Having established in previous articles that the principle of the constancy of speed of light of Special Relativity Theory is false in general, we examine some consequences of the non-constancy of speed of light in vacuum for different Galilean reference systems. We consider the modified Lorentz transformation incorporating different speeds of light for different inertial frames and which is a result of the non-constancy of speed of light in vacuum for different Galilean reference systems, i.e., reference systems in uniform rectilinear motion with respect to each other. Some consequences of this transform including the limit speed concept, transformation of lengths, summation and transformation of velocities are considered. Results of the transformation of the electromagnetic field are given. Also discussed are some consequences of the relativity of the electromagnetic field, all under the modified Lorentz transformation. These include variance of the electric charge, transformation of the potentials, transformation of the force.