We present direct kinematic evidence for bar streaming motions in two active galaxies with boxy stellar bulges. The Hawaii Imaging Fabry-Perot Interferometer was used on the 3.6 m Canada-France-Hawaii Telescope and the University of Hawaii 2.2 m telescope to derive the two-dimensional velocity field of the line-emitting gas in the disks of the Sc galaxy NGC 3079 and the Sb galaxy NGC 4388. In contrast to previous work based on long-slit data, the detection of the bar potential from the Fabry-Perot data does not rely on the existence of inner Lindblad resonances or strong bar-induced shocks. Simple kinematic models that approximate the intrinsic gas orbits as nonintersecting, inclined elliptical annuli that conserve angular momentum characterize the observed velocity fields. In NGC 3079, bar streaming motions with moderately eccentric orbits (e = b/a ~ 0.7) aligned along P.A. = 130° intrinsic to the disk (P.A. = 97° on the sky) are detected out to Rb = 3.6 kpc. The orbits become increasingly circular beyond that radius (e = 1 at Rd ≈ 6 kpc). The best model for NGC 4388 includes highly eccentric orbits (e ~ 0.3) for Rb 1.5 kpc, which are aligned along P.A. = 135° intrinsic to the disk (P.A. = 100° on the sky). The observed "spiral arms" are produced by having the orbits become increasingly circular from the ends of the bar to the edge of the disk (Rd ≈ 5 kpc) and the intrinsic bar position angle shifting from 135° to 90°. Box-shaped bulges in both NGC 3079 and NGC 4388 are confirmed using new near-infrared images to reduce dust obscuration. Morphological analysis of starlight in these galaxies is combined with the gas kinematics derived from the Fabry-Perot spectra to test evolutionary models of stellar bars that involve transitory, boxy bulges and to quantify the importance of such bars in fueling active nuclei. Our data support the evolutionary bar models but fail to prove convincingly that the stellar bars in NGC 3079 and NGC 4388 directly trigger or sustain the nuclear activity.
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