  The Bjorken sum rules for the $A=3$ and $A=1$ are used as a guide to estimate
nuclear effects in extracting $g_{1n}(x,Q^{2})$ from the
$\vec{e}\,\vec{^3\rm{He}}$ data. We estimate that the combination of the spin
depolarization, the nonnucleonic degrees of freedom in the $A=3$ system and
nuclear shadowing is likely to reduce $g_{1^3\rm{He}}(x\le 0.05)$ by $\sim 15
\%$ while a significant enhancement of the structure functions $g_{1^3\rm{He}},
g_{1^3\rm{H}}$ at $x \sim 0.1$ is predicted.
