The abdomen of adult Drosophila consists of a chain of alternating anterior (A) and posterior (P) compartments which are themselves subdivided into stripes of different types of cuticle. Most of the cuticle is decorated with hairs and bristles that point posteriorly, indicating the planar polarity of the cells. Here we research the link between pattern and polarity. Previously we showed that the pattern of the A compartment depends on the local concentration (the scalar) of a Hedgehog morphogen produced by cells in the P compartment. Here we present evidence that the P compartment is patterned by another morphogen, Wingless, which is induced by Hedgehog in A compartment cells and then spreads back into the P compartment. We also find that both Hedgehog and Wingless appear to specify pattern by activating the optomotor blind gene, which encodes a transcription factor. We re-examine our working model that planar polarity is determined by the cells reading the gradient in concentration (the vector) of a morphogen 'X' which is produced on receipt of Hedgehog. We present evidence that Hedgehog induces X production by driving optomotor blind expression. We tried but failed to identify X and present data that X is not likely to operate through the conventional Notch, Decapentaplegic, EGF or FGF transduction pathways, or to encode a Wnt. However, we argue that Wingless may act to enhance the production or organise the distribution of X. A simple model that accommodates our results is that X forms a monotonic gradient extending from the back of the A compartment to the front of the P compartment in the next segment, a unit constituting a parasegment.