The properties of conformal transformations developed in the previous paper (Hotine 1965) are used to construct triply orthogonal coordinate systems from a scalar N. Classical doctrine on the subject requires that N should satisfy a third-order partial differential equation known as the Darboux equation, whereas no such restriction seems necessary in the conformal approach. If the Darboux equation is not a condition for triple orthogonality, but a property of the space, as this investigation suggests may be the case, then the effect on the geometry of the gravitation field would be considerable. It is accordingly important to resolve the question.