  A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics
about a steadily rotating lattice state is developed by two separate methods:
firstly by a direct procedure, secondly by taking the long-wavelength limit of
Tkachenko's exact solution for a triangular vortex lattice. Solutions to the
continuum theory are found, described by arbitrary anti-holomorphic functions,
and give power-law localized edge modes. Numerical results for finite lattices
show excellent agreement to the theory.
