  We report measurements of geometric offsets between gas spiral arms and
associated star forming regions in the grand-design spiral galaxy M51. These
offsets are a suggested measure of the star formation timescale after the
compression of gas at spiral arm entry. A surprising discrepancy, by an order
of magnitude, has been reported in recent offset measurements in nearby spiral
galaxies. Measurements using CO and H-alpha emission find large and ordered
offsets in M51. On the contrary, small or non-ordered offsets have been found
using the HI 21cm and 24 micron emissions, possible evidence against gas flow
through spiral arms, and thus against the conventional density-wave theory with
a stationary spiral pattern. The goal of this paper is to understand the cause
of this discrepancy. We investigate potential causes by repeating those
previous measurements using equivalent data, methods, and parameters. We find
offsets consistent with the previous measurements and conclude that the
difference of gas tracers, i.e., HI versus CO, is the primary cause. The HI
emission is contaminated significantly by the gas photo-dissociated by
recently-formed stars and does not necessarily trace the compressed gas, the
precursor of star formation. The HI gas and star forming regions coincide
spatially and tend to show small offsets. We find mostly positive offsets with
substantial scatter between CO and H-alpha, suggesting gas flow through spiral
arms (i.e., density-wave) though the spiral pattern may not necessarily be
stationary.
