  We present the results of a Hubble Space Telescope (HST) study of dwarf
galaxies in the outer regions of the nearby rich Perseus Cluster, down to M_V =
-12, and compare these with the dwarf population in the cluster core from our
previous HST imaging. In this paper we examine how properties such as the
colour magnitude relation, structure and morphology are affected by environment
for the lowest mass galaxies. Dwarf galaxies are excellent tracers of the
effects of environment due to their low masses, allowing us to derive their
environmentally based evolution, which is more subtle in more massive galaxies.
We identify 11 dwarf elliptical (dE) and dwarf spheroidal (dSph) galaxies in
the outer regions of Perseus, all of which are previously unstudied. We measure
the (V-I)_0 colours of our newly discovered dEs, and find that these dwarfs lie
on the same red sequence as those in the cluster core. The morphologies of
these dwarfs are examined by quantifying their light distributions using CAS
parameters, and we find that dEs in the cluster outskirts are on average more
disturbed than those in the core, with <A> =0.13\pm0.09 and <S> =0.18\pm0.08,
compared to <A> =0.02\pm0.04, <S> =0.01\pm0.07 for those in the core. Based on
these results, we infer that these objects are ``transition dwarfs'', likely in
the process of transforming from late-type to early type galaxies as they
infall into the cluster, with their colours transforming before their
structures. When we compare the number counts for both the core and outer
regions of the cluster, we find that below M_V = -12, the counts in the outer
regions of the cluster exceed those in the core. This is evidence that in the
very dense region of the cluster, dwarfs are unable to survive unless they are
sufficiently massive to prevent their disruption by the cluster potential and
interactions with other galaxies.
