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