A modified Poisson-Boltzmann analysis is made of the double layer interaction between two silica surfaces and two alumina surfaces in chloride electrolyte. The analysis incorporates nonelectrostatic ion-surface dispersion interactions based on ab initio ionic excess polarizabilities with finite ion sizes. A hydration model for the tightly held hydration shell of kosmotropic ions is introduced. A direct Hofmeister series (K > Na > Li) is found at the Silica surface while the reversed series (Li > Na > K) is found at alumina, bringing theory in line with experiment for the first time. Calculations with unhydrated ions also suggest that surface-induced dehydration may be occurring at the alumina surface.