Having established in a previous article that the postulate of the constancy of speed light of Special Relativity Theory is false in general, we investigate a procedure to determine the different speeds of light in vacuum for different Galilean reference frames attached to a particular electromagnetic system. As it was done in the previous paper, we consider a modified Lorentz transformation incorporating different speeds of light for different inertial frames, and based on it we examine two media that axe observed from the two reference systems, to be simple and lossy. In other words we consider an electromagnetic system that consists of a rest frame (to be denoted by K), constituted by a simple medium but with loss, and a frame (to be denoted by K) in uniform rectilinear motion with respect to the first, wherein another simple, lossy medium fills the half space such that the interface of the two media is an infinite plane, perpendicular to the direction of motion of K'. The electromagnetic fields are derived for the electromagnetic system in hand and using the boundary conditions on the plane interface of the two media, a relation is derived, using which together with a relationship obtained in above mentioned paper, we obtain the speeds of light in vacuum for the two inertial reference frames. The speeds found, are functions of the material properties of the two media such as conductivity, magnetic permeability, dielectric permittivity, frequency, and the relative speeds of the reference frames. This result suggests that speed of light in vacuum for a particular inertial reference frame is merely a constant and the expectation that it be independent of material proper-ties of the media, frequency, and the relative speeds of the reference frames is not necessarily true, at least where Special Relativity Theory fails to account for the loss in the system. The results of this work axe a direct consequence of the above mentioned paper in which Special Relativity Theory is negated.