Abstract: The problem concerning the ray theory fcr lossy media seems to have been left untouched in the field of acoustics.
In this paper, starting from the basic equations for a viscous and heat-conducting fluid medium and taking into account also the influences due to gravitational field and the steady motion of the medium, the "local" dispersion relation for the stratified atmosphere has been derived. Furthermore, an extension of Hamilton equations, which have been deduced from the Sommerfeld-Runge refraction law and Whitham ’s conservation law of wave crests, leads to a corresponding extension of Haselgrove ’s equations for calculating the ray paths. This set of equations can be used as the basis for numerical integration and thus yields the acoustic ray paths as referring to some specific atmosphere models. Although such paths can have complex space coordinates, only those with end points in real space are physically significant.