  In the inner 3kpc of M51 we find that logarithmic spirals provide good fits
to the peak intensities in molecular gas observed by BIMA in the CO (J=1-0)
emission line along the spiral arms. However, we measure significant
asymmetries between the location and density of the arms observed on one side
of the galaxy compared to those on the opposite side. Between a radius of 1 and
2.2 kpc the gas distribution traced in CO is lopsided with densities twice as
large in one arm compared to the opposite one. In the same region, the spiral
arms are offset by 20 degrees from the position of the arm on the opposite side
of the galaxy after a rotation of 180 degrees. We use the ratio of CO emission
to that in the Pa alpha hydrogen recombination line to estimate the efficiency
of star formation along each arm. Except for a narrow region at about 2kpc
where star formation is surprisingly inefficient, the gas depletion time is
approximately 200 million years despite large variations in the molecular gas
density in the arms.
  We account for the deviations from two armed bi-symmetric structure with a
simple model that includes an additional three-armed spiral density wave. This
model accounts for the angular offset between the arm on one side compared to
its opposite, the lopsided distribution in molecular gas, and inter-arm star
formation to the north east of the galaxy nucleus. Since the star formation
efficiency is unaffected by the variations in gas density, and the variations
in gas density can be accounted for by the presence of an additional
three-armed density wave, we suggest that the star formation rate is variable,
and is highest where and when the maxima of the two spiral density waves
coincide or constructively add.
