A theoretical and experimental study is made of the phenomenon. It is shown that for inertial waves, just as for gravity waves in a two‐component liquid, there are discontinuities in the tangential particle velocities at the interface, a fact implying the existence of a vortex sheet for a real liquid. For the particular case wherein the two liquids completely fill the cylinder, other results are obtained that are analogous to those for gravity waves. In particular, if the liquids are nearly of the same density, there are two sets of frequencies, one set characterizing oscillations of the liquid mass as a whole, the other set characterizing very low frequency oscillations at the interface. For the case in which the two liquids have markedly different densities, there are again two sets of frequencies, one set characterizing oscillations of the inner liquid as though the outer liquid were a solid mass, the other set characterizing oscillations of the outer liquid as though the inner liquid were absent. For the general case, physical interpretations are difficult; hence, a table of frequencies versus composition is given.