Time series of reciprocal ray travel times were obtained at 350-, 410-, and 670-km ranges in the western North Atlantic during the 1991--1992 Acoustic Mid-Ocean Dynamics Experiment (AMODE). Transmissions were recorded for approximately 300 days between six transceivers in a pentagonal array. Barotropic current along each of the 15 propagation paths is derived from the difference of reciprocal ray travel times, while ten independent estimates of areal-averaged relative vorticity are found by integrating current around triangles in the pentagonal array. The estimated tidal currents are highly accurate, and tidal relative vorticity at the M[inf 2] frequency is detected. This vorticity is induced primarily by the stretching of vortex lines by tidal elevation. Harmonic constants (amplitude, phase) of M[inf 2] tidal vorticity are about (4--8(plus or minus)2x10[sup -9] s[sup -1], 270(degrees)-320(degrees)(plus or minus)20(degrees)), while harmonic constants of about (2--3x10[sup -9] s[sup -1], 300(degrees)-340(degrees)) are predicted using the shallow-water equations. The measured tidal harmonic constants are compared with those derived from a global barotropic tidal model.