and the diagram of
stress are as follows:--To every link in the frame corresponds a
straight line in the diagram of stress which represents in magnitude
and direction the stress acting in that link; and to every joint of
the frame corresponds a closed polygon in the diagram, and the forces
acting at that joint are represented by the sides of the polygon taken
in a certain cyclical order, the cyclical order of the sides of the
two adjacent polygons being such that their common side is traced in
opposite directions in going round the two polygons.

The direction in which any side of a polygon is traced is the
direction of the force acting on that joint of the frame which
corresponds to the polygon, and due to that link of the frame which
corresponds to the side. This determines whether the stress of the
link is a pressure or a tension. If we know whether the stress of any
one link is a pressure or a tension, this determines the cyclical
order of the sides of the two polygons corresponding to the ends of
the links, and therefore the cyclical order of all the polygons, and
the nature of the stress in every link of the frame.

_Reciprocal Diagrams._--When to every point of concourse of the lines
in the diagram of stress corresponds a closed polygon in the skeleton
of the frame, the two diagrams are said to be reciprocal.

The first extensions of the method of diagrams of forces to other
cases than that of the funicular polygon were given by Rankine in his
_Applied Mechanics_ (1857). The method was independently applied to a
large number of cases by W. P. Taylor, a practical draughtsman in the
office of J. B. Cochrane, and by Professor Clerk Maxwell in his
lectures in King's College, London. In the _Phil. Mag._ for 1864 the
latter pointed out the reciprocal properties of the two diagrams, and
in a paper on "Reciprocal Figures, Frames and Diagrams of Forces,"
_Trans. R.S. Edin._ vol. xxvi., 1870, he showed the relation of the
method to Airy's function of stress and to other mathematical methods.
Professor Fleeming Jenkin has given a number of applications of the
method to practice (_Trans. R.S. Edin._ vol. xxv.).

L. Cremona (_Le Figure reciproche nella statica grafica_, 1872)
deduced the construction of reciprocal figures from the theory of the
two components of a wrench as developed by Moebius. Karl Culmann, in
his _Graphische Statik_ (1st ed. 1864-18