular cylinder floating in a homogeneous liquid is discussed, with a special intention of studying the case when the cylinder floats at rest in the liquid with its axis inclined at some angle to the vertical.
Confining ourselves to a special but rather interesting case in which the density of the liquid is twice as large as that of the cylinder so that the centre of gravity of the body lies on the surface of the liquid, a detailed discussion is made on the stability of the equilibrium of the cylinder.
Thus, it is found that four different typical configurations are possible for the circular cylinder in stable equilibrium, corresponding with four different groups of values of the ratio l/a (=λ), where 2l is the height of the cylinder and 2a its diameter