  We apply the methods of continuum mechanics to the study of the collective
modes of the fractional quantum Hall liquid. Our main result is that at long
wavelength there are {\it two} distinct modes of oscillations, while previous
theories predicted only {\it one}. The two modes are shown to arise from the
internal dynamics of shear stresses created by the Coulomb interaction in the
liquid. Our prediction is supported by recent light scattering experiments,
which report the observation of two long-wavelength modes in a quantum Hall
liquid.
