An exact analysis from the operational point of view of the significance of the equations at high velocities has perhaps never been made, and is not necessary for our immediate purpose. The discussion has brought out, however, that the number of physically independent concepts has been cut down by two at least, in that we have made purely formal definitions of the meaning of quantity of electricity, and of the force exerted by a field on a charge at high velocity. There is no reason to think that there is anything unique about this analysis, or that formal definitions might not have been given to other concepts than charge and force. We can only state that as far as physical content goes the equations have at least two degrees of freedom. It should then be possible to find quite different sorts of equations which agree equally well with experience. In particular, since we have seen that the force on a moving charge has no meaning in terms of independent operations, it should be possible by arbitrary definition to make this force any function of velocity that we please (of course reducing to the proper value at low velocities), and then to determine the other equations so that the entire group of equations is consistent with experiment. So far as I know, no one has tried to give such a modified set of equations, and indeed there is no particular reason why anyone should bother to do this, because the present equations are simple enough, and the modified equations, although perhaps differing greatly in appearance from the present ones, would have no advantage in any greater or different physical content. But there is no reason to think that the present state of affairs will always continue. We have seen that the decrease in the number of concepts corresponds to our inability to measure as many sorts of physical things at high velocities as at low. Now it is the task of the future experimenter so to refine the possibilities of measurement at high velocities as to restore these two degrees of freedom. In particular, mass should be made measurable in mechanical terms at high velocities. When this restoration has been made, and all the quantities in our equations receive independent physical meaning, the significance of the equations in terms of operations will be quite altered, although the formal appearance will be unchanged. We must then be prepared to find, as always when we change the range of phenomena, that the equations in their present form do not correspond to the facts at all, and that one of the alternative forms allowed by our present two degrees of freedom is the correct form. But until the new experimental facts have been obtained, it seems hardly worth while to attempt to specify the doubly infinite variety of forms which the equations might have consistently with present experiment.[23]