  We give conceptual proofs of some results on the automorphism group of an
Enriques surface X, for which only computational proofs have been available.
Namely, there is an obvious upper bound on the image of Aut(X) in the isometry
group of X's numerical lattice, and we establish a lower bound for the image
that is quite close to this upper bound. These results apply over any
algebraically closed field, provided that X lacks nodal curves, or that all its
nodal curves are (numerically) congruent to each other mod 2. In this
generality these results were originally proven by Looijenga and
Cossec-Dolgachev, developing earlier work of Coble.
