  We present cross sections and reaction rates for merging to occur during
encounters of equal-mass spherical galaxies. As an application, we determine
the rate of galaxy merging in clusters of galaxies. We present results for two
types of Plummer models (a full and a truncated one), two King models and the
Hernquist model. Cross sections are determined on the basis of a large number
($\sim 500$) of simulations of galaxy encounters, using the 10-Gigaflops GRAPE
3A special-purpose computer. We characterize the overall merger rate of
galaxies in a galaxy cluster by a single number, derived from our cross
sections by an integration over galaxy encounter velocities in the limit of a
constant density in velocity space. For small clusters, where the cluster
velocity dispersion may not significantly exceed the internal velocity
dispersion of the individual galaxies, this constant-density approximation may
not be valid. For those cases, we present separate results, based on
integrations of our cross sections over Maxwellian velocity distributions.
Finally, tidal effects from the cluster potential as well as from neighboring
galaxies may prevent a barely bound galaxy pair from spiraling in after their
first encounter. We give a quantitative estimate of the resulting reduction in
the actual merger rate, due to these tidal interactions.
