Now we have seen that fields of force are accompanied by potential distributions. Hence it follows that, whereas, with respect to a Galilean frame, the inertial potential is zero at every point, or at least maintains some constant value, in the case of accelerated frames this inertial potential must vary from place to place in the frame. The magnitude of the force at any point of an accelerated frame is given, therefore, by a mathematical expression involving the variations in value of the potential in the neighbourhood of the point considered. All we have explained so far pertains to classical science, but it appeared necessary to mention these results briefly before proceeding to a more systematic study of Einstein’s theory. We shall now see how all these results find a natural place in the space-time theory. Consider a Galilean frame and an object moving freely in this frame. Its path will of course be rectilinear and its speed uniform, hence it will possess no acceleration, in accordance with Newton’s law of inertia. If we interpret these results in terms of space-time, we see that the world-line of the body is a straight line in space-time as referred to our mesh-system of equal four-dimensional cubes. If we now examine the motion of this same free body from some definite accelerated frame, all we have to do is to change our four-dimensional space-time mesh-system in an appropriate way. This change of mesh-system does not affect the world-line of the body, since this line remains a straight line or geodesic through flat space-time; but, on the other hand, it will certainly alter the appearance of the straight line when we refer our measurements to our curvilinear mesh-system. The erstwhile straight world-line will now appear curved in a definite way, and its precise mathematical equation as referred to our new curved mesh-system can be obtained without difficulty. The physical significance of this apparent curvature of the world-line of the body will be that the body will now appear to possess acceleration with respect to our new non-Galilean frame. The precise magnitude of this acceleration will therefore be given by the apparent curvature of the world-line followed by the body, and this curvature is of course expressed implicitly by the equation of the world-line when referred to our curvilinear mesh-system. But for a given test-body the acceleration is related to the force acting on the body. From this it follows that the mathematical expression of the force can be obtained immediately.