Abstract. The ground- and space-based missions detected the presence of small-amplitude periodic oscillations or waves in coronal structures. Observations of oscillations in prominences and in surrounding plasma suggest that they are of small amplitude and therefore can be interpreted in terms of linear MHD waves. Prominence seismology allows us to combine wave observations and theory to determine unknown parameters. The departure of period ratio P1/2P2 (between the period of fundamental mode and twice that of its first overtone) from unity provides information about the structure of prominence. We consider analytically the effects of radiation, thermal conduction and compressive viscosity on the period ratio P1/2P2 for a longitudinal propagating slow wave in solar prominence. We investigate the dependence of this ratio on the equilibrium parameters of prominence and its possible use as a diagnostic tool for prominence seismology.