  The generalised longitudinal susceptibility $\chi({\bf q}, \omega)$ affords a
sensitive measure of the spatial and temporal correlations of magnetic
monopoles in spin ice. Starting with the monopole model, a mean field
expression for $\chi({\bf q}, \omega)$ is derived as well as expressions for
the mean square longitudinal field and induction at a point. Monopole motion is
shown to be strongly correlated, and both spatial and temporal correlations are
controlled by the dimensionless monopole density $x$ which defines the ratio of
the magnetization relaxation rate and the monopole hop rate. Thermal effects
and spin lattice relaxation are also considered. The derived equations are
applicable in the temperature range where the Wien effect for magnetic
monopoles is negligible. They are discussed in the context of existing theories
of spin ice and the following experimental techniques: dc and ac-magnetization,
neutron scattering, neutron spin echo, and longitudinal and transverse field
$\mu$SR. The monopole theory is found to unify diverse experimental results,
but several discrepancies between theory and experiment are identified. One of
these, concerning the neutron scattering line shape, is explained by means of a
phenomenological modification to the theory.
