Two forms of the transport equation for the wave energy density inherent in two (apparently diverse) formulations of geometrical optics (GO) are discussed on the basis of the relationships among the plane-wave dielectric tensor, the effective dielectric tensor and the effective conductivity tensor. For a generic space- and time-varying medium, a novel relationship between the dielectric tensor and the conductivity tensor is obtained whereupon the equivalence of the two GO formulations is established. The conditions for which either the wave action density or the wave energy density is conserved are discussed.