  An analytic formula is given for the traceless transverse part of the
anisotropic stress tensor due to free streaming neutrinos, and used to derive
an integro-differential equation for the propagation of cosmological
gravitational waves. The solution shows that anisotropic stress reduces the
squared amplitude by 35.6 % for wavelengths that enter the horizon during the
radiation-dominated phase, independent of any cosmological parameters. This
decreases the tensor temperature and polarization correlation functions for
these wavelengths by the same amount. The effect is less for wavelengths that
enter the horizon at later times. At the longest wavelengths the decrease in
the tensor correlation functions due to neutrino free streaming ranges from
10.7% for $\Omega_Mh^2=0.1$ to 9.0% for $\Omega_Mh^2=0.15$. An Appendix gives a
general proof that tensor as well as scalar modes satisfy a conservation law
for perturbations outside the horizon, even when the anisotropic stress tensor
is not negligible.
