The inelastic scattering of high energy electrons with excitation of collective nuclear transitions is treated using a simple hydrodynamical model in which the collective nuclear motion is assumed to be irrotational and incompressible. The effects of nuclear compressibility are discussed. Using the Born approximation, scattering form factors are calculated for several charge distributions for electric quadrupole transitions, and the sensitivity of the scattering to the form of the nuclear charge distribution is examined.