We investigate rigorously the behaviour of light propagation in the closed contour of the linear Sagnac effect. Assuming that the local light speed is c in a section of the contour, our approach makes it possible to determine the local speed in the other sections. We show that, if standard clock synchronization is adopted, the speed c turns out to be invariant in an open section of the contour only. Our result is due to the distinctive physical feature of the 'time gap' introduced by relative simultaneity in the closed contour.
