  We consider the effect of the transitions $n \to \Delta^{0}$ and $p \to
\Delta^{+}$ in deep inelastic scattering on polarized $^3$He on the extraction
of the neutron spin structure function $g_{1}^{n}(x,Q^2)$. Making the natural
assumption that these transitions are the dominant non-nucleonic contributions
to the renormalization of the axial vector coupling constant in the A=3 system,
we find that the effect of $\Delta$ increases $g_{1}^{n}(x,Q^2)$ by $10 \div
40$% in the range $0.05 \le x \le 0.6$, where our considerations are applicable
and most of the data for $g_{1}^{n}(x,Q^2)$ exist.
