On this assumption, the reactions on any member at its two joints must be equal and opposite. This combination of equal and opposite forces is called the _stress_ in the member; it may be a _tension_ or a _thrust_. For diagrammatic purposes each member is sufficiently represented by a straight line terminating at the two joints; these lines will be referred to as the _bars_ of the frame. [Illustration: FIG. 32.] In structural applications a frame must be _stiff_, or _rigid_, i.e. it must be incapable of deformation without alteration of length in at least one of its bars. It is said to be _just rigid_ if it ceases to be rigid when any one of its bars is removed. A frame which has more bars than are essential for rigidity may be called _over-rigid_; such a frame is in general self-stressed, i.e. it is in a state of stress independently of the action of extraneous forces. A plane frame of n joints which is just rigid (as regards deformation in its own plane) has 2n - 3 bars, for if one bar be held fixed the 2(n - 2) co-ordinates of the remaining n - 2 joints must just be determined by the lengths of the remaining bars. The total number of bars is therefore 2(n - 2) + 1. When a plane frame which is just rigid is subject to a given system of equilibrating extraneous forces (in its own plane) acting on the joints, the stresses in the bars are in general uniquely determinate. For the conditions of equilibrium of the forces on each pin furnish 2n equations, viz. two for each point, which are linear in respect of the stresses and the extraneous forces. This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n - 3 independent relations to determine the 2n - 3 unknown stresses. A frame of n joints and 2n - 3 bars may of course fail to be rigid owing to some parts being over-stiff whilst others are deformable; in such a case it will be found that the statical equations, apart from the three identical relations imposed by the equilibrium of the extraneous forces, are not all independent but are equivalent to less than 2n - 3 relations. Another exceptional case, known as the _critical case_, will be noticed later (§ 9).