Frequently, it was thought that frictional slip would occur in direction of least resistance, which was unfortunately taken as direction of shortest normal to free boundary. In this paper, condition of least resistance is accepted, but direction of resistance is properly determined without assumption. The result is the rule of gredient, that is, at a given point on contact surface, direction of least resistance is direction of gredient of unit r, which is related to unit pressure P and of friction, f, by γ=fP, gredient lines of γ and P coincide with each other. Consequently, family of least resistance lines of is exactly family of curves orthogonal to pressure contours, and can be determined from experimental surface distribution of pressure. One case of such friction-lines in rolling is presented, curves bear remarkable resemblance to under-evalu-ted probable lines of derived by siebel from deformation meassurements. The way to consider change in direction of γ in one-dimensional theory of rolling is to take an average line whose direction cosine, cos φ, vanishes at neutral section according to gredient rule. By doing so, f cos φ corresponds to coefficient of friction which vanishes at neutral section according to Brown's theory. The Karman's equation is written in mean value form by taking γ_x=fP cos φ instead of γ_x =fP. The modified equation yields solutions smoothly continuous at neutral section, and two such continuous solution to Karman's equation for case of solid are presented, detailed investigation is left to another paper~[15]. By simple arguement, it is thought that boundary of no-slip region should be a crossed curve given by a pressure contour which is a roop according to experimental results. The rule of gradient has already led to three concequences~[15-17], and is expected to be a very useful relation for plasticity under compression, because up to this paper differential equation for slip direction remains unknown.