This mathematical expression of the curved world-line, hence of the force of inertia at any particular point, is seen to be built up with the variations in value of the ’s around this point. Were the ’s to remain constant in value throughout, as would be the case in a Galilean frame, this mathematical expression would vanish in [Pg 249] value. It follows that the ’s, of which this expression of the force is built, must correspond to the potentials of inertia. We have thus discovered the physical significance of the ’s of space-time: they define potentials. We see, indeed, that this identification is legitimate in every respect. Thus, in a Galilean frame, there are no forces of inertia, so that the potentials of inertia must be constants; and we know that in a mesh-system of equal four-dimensional cubes, which corresponds to a Galilean system, the ’s are all constants and are given by , all other ’s being zero. Again, in an accelerated frame, a field of inertial forces appears; hence the potential must vary from place to place; and we know that in a curvilinear mesh-system (corresponding to an accelerated frame) the ’s lose their constant values and vary from place to place. So far the reason for the existence of forces of inertia has been made apparent. They arise owing to the uneven spread of numbers which accompanies all curvilinear mesh-systems (accelerated frames).[79] When this occurs, the mathematical expression of the force of inertia assumes a definite numerical value at each point, whereas, when the ’s are constants, as in a Cartesian mesh-system, this expression of the force maintains a zero value. From this we see that forces of inertia arise from an attempt on our part to cut up space-time with curvilinear mesh-systems instead of Cartesian ones, just as they arise from our substitution of accelerated frames for Galilean ones. We cannot help but feel, however, that having proceeded thus far, a further generalisation is required. To be more explicit, it should be understood that the scheme of physics we have developed has compelled us to attribute a fundamental rôle to space-time. But Newton’s great law of universal attraction is expressed in terms of the separate space and time of classical science. If space-time is indeed as fundamental as Einstein has led us to believe, it appears incredible that Newton’s law should remain outside its scope. Yet this it certainly does, for if Newton’s law were a space-time law, it would preserve the same form in spite of any change in our space-time mesh-system. And this it fails to do.