If φ(x, y, z) be any homogeneous quadratic function of x, y, z, we have
Σ {mφ (x, y, z)} = Σ {mφ (x + ξ, y + η, z + ζ) }
= Σ {mφ (x, y, z)} + Σ {mφ (ξ, η, ζ)},
(14)
since the terms which are bilinear in respect to x, y, z, and ξ, η, ζ vanish, in virtue of the relations (7). Thus
Ix = Iξ + Σ(m)x2,
(15)
Iyz = Iηζ + Σ(m) · (y2 + z2),
(16)
with similar relations, and
IO = IG + Σ(m) · OG2.