  Elastic and inelastic neutron scattering studies have been carried out on the
pyrochlore magnet Ho2Ti2O7. Measurements in zero applied magnetic field show
that the disordered spin ice ground state of Ho2Ti2O7 is characterized by a
pattern of rectangular diffuse elastic scattering within the [HHL] plane of
reciprocal space, which closely resembles the zone boundary scattering seen in
its sister compound Dy2Ti2O7. Well-defined peaks in the zone boundary
scattering develop only within the spin ice ground state below ~ 2 K. In
contrast, the overall diffuse scattering pattern evolves on a much higher
temperature scale of ~ 17 K. The diffuse scattering at small wavevectors below
[001] is found to vanish on going to Q=0, an explicit signature of expectations
for dipolar spin ice. Very high energy-resolution inelastic measurements reveal
that the spin ice ground state below ~ 2 K is also characterized by a
transition from dynamic to static spin correlations on the time scale of
10^{-9} seconds. Measurements in a magnetic field applied along the
[1${\bar1}$0] direction in zero-field cooled conditions show that the system
can be broken up into orthogonal sets of polarized alpha chains along
[1${\bar1}$0] and quasi-one-dimensional beta chains along [110]. Three
dimensional correlations between beta chains are shown to be very sensitive to
the precise alignment of the [1${\bar1}$0] externally applied magnetic field.
