  We have calculated the general dispersion relationship for surface waves on a
ferrofluid layer of any thickness and viscosity, under the influence of a
uniform vertical magnetic field. The amplification of these waves can induce an
instability called peaks instability (Rosensweig instability). The expression
of the dispersion relationship requires that the critical magnetic field and
the critical wavenumber of the instability depend on the thickness of the
ferrofluid layer. The dispersion relationship has been simplified into four
asymptotic regimes: thick or thin layer and viscous or inertial behaviour. The
corresponding critical values are presented. We show that a typical parameter
of the ferrofluid enables one to know in which regime, viscous or inertial, the
ferrofluid will be near the onset of instability.
