x² y² z²
------------- + ------------- + ------------- = 1 (3)
a² + [lambda] b² + [lambda] c² + [lambda]
and a velocity function of the form
[phi] = x[psi], (4)
where [psi] is a function of [lambda] only, so that [psi] is constant
over an ellipsoid; and we seek to determine the motion set up, and the
form of [psi] which will satisfy the equation of continuity.
Over the ellipsoid, p denoting the length of the perpendicular from
the centre on a tangent plane,
px py pz
l = -------------, m = -------------, n = ------------- (5)
a² + [lambda] b² + [lambda] c² + [lambda]
p²x² p²y² p²z²
1 = ---------------- + ---------------- + ----------------, (6)
(a² + [lambda])² (b² + [lambda])² (c² + [lambda])²
p² = (a² + [lambda])l² + (b² + [lambda])m² + (c² + [lambda])n², (7)
= a²l² + b²m² + c²n² + [lambda],
dp d[lambda]
2p-- = ---------; (8)
ds ds