(1.) The relation dσ = uqdρq–1 ensures that the tensor of dσ shall always be u times that of dρ Hence, if ρ be the common vector of three series of surfaces which together cut space into cubes, σ possesses the same property. (See § 6 of my paper On Orthogonal Isothermal Surfaces, Trans. R.S.E., 1873–4. In what follows this paper will be referred to as Ω.)