  We report the discovery of 0.59 s X-ray pulsations from the low-mass X-ray
binary, 5.57 hr dipping and eclipsing ADC source 2A 1822-371. Pulse arrival
time analysis indicates a circular orbit with e < 0.03 (95% confidence) and an
asini for the neutron star of 1.006(5) lightseconds, implying a mass function
of (2.03+-0.03) x 10^-2 M_sun. The barycentric pulse period was 0.59325(2) s in
1996.270 and 0.59308615(5) s in 1998.205, indicating an average spin up with
P_dot/P = (-1.52+-0.02) x 10^-4 yr^-1. For a magnetic field strength of ~1--5 x
10^12 G as derived from the X-ray spectrum the implied intrinsic X-ray
luminosity is ~2-4 x 10^37 erg s^-1. The pulse amplitude is low, but increases
steeply as a function of energy from a sinusoidal amplitude of 0.25% in 2-5.4
keV to ~3% above 20 keV. We discuss the constraints on the masses of the
companion star and the fact that several aspects of the energy spectrum are in
qualitative accordance with that of a strongly magnetised neutron star.
