Neutron diffraction data, in conjunction with isotopic substitution of deuterium (D) for hydrogen (H), have been analyzed to determine the three-dimensional structure of water confined in vycor, an archetypal hydrophilic porous silica glass containing channels or pores of approximately 40 A diameter. The data have been incorporated into a Monte Carlo computer simulation of the confined water system, and the site-site potentials have been iteratively refined in order to produce a model ensemble which is consistent with both the neutron diffraction data and two possible geometries of the vycor pores (cylindrical and spherical). This approach has allowed us to investigate in detail the contributions to the experimentally accessible partial pair correlation functions, and ascertain whether particular features arise from interactions of the water molecules with the substrate surface, or from purely geometrical confinement effects. We observe a significant decrease in the first shell water oxygen-oxygen co-ordination number, and a decrease in the number of hydrogen bonds per water molecule from approximately 3.6 in bulk water to approximately 2.2 in confinement. In addition, we observe a significant shift inward of the second peak in the water oxygen-water oxygen coordination shell. Overall, we therefore find that the structure of the water in vycor is strongly perturbed relative to the bulk.