(23)

and therefore varies as the square of the perpendicular drawn from O to a tangent plane of a certain quadric surface, the tangent plane in question being parallel to (22). If the co-ordinate axes coincide with the principal axes of this quadric, we shall have

Σ(myz) = 0,   Σ(mzx) = 0,   Σ(mxy) = 0;

(24)

and if we write

Σ(mx2) = Ma2,   Σ(my2) = Mb2,   Σ(mz2) = Mc2,

(25)

where M = Σ(m), the quadratic moment becomes M(a2λ2 + b2μ2 + c2ν2), or Mp2, where p is the distance of the origin from that tangent plane of the ellipsoid

x2+ y2+ z2= 1,
a2 b2c2

(26)