One of the daunting problems in searching for a correct model of the speed of light is the contradiction between the Michelson-Morley experiment and the Sagnac effect. I have been working on a new theory called Apparent Source Theory (AST ), which is based on three assumptions: 1. The effect of absolute motion of an inertial observer is to create an apparent change in the time of light emission. 2. The center of the light wave fronts moves with the same velocity as the absolute velocity of the inertial observer and the velocity of light depends on the mirror velocity relative to the observer 3. Two observers/detectors that happen to be at the same point in space at the same time instant and moving with equal velocities will observe identical physical phenomena (for example, fringe position). The third postulate is used to analyze light speed problems involving accelerating observers/detectors. AST has been successful in providing consistent explanations for many light speed experiments. However, the precise application of AST to the Sagnac effect has been a challenge for AST. In this paper, a new analysis of Sagnac effect based on AST is presented. One of the unexpected findings is that the light beam propagating in the same direction as the observer will take less time to reach the observer than the light beam propagating in the opposite direction. Unconventionally, the fringe shift in the Sagnac effect is not due to a difference in path lengths of the counter-propagating light beams, but due to difference in their velocities according to the ballistic hypothesis. Experimental testing of this claim is proposed.