(29)
will be M (a2λ2 + b2μ2 + c2ν2 + p2), by (15). This will have a given value Mk2, provided
p2 = (k2 − a2) λ2 + (k2 − b2) μ2 + (k2 − c2) ν2.
(30)
Hence the planes of constant quadratic moment Mk2 will envelop the quadric
| x2 | + | y2 | + | z2 | = 1, |
| k2 − a2 | k2 − b2 | k2 − c2 |
(31)
and the quadrics corresponding to different values of k2 will be confocal. If we write
k2 = a2 + b2 + c2 + θ,
b2 + c2 = α2, c2 + a2 = β2, a2 + b2 = γ2
(32)