We describe a new technique for measuring the relationship between electrical mobility and mass. For spherical particles, the mass-mobility relationship can be used to determine particle density. For nonspherical particles, this relationship is affected by both the density and the dynamic shape factor; additional information would be required to determine either one. However, combinations of shape factors and densities that are consistent with measurements can be obtained. We show that the density of spherical particles of known composition can be measured to within ∼5 % with this approach. We applied the technique to urban atmospheric aerosols of ∼1 and ∼3 μm in Atlanta, GA, during August 1999. The Atlanta data show that particles of a given mobility often have several distinct masses. Based on complementary measurements, we argue that the most abundant mass consists of spherical hygroscopic particles. The measured mass for these particles (assuming that they are spherical) fell into the range of 1.54 to 1.77 g cm-3 at 3-6 % relative humidity, which agreed to within about 5% of values calculated based on the measured size-resolved composition. Particles that were more and less massive than these were also observed. The less massive particles had "effective densities" of 0.25-0.64 g cm-3 and the more massive particles had "effective densities" of 1.7-2.2 g cm-3. We hypothesize that the less massive particles consist of chain agglomerate soot.