The effects of cholesterol on membrane bending modulus K(C), membrane thickness D(HH), the partial and apparent areas of cholesterol and lipid, and the order parameter S(xray) are shown to depend upon the number of saturated hydrocarbon chains in the lipid molecules. Particularly striking is the result that up to 40% cholesterol does not increase the bending modulus K(C) of membranes composed of phosphatidylcholine lipids with two cis monounsaturated chains, although it does have the expected stiffening effect on membranes composed of lipids with two saturated chains. The B fluctuational modulus in the smectic liquid crystal theory is obtained and used to discuss the interactions between bilayers. Our K(C) results motivate a theory of elastic moduli in the high cholesterol limit and they challenge the relevance of universality concepts. Although most of our results were obtained at 30 degrees C , additional data at other temperatures to allow consideration of a reduced temperature variable do not support universality for the effect of cholesterol on all lipid bilayers. If the concept of universality is to be valid, different numbers of saturated chains must be considered to create different universality classes. The above experimental results were obtained from analysis of x-ray scattering in the low angle and wide angle regions.