The effective veiling glare has been measured in a linear, 64 element Si(Li) detector of 5 mm thickness and 0.5 mm center-to-center spacing between adjacent sensitive areas. Each elemental contact was 6 mm high and 0.4 mm wide. The measurement was made in two different ways, both employing a 33 keV beam of synchrotron x-rays at the Stanford Synchrotron Radiation Laboratory. In one method, a lead phantom in the shape of an isosceles triangle was illuminated across its width with a fan beam of 33 keV x-rays 0.5 mm high by 20 mm wide. The x-ray flux passing by the phantom was measured in each channel of the Si(Li) detector. In the second method, a highly collimated beam of 33 keV x-rays (0.5 mm high by 0.025 mm wide) was scanned across 15 channels of the detector in 0.01 mm steps. The measured intensity in each channel of the detector was recorded at each position of the beam. The photon flux fell to less than 0.1% at a distance of 3 mm from the edge of the beam. The results of both measurements were in agreement. They were also compared to calculated results based on the known total x-ray cross sections for Compton scattering and photoelectric absorption. To within the experimental error, the observed and calculated results were found to be in good agreement.