  The goal of this paper is to test whether the formation rate of star clusters
is proportional to the star formation rate (SFR) in galaxies. As a first step,
we present the mass functions of compact clusters younger than 10 Myr in seven
star-forming galaxies of diverse masses, sizes, and morphologies: the Large and
Small Magellanic Clouds, NGC 4214, NGC 4449, M83, M51, and the Antennae. These
cluster mass functions (CMFs) are well represented by power laws, dN/dM~M^b,
with similar exponents b=-1.92+/-0.27, but with amplitudes that differ by
factors up to ~10^3, corresponding to vast differences in the sizes of the
cluster populations in these galaxies. We then normalize these CMFs by the SFRs
in the galaxies, derived from dust-corrected H-alpha luminosities, and find
that the spread in the amplitudes collapses, with a remaining rms deviation of
only sigma_(logA)= 0.2. This is close to the expected dispersion from random
uncertainties in the CMFs and SFRs. Thus, the data presented here are
consistent with exact proportionality between the formation rates of stars and
clusters. However, the data also permit weak deviations from proportionality,
at the factor of two level, within the statistical uncertainties. We find the
same spread in amplitudes when we normalize the mass functions of much older
clusters, with ages in the range 100 to 400 Myr, by the current SFR. This is
another indication of the general similarity among the cluster populations of
different galaxies.
