  In the interaction of a transversely polarized nuclear beam with a
tensor-polarized deuteron target, a nonzero value of the component of the total
cross section of the process corresponding to this combination of polarizations
is an unambiguous signal of $T$-invariance violation while $P$-parity is
preserved. The method developed earlier for calculating this component of the
total cross section for $pd$ scattering based on the Glauber theory has been
generalized by us to the case of $^3$He$d$ scattering, and its energy
dependence in the range of beam energies 0.1--1 GeV/nucleon has been
calculated. It is found that in $^3$He$d$ collisions, in contrast to $pd$
scattering, the contribution of only one type of $T$-violating nucleon-nucleon
forces dominates, which is essential for extraction of the unknown constant of
this interaction from the corresponding data.
