v′ = v + zP − xR = 2b2Ω1z − 2b2Ω3x,
b2 + c2 a2 + b2

(5)

w′ = w + xQ − yP = 2c2Ω2x − 2c2Ω1y,
c2 + a2 b2 + c2

(6)

P = Ω1 + ξ, Q = Ω2 + η, R = Ω3 + ζ.

(7)

Thus

u′ x+ v′ y+ w′ z= 0,
a2 b2c2

(8)

so that a liquid particle remains always on a similar ellipsoid.