In this paper a further generalization of the theory of multilayer physical adsorption previously developed by the authors is attempted so that the effect of vertical interactions between adsorbent and adsorbate can be explicitly taken into account. In this attempt we have to discard the previously adopted assumption that the molecules in the second layer or above are all in the same physical state. In order to estimate the effect of vertical interactions on the adsorption isotherm the interaction energy between an adsorbed molecule and the adsorbent surface is assumd to vary as $r^{-3}$ where r is the distance that the molecule under consideration is separated from the adsorbent surface. Resulting adsorption isotherm is applied to interpret the adsorption data of tetramethylsilane vapor on iron film and good agreements between observed and calculated values are obtained over wide range of pressure.