(8)
Thence
| dφ | = | dx | ψ + x | dψ |
| ds | ds | ds |
| = | dx | ψ + 2 (a2 + λ) | dψ | l | dp | , |
| ds | dλ | ds |
(9)
so that the velocity of the liquid may be resolved into a component -ψ parallel to Ox, and −2(a2 + λ)l dψ/dλ along the normal of the ellipsoid; and the liquid flows over an ellipsoid along a line of slope with respect to Ox, treated as the vertical.
Along the normal itself
| dφ | { ψ + 2(a2 + λ) | dψ | } l, |
| ds | dλ |
(10)
so that over the surface of an ellipsoid where λ and ψ are constant, the normal velocity is the same as that of the ellipsoid itself, moving as a solid with velocity parallel to Ox