The minimum time (E) required for a new pair of replication origins (oriCs) produced upon initiating a round of replication to be ready to initiate the next round after one cell mass doubling, the 'eclipse', is explained in terms of a minimal distance (lmin) that the replication forks must move away from oriC before oriCs can 'fire' again. In conditions demanding a scheduled initiation event before the relative distance lmin/L0.5 (L being the total chromosome length) is reached, initiation is presumably delayed. Under such circumstances, cell mass at the next initiation would be greater than the usual, constant Mi (cell mass per copy number of oriC) prevailing in steady state of exponential growth. This model can be tested experimentally by extending the replication time C using thymine limitation at short doubling times τ in rich media to reach a relative eclipse E/C < lmin/L0.5. It is consistent with results obtained in experiments in which the number of replication 'positions' n (= C/τ) is increased beyond the natural maximum, causing the mean cell size to rise continuously, first by widening, then by lengthening, and finally by splitting its poles. The consequent branching is associated with casting off a small proportion of normal-sized cells and lysing DNA-less cells. Whether or how these phenomena are related to peptidoglycan composition and synthesis are moot questions.