d then write down on each link the pressure
or the tension which acts in it.

We should in this way obtain a mixed diagram in which the stresses are
represented graphically as regards direction and position, but
symbolically as regards magnitude. But we know that a force may be
represented in a purely graphical manner by a straight line in the
direction of the force containing as many units of length as there are
units of force in the force. The end of this line is marked with an
arrow head to show in which direction the force acts. According to
this method each force is drawn in its proper position in the diagram
of configuration of the frame. Such a diagram might be useful as a
record of the result of calculation of the magnitude of the forces,
but it would be of no use in enabling us to test the correctness of
the calculation.

But we have a graphical method of testing the equilibrium of any set
of forces acting at a point. We draw in series a set of lines parallel
and proportional to these forces. If these lines form a closed polygon
the forces are in equilibrium. (See MECHANICS.) We might in this way
form a series of polygons of forces, one for each joint of the frame.
But in so doing we give up the principle of drawing the line
representing a force from the point of application of the force, for
all the sides of the polygon cannot pass through the same point, as
the forces do. We also represent every stress twice over, for it
appears as a side of both the polygons corresponding to the two joints
between which it acts. But if we can arrange the polygons in such a
way that the sides of any two polygons which represent the same stress
coincide with each other, we may form a diagram in which every stress
is represented in direction and magnitude, though not in position, by
a single line which is the common boundary of the two polygons which
represent the joints at the extremities of the corresponding piece of
the frame.

We have thus obtained a pure diagram of stress in which no attempt is
made to represent the configuration of the material system, and in
which every force is not only represented in direction and magnitude
by a straight line, but the equilibrium of the forces at any joint is
manifest by inspection, for we have only to examine whether the
corresponding polygon is closed or not.

The relations between the diagram of the frame