(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 − b2k2 − 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)