One aspect of the strong relationship that is known to exist between the processes of DNA replication and transcription is manifest in the coupling of the rates of movement of the replication fork (rf) and RNA polymerase (rt). We address two issues concerning the largely unexplored area of polymerase dynamics: (i) The validity of an approximate kinematic formula linking rf and rt suggested by experiments in which transcription is inhibited in some prokaryotes with the antibiotic streptolydigin, and (ii) What are the molecular bases of the kinematic formula? An analysis of the available data suggests possible molecular bases for polymerase dynamics. In particular, we are led to a hypothesis: In active chromatin rt may depend on the length (lambda t) of the transcript of the primary messenger RNA (pre-mRNA). This new effect is subject to experimental verification. We discuss possible experiments that may be performed in order to test this prediction.