  We calculate the string tension, K, and some of the lightest glueball masses,
M, in 3+1 dimensional SU(N) lattice gauge theories for N=2,3,4,5 . From the
continuum extrapolation of the lattice values, we find that the mass ratios,
M/sqrt(K), appear to show a rapid approach to the large-N limit, and, indeed,
can be described all the way down to SU(2) using just a leading O(1/NxN)
correction. We confirm that the smooth large-N limit we find, is obtained by
keeping a constant 't Hooft coupling. We also calculate the topological charge
of the gauge fields. We observe that, as expected, the density of small-size
instantons vanishes rapidly as N increases, while the topological
susceptibility appears to have a non-zero N=infinity limit.
