φ = xψ,
(4)
where ψ is a function of λ only, so that ψ is constant over an ellipsoid; and we seek to determine the motion set up, and the form of ψ which will satisfy the equation of continuity.
Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane,
| l = | px | , m = | py | , n = | pz |
| a2 + λ | b2 + λ | c2 + λ |
(5)
| 1 = | p2x2 | + | p2y2 | + | p2z2 | , |
| (a2 + λ)2 | (b2 + λ)2 | (c2 + λ)2 |
| p2 = (a2 + λ) l2 + (b2 + λ) m2 + (c2 + λ) n2, = a2l2 + b2m2 + c2n2 + λ, |
(7)
| 2p | dp | = | dλ | ; |
| ds | ds |