In the kinematic theory of wave propagation (e.g. geometrical optics) a quantity J is needed in the calculation of wave intensity either through transport equations or the principle of conservation of wave action. This quantity is a spatial Jacobian with respect to a parameter space and represents a volume element convected with the rays. To avoid its direct computation as a Jacobian, derived ray equations are obtained whose solutions lead to alternative ways of calculating J. This approach is specialized to cases involving Snell's law (with cylindrical and spherical as well as planar symmetry) and non-dispersive propagation. The behaviour of the theory under Lorentz transformations is shown.