## Abstract

Measurements have been made of the period (2$\pi $/$\Omega $) of small torsional oscillations of an Andronikashvili disk system, superposed on a uniform rotation with angular velocity $\omega _{0}$. If the changes in period are expressed formally as an effective density of liquid $\rho ^{\prime}$ that moves with the disks it is found that, for sufficiently rough disk surfaces and sufficiently small amplitudes of oscillation: (i) for $\omega _{0}\gg \Omega $, $\rho ^{\prime}$/$\rho _{s}$ increases monotonically from 0 to 1 with increasing $\omega _{0}$ and increasing disk separation; (ii) for $\omega _{0}\ll \Omega $, $\rho ^{\prime}$ can be either positive or negative; when plotted as a function of disk separation it shows a resonance-dispersion type of behaviour. These results can be explained by the vortex line model of Onsager and Feynman in terms of a transverse wave motion of the vortex lines, if it is supposed that the ends of the lines tend to stick to a sufficiently rough surface. The theory of these vortex waves has been worked out in some detail. The behaviour of the liquid is determined by a parameter $\nu $ = $\epsilon $/$\rho _{s}\kappa $, where $\epsilon $ is the energy of unit length of vortex line and $\kappa $ is the circulation round a line; comparison of theory and experiment gives $\nu $ = (8$\cdot $5 $\pm $ 1$\cdot $5) $\times $ 10$^{-4}$ cm$^{2}$s$^{-1}$, some 25% less than Feynman's theoretical estimate. In the final section some consequences of the existence of vortex waves are discussed.