Creeping waves for objects of finite conductivity

It is shown that it is not necessary to apply the van der Pol-Bremmer expansion in order to obtain the Watson residue series without remainder integral. There appear two kinds of residual waves. Those of the first kind do not enter the object and correspond to the usual creeping waves for objects of infinite conductivity. They arise from poles in the vicinity of the zeros of
H\upsilon(ka)
. Residual waves of the second kind correspond to waves transversing the object and arise from poles in the vicinity of the zeros of
J\upsilon(nka)
. They are of no importance in the case of strongly absorbing materials. Waves which are expected according to geometrical optics are obtained-as in the case of infinite conductivity-by splitting off an integral. Primary and reflected waves arise from two different saddle points of the same integrand which was thought of till now as only yielding the reflected waves. On the other hand the terms corresponding to the ingoing part of the primary wave give no contribution at all, but must be kept in order to assure the convergence of the integrals when shifting the path of integration.