  We derive the "conservation law" for nematic polymers in tensorial form valid
for quadrupolar orientational order in contradistinction to the conservation
law in the case of polar orientational order. Due to microscopic differences in
the coupling between the orientational field deformations and the density
variations for polar and quadrupolar order, we find that respective order
parameters satisfy fundamentally distinct constraints. Being necessarily scalar
in its form, the tensorial conservation law is obtained straightforwardly from
the gradients of the polymer nematic tensor field and connects the spatial
variation of this tensor field with density variations. We analyze the
differences between the polar and the tensorial forms of the conservation law,
present some explicit orientational fields that satisfy this new constraint and
discuss the role of singular "hairpins", which do not affect local quadrupolar
order of polymer nematics, but nevertheless influence its gradients.
