We present images of the peculiar galaxy Arp 10 which reveal two rings
of concurrent star formation. Apart from a bright ring visible on ear
ly photographs of the system, an even brighter inner ring of H II regi
ons is found within the nuclear bulge of the galaxy. A very faint ring
-arc of H II regions is also seen associated with a third outer ring o
r shell. We detect a small companion galaxy on the minor axis of Arp 1
0 and an extended extra-nuclear knot which lies between the first and
second rings. An investigation of the Halpha fluxes in the rings revea
ls an increase in the emission where the ring surface density in the R
-band light exceeds 21.3 +/- 0.2 mag arcsec-2. If the R-band light is
dominated by old stars in the underlying density wave, then the result
s suggest evidence for a star-formation law which exhibits a threshold
dependence on the strength of the density wave in the rings. Even if
the R-band continuum in the ring is heavily contaminated with red ligh
t from the underlying young stars (a result at odds with the smooth co
ntinuum morphology of the ring) then a smaller, but still significant
nonlinear enhancement in the star-formation rates in one segment of th
e second ring is required to explain the results. In either case, stro
ng trends in the star-formation rate with azimuth around Ring 2 are in
good agreement with off-center collisional ring galaxy models.