It has been shown elsewhere that in the case of relativistic theories, ther
e exists a local differential-topological criterion which distinguishes sha
rply between geometry and forces. This criterion is also epistemologically
effective. In this paper, we explain why this local criterion fails in the
pre-relativistic context. The principal reason for the difference is that t
he causal structure is determined by a quadratic function of 3-velocity in
the relativistic case and by a linear function of 3-velocity in the pre-rel
ativistic case.