  We have conducted a programme to determine the fundamental parameters of a
substantial number of eclipsing binaries of spectral types O and B in the Small
Magellanic Cloud. New spectroscopic data, obtained with the two-degree-field
multi-object spectrograph on the 3.9-m Anglo-Australian Telescope, have been
used in conjunction with photometry from the Optical Gravitational Lens
Experiment (OGLE-II) database of SMC eclipsing binaries. Previously we reported
results for 10 systems; in this second and concluding paper we present spectral
types, masses, radii, temperatures, surface gravities and luminosities for the
components of a further 40 binaries. The full sample of 50 OB-type eclipsing
systems is the largest single set of fundamental parameters determined for
high-mass binaries in any galaxy. We find that 21 of the systems studied are in
detached configurations, 28 are in semi-detached post-mass-transfer states, and
one is a contact binary.
  Each system provides a primary distance indicator. We find a mean distance
modulus to the SMC of 18.91+/-0.03+/-0.1 (internal and external uncertainties;
D=60.6+/-1.0 kpc). This value represents one of the most precise available
determinations of the distance to the SMC.
