and first suppose the liquid to be frozen, and the ellipsoid to be rotating about the centre with components of angular velocity ξ, η, ζ; then
u = − yζ + zη, v = − zξ + xζ, w = − xη + yξ.
(2)
Now suppose the liquid to be melted, and additional components of angular velocity Ω1, Ω2, Ω3 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function
| φ = − Ω1 | b2 − c2 | yz − Ω2 | c2 − a2 | zx − Ω3 | a2 − b2 | xy, |
| b2 + c2 | c2 + a2 | a2 + b2 |
(3)
as may be verified by considering one term at a time.
If u′, v′, w′ denote the components of the velocity of the liquid relative to the axes,
| u′ = u + yR − zQ = | 2a2 | Ω3y − | 2a2 | Ω2z, |
| a2 + b2 | c2 + a2 |
(4)