We derive the van der Waals induced moment using a reaction field approach based on charge density susceptibilities of several bodies interacting through Coulomb operators. We extend previous results to include nonadditive contributions from up to four bodies. We then expand the Coulomb operators in a moment T-tensor series. The lowest hyperpolarizability terms yielding nonzero values are products of the dipole-dipole quadrupole hyperpolarizability, B, for the body whose dipole moment is being evaluated and the dipole-dipole polarizabilities, alpha, of the other interacting bodies. We then introduce the image approximation for the case where one body is a solid and apply our results to the cases of argon and xenon on magnesium and on palladium. By closure, we are able to separate the frequency dependencies of the various factors so that this contribution can be reduced to a numerical factor that is then calculated by numerical integration. Our present results show that the work function reductions of magnesium by argon and xenon can be accounted for by our calculations. Our calculated reductions for palladium suggest that in the high work-function metals another mechanism enters in an important way, as has been suggested by others. The relationship between our present results and earlier estimates by ourselves and others is discussed.