The extension to the case where the liquid is bounded externally by a fixed ellipsoid λ = λ1 is made in a similar manner, by putting

φ = xy (χ + M),

(10)

and the ratio of the effective angular inertia in (9) is changed to

(B0 − A0) − (B1 − A1) + a12 − b12 abc
a12 + b12 a1b1c1
.
a2 − b2− a12 − b12 abc− (B0 − A0) + (B1 − A1)
a2 + b2 a12 + b12a1b1c1

(11)

Make c = ∞ for confocal elliptic cylinders; and then

Aλ = ∫∞λ ab= ab( 1 − √ b2 + λ),
(a2 + λ) √ (4a2 + λb2 + λ) a2 − b2a2 + λ

(12)

Bλ = ab( √ a2 + λ− 1 ),   Cλ = 0;
a2 − b2 b2 + λ