  We analyze the relationship between maximum cluster mass, and surface
densities of total gas (Sigma_gas), molecular gas (Sigma_H_2), neutral gas
(Sigma_HI) and star formation rate (Sigma_SFR) in the grand design galaxy M51,
using published gas data and a catalog of masses, ages, and reddenings of more
than 1800 star clusters in its disk, of which 223 are above the cluster mass
distribution function completeness limit. We find for clusters older than 25
Myr that M_3rd, the median of the 5 most massive clusters, is proportional to
Sigma_HI^0.4. There is no correlation with Sigma_gas, Sigma_H2, or Sigma_SFR.
For clusters younger than 10 Myr, M_3rd is proportional to Sigma_HI^0.6, M_3rd
is proportional to Sigma_gas^0.5; there is no correlation with either Sigma_H_2
or Sigma_SFR. The results could hardly be more different than those found for
clusters younger than 25 Myr in M33. For the flocculent galaxy M33, there is no
correlation between maximum cluster mass and neutral gas, but M_3rd is
proportional to Sigma_gas^3.8; M_3rd is proportional to Sigma_H_2^1.2; M_3rd
proportional to Sigma_SFR^0.9. For the older sample in M51, the lack of tight
correlations is probably due to the combination of the strong azimuthal
variations in the surface densities of gas and star formation rate, and the
cluster ages. These two facts mean that neither the azimuthal average of the
surface densities at a given radius, nor the surface densities at the
present-day location of a stellar cluster represent the true surface densities
at the place and time of cluster formation. In the case of the younger sample,
even if the clusters have not yet traveled too far from their birthsites, the
poor resolution of the radio data compared to the physical sizes of the
clusters results in measured Sigmas that are likely quite diluted compared to
the actual densities relevant for the formation of the clusters.
