Measurements of the charge and size of heptane droplets generated by electrostatic sprays showed that the droplet charge-to-volume ratio is a monotonically decreasing function of size. In the useful range of electrospray operation, characterized by droplets smaller than the size of the orifice from which the liquid is issued, it was found that the larger were the droplets the closer they were to the Rayleigh limit. In particular, when droplets had charging levels between 70% and 80% of such limit, they were observed to rupture because the repulsive force due to surface charge evidently overcame surface tension. The rupture phenomenon, here termed Coulomb fission, was also captured in microphotographs that typically showed a droplet with one or two, diametrically opposed, conical protrusions terminating in a fine jet ejecting a stream of much smaller, apparently equisized offsprings. The process appeared swift and, yet, well ordered, quite different from the common view of a violent, convulsive explosion. Corroborating evidence on the disruption pattern was also gathered by quantitative measurements of the evolution of the droplet size distribution in evaporating sprays using phase Doppler anemometry (PDA). Implications of these findings are finally discussed in the context of a particular application of electrostatic sprays, electrospray ionization, a technique that is revolutionizing the mass-spectrometric analysis of large biomolecules.