Effects of frame-dragging on the polarization of an electromagnetic (spin-1) wave result in adispersive rotation of the polarization plane, as we have explored in a previous paper (paper I). Similar results have been expected for the electromagnetic wave propagating in a metric in which the space-time orthogonal to the light ray is anisotropic. In the present paper, we generalize the investigation to include arbitrary-spin waves under the influence of either of these effects. Starting from spin-1/2 (mass zero) waves, based on a discussion analogous to the two-state transition problem in quantum mechanics, we arrive at a general formula for the dragged frequency for arbitrary-spin waves. This formula involves an unknown function (the off-diagonal Hamiltonian matrix elementH12 in the usual sense) which must satisfy a few criteria in order that Mach’s principle be properly taken into account. When compared with our previous result for the electromagnetic polarization under the effect of frame-dragging, the form ofH12 can roughly be fixed. The present analysis demonstrates that higher-spin waves in general experience stronger Machian interaction. And if there is any field (in addition to the usual tensor field in general relativity) playing the role of Machian interaction, the most probable one must be the scalar field, as suggested by the Brans-Dicke theory.