Previous reports have shown that dielectric liquids such as hexane, containing traces of polycyclic hydrocarbons such as anthracene, will exhibit luminescence when subjected to a static electric stress above about 500 kv cm^-1. By subjecting such liquids to step-function stresses and observing the light output with a photomultiplier it has been possible to demonstrate that the light consists of a series of pulses which occur randomly. A statistical analysis of the time intervals between applications of the stress and the first and second light pulses allows the mean rate of occurrence of light pulses to be determined. This function is found to depend on the stress and on the electrode material. It is suggested that the pulses are microdischarges on the electrode surfaces due to the incidence of charged particles and are therefore likely to be related to the initiating events which cause breakdown and give rise to statistical time lags at much higher stresses.