  We show that the space of all bounded derivations from the disc algebra into
its dual can be identified with the Hardy space $H^1$; using this, we infer
that all such derivations are compact. Also, given a fixed derivation $D$, we
construct a finite, positive Borel measure $\mu_D$ on the closed disc, such
that $D$ factors through $L^2(\mu_D)$. Such a measure is known to exist, for
any bounded linear map from the disc algebra to its dual, by results of
Bourgain and Pietsch, but these results are highly non-constructive.
