This addition to a recent paper by Chadwick (
Proc. R. Soc. Lond
. A 430, 213 (1990); hereafter referred to as part I) has been prompted mainly by the discovery of
secluded supersonic surface waves
propagating in configurations of transversely isotropic elastic media in which the reference plane is not a plane of material symmetry and coexisting with a subsonic surface wave. The occurrence of a supersonic surface wave travelling in a direction
e
1
with speed
v
s
implies that there are two homogeneous plane waves, with slowness vectors
s
i
and
s
r
such that
s
i
.
e
1
=
S
r
.
e
1
=
v
-1
s
, which comprise the incident and reflected waves in a case of simple reflection at the traction-free boundary. Supersonic surface waves may therefore be found by searching within a suitably defined
space of simple reflection, R
. This is the approach which has led to the new results mentioned above and the principal conclusions of part I are re-examined here from the same point of view. It is found that, whereas the secluded supersonic surface waves in transversely isotropic media correspond to isolated points on a curvilinear projection of
R
which does not intersect the curve representing subsonic surface waves, the symmetric surface waves studied in part I define a curve which may lie partly inside and partly outside a projection of
R
in the form of a region, the interior points representing supersonic and the exterior points subsonic surface waves. This discussion is preceded by a simplification of the existence-uniqueness theorem proved in part I and followed by a reconsideration of the possibility that an inhomogeneous plane elastic wave can qualify as a surface wave. Such one-component surface waves do exist, but a symmetric surface wave necessarily contains two inhomogeneous plane waves.
