  We use stable maps, and their stable lifts to the Semple bundle variety of
second-order curvilinear data, to calculate certain characteristic numbers for
rational plane curves. These characteristic numbers involve first-order
(tangency) and second-order (inflectional) conditions. Although they may be
virtual, they may be used as inputs in an enumeratively significant formula for
the number of rational curves having a triple contact with a specified plane
curve and passing through 3d-3 general points.
