(13)
for liquid filling the cylinder; and
| φ | = | th η | , |
| φ1 | th (η − α) |
(14)
over the surface of η; so that parallel to Ox, the effective inertia of the cylinder η, displacing M′ liquid, is increased by M′th η/th(η- α), reducing when α = ∞ to M′ th η = M′ (b/a).
Similarly, parallel to Oy, the increase of effective inertia is M′/th η th (η − α), reducing to M′/th η = M′ (a/b), when α = ∞, and the liquid extends to infinity.
32. Next consider the motion given by
φ = m ch 2 (η − α) sin 2ξ, ψ = −m sh 2 (η − α) cos 2ξ;
(1)
in which ψ = 0 over the ellipse α, and