  The measurement of small-angle Bhabha scattering is used to determine the
luminosity at the OPAL interaction point for the LEP I data recorded between
1993 and 1995. The measurement is based on the OPAL Silicon-Tungsten
Luminometer which is composed of two calorimeters encircling the LEP beam pipe,
on opposite sides of the interaction point. The luminometer detects electrons
from small-angle Bhabha scattering at angles between 25 and 58mrad. At LEP
center-of-mass energies around the Z0, about half of all Bhabha electrons
entering the detector fall within a 79nb fiducial acceptance region. The
electromagnetic showers generated in the stack of 1 radiation length tungsten
absorber plates are sampled by 608 silicon detectors with 38,912 radial pads of
2.5mm width.The fine segmentation of the detector, combined with the precise
knowledge of its physical dimensions, allows the trajectories of incoming 45GeV
electrons or photons to be determined with a total systematic error of less
than 7microns. We have quantified all significant sources of systematic
experimental error in the luminosity determination by direct physical
measurement. All measured properites of the luminosity event sample are found
to be in agreement with current theoretical expectations. The total systematic
measurement uncertainty is 3.4x10^-4, significantly below the theoretical error
of 5.4x10^-4 currently assigned to the QED calculation of the Bhabha
acceptance, and contributes negligibly to the total uncertainty in the OPAL
measurement of Gamma{invisible}/Gamma{l+l-}, a quantity of basic physical
interest which depends crucially on the luminosity measurement.
