  We find the renormalisation coefficients of the quark field and the flavour
non-singlet fermion bilinear operators for the domain wall fermion action, in
the regularisation independent (RI) renormalisation scheme. Our results are
from a quenched simulation, on a 16^3x32 lattice, with beta=6.0 and an extent
in the fifth dimension of 16. We also discuss the expected effects of the
residual chiral symmetry breaking inherent in a domain wall fermion simulation
with a finite fifth dimension, and study the evidence for both explicit and
spontaneous chiral symmetry breaking effects in our numerical results. We find
that the relations between different renormalisation factors predicted by
chiral symmetry are, to a good approximation, satisfied by our results and that
systematic effects due to the (low energy) spontaneous chiral symmetry breaking
and zero-modes can be controlled. Our results are compared against the
perturbative predictions for both their absolute value and renormalisation
scale dependence.
