The fundamental fact on which the kinematic transformations of the Special Theory were based was that light was found to travel with the same velocity, and in a straight line, relative to all the observers, although they were in motion relatively to each other. Now it is a fundamental assumption of the General Theory that the analogy between the g's of a non-Newtonian frame and the potentials of the non-Newtonian forces which act on particles with respect to that frame is to be extended to the potentials of Newtonian forces. Suppose the equations are found for the path of a beam of light with respect to any frame, in terms of the g's of that frame, on the assumption that it would move accurately in a straight line with a uniform velocity relative to a Newtonian frame in the absence of gravitation.