Coulombs law of friction, in which the coefficient of friction is constant independently of apparent area of contact and applied load, is deduced from the modern adhesion theory. That is, the friction resistance is caused by shearing of solid/solid junctions which are formed through plastic deformation of surface asperities of mating solids. In so-called point contact, on the other hand, different experimental results from Coulombs law have been sometimes reported. In these cases, coefficient of friction is not constant, but reduces with increasing normal load. A weighty interpretation for these facts developed formerly is that Hertzian contact area acts as an effective zone to generate the friction resistance. This interpretation has, however, an important doubt, as the Hertzian contact area is not formed through plastic but through elastic deformation of solids. If the friction resistance is generated in an elastic contact area, the adhesion theory of friction would be shaken at its standing basis. To give an explanation of this inconsistency between the experimental facts reported previously and the adhesion theory of friction, the authors propose a new idea in this paper. The plastic deformation occurs at surface asperities even in Hertzian contact. If the rubbing condition is kept dry, the friction resistance would be generated only at those plastically deformed zone dotted in the elastic contact area, so that Coulombs law is realized. If the rubbing condition is kept wet, the clearance between mating surfaces in the elastic contact zone is filled with any lubricant or contaminant molecules, the friction resistance would be generated through shearing of them within the Hertzian area. In this case, the coefficient of friction would be proportional to(load)-1/3, which is close to observational facts reported previously. An experimental verification made in this study can describe the authors proposal.