The spatial and radial velocity distribution of broad-line--emitting gas in the Seyfert 1 galaxy NGC 5548 is examined through the process of reverberation mapping, which is done by detailed comparison of continuum and emission-line variations. Recent spectroscopic monitoring of NGC 5548 with HST and IUE allows us to resolve the "transfer function" (TF) that relates the continuum and emission-line variability. We also examine the radial velocity--resolved TFs, and confirm that predominantly radial motions of the line-emitting clouds can be excluded. We find that a broad-line region comprised of clouds that are orbiting a central source of mass ~108 M⊙ along randomly inclined Keplerian orbits and irradiated by a beamed continuum source yields a TF and line profile that are qualitatively consistent with the observations. In this model, the clouds that produce the variable C IV emission lie within 12 lt-days of the central source, and the continuum radiation is confined to a wide biconical beam (semi--opening angle 35 deg--60 deg) with the observer viewing into the cone.