  Details of simultaneous photometric and spectroscopic observations of the
optical counterpart of the `supersoft' X-ray source 1E 0035.4-7230 (SMC 13) are
presented. Although the spectrum is dominated by emission lines of He II, the
Balmer series of hydrogen is also present in emission with a strong decrement,
and Balmer lines are seen as broad absorptions. Several high ionization
emission features are also present including O VI (3811, 3834, and 5290A).
Radial velocities and photometry confirm that the binary period is ~0.1719d,
and an improved value of the period is derived from four years of photometry
and analysis of ROSAT-HRI X-ray data. The orbital light variation is primarily
due to an eclipse of the extensive accretion disk. X-ray and optical minima
occur together. The UBV light curves are similar to each other, and no clear
phase-related color variations are found. He II emission-line velocities show a
semi-amplitude of K ~100 km/s, and maximum velocity occurs when the light curve
indicates the compact star would be moving away from the observer, suggesting
this emitting region may trace the orbital motion of the compact star. The
range of possible masses implied for the X-ray source lies between 0.5 and 1.5
solar masses if the mass donor is a main sequence star filling its Roche lobe.
The light curve suggests values at the high end of this range. The broad H
absorption lines appear to have a much larger velocity amplitude and lower
systemic velocity, making it difficult to understand their origin. We discuss
possible models for the system.
