We derive an integral formula as an estimate of the averaged, steady-state transmission ratio for two points in a channel whose environmental parameters vary slowly with range. We base the derivation on the theory of ray acoustics with lossy specular reflection from the boundaries. The averaging eliminates all but gradual changes with range of the transmission loss (TL); dependence on the depth of each point is retained. Detailed tracing of ray paths over many cycles is not required. Numerical results for an isogradient channel with constant bottom slope are exhibited, and an appendix contains modal interpretation of the general formulation.