  We present J, H and K-band spectroscopy of Cygnus A, spanning 1.0-2.4 micron
in the rest-frame and hence several rovibrational H2, H recombination and
[FeII] emission lines. The lines are spatially extended by up to 6kpc from the
nucleus, but their distinct kinematics indicate that the three groups (H, H2
and [FeII]) are not wholly produced in the same gas. The broadest line,
[FeII]1.644, exhibits a non-gaussian profile with a broad base (FWHM=1040
km/s), perhaps due to interaction with the radio source. Extinctions to the
line-emitting regions substantially exceed earlier measurements based on
optical H recombination lines.
  Hard X-rays from the quasar nucleus are likely to dominate the excitation of
the H2 emission. The results of Maloney, Hollenbach and Tielens (1996) are thus
used to infer the total mass of gas in H2 v=1-0 S(1)-emitting clouds as a
function of radius, for gas densities of 10^3 and 10^5 cm^-3, and stopping
column densities N_H=10^22-10^24 cm^-2. Assuming azimuthal symmetry, at least
2.3E8 Msun of such material is present within 5kpc of the nucleus, if the
line-emitting clouds see an unobscured quasar spectrum. Alternatively, if the
bulk of the X-ray absorption to the nucleus inferred by Ueno et al. (1994)
arises in a circumnuclear torus, the implied gas mass rises to 10^10 Msun. The
latter plausibly accounts for 10^9 yr of mass deposition from the cluster
cooling flow, for which Mdot \simeq 10 Msun/yr within this radius.
