  Intensity distribution of the neutron magnetic scattering has been taken in
the reciprocal space of a single crystal of the "spin ice" system Ho2Ti2O7 at
the elastic energy position in the temperature (T) region between 0.4 K and 50
K. The short range magnetic correlation becomes appreciable with decreasing T
at around 30 K. The freezing of the moment system takes place at around 1.5 K
with decreasing T. Based on the mean field treatment of the moment system, the
distribution of the observed intensity has been reproduced, where the dipolar
interaction is confirmed to be primarily important for the determination of the
magnetic correlation. Simple calculations of the scattering intensity carried
out by using a cluster of 25 moments of Ho3+ ions indicate that there are many
types of the moment arrangement within a cluster which have almost degenerated
energies, indicating that the system cannot uniquely select the correlation
pattern down to rather low temperature, and before going to the lowest energy
state, the system undergoes the gradual slowing down to the glassy state.
