Corrective procedures have been undertaken that will permit quantitative polarimetry using the 75 cm Sacramento Peak Vacuum Tower Telescope. A new vacuum entrance window provides an improvement in the spatial uniformity of the polarization effect over the old strongly stressed window of almost two orders of magnitude. Even though the intrinsic spatial variation of the polarization effect is less than 5 x 10-4, a constant residual birefringence in the vacuum entrance and exit windows and 45° mirror reflections introduces a uniform retardance that is as large as 1/8 wave and is a function of the telescope pointing parameters. However, a particular sampling of input polarization states and corresponding measurements of the output polarization states determines uniquely the matrix of a serial system consisting of n spatially uniform, nonscattering, rotatable, nonsingular polarization modification elements. A numerical method is given for inverting measurements taken in a way that did not strictly conform to the nominal sampling. The method was applied to polarization measurements obtained with the National Solar Observatory polarimeter mounted at the prime focus of the Vacuum Tower Telescope over the course of a day as the telescope pointing changed to track the sun. The resulting matrix model for the telescope is a function of its three pointing parameters and is applicable for telescope pointing to all sky angles. The accuracy of the present model, 2.5%, is limited by the quality of the polarimeter calibration and by simplifying assumptions.