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drawing the line representing a force from its point of appli- 
cation, for all the sides of a 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 be- 
tween 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 force coin- 
cide 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 points of concourse of the 
pieces of the frame. 
Here we have a pure diagram of forces, 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 is manifest by inspection, for we have only to examine 
whether each polygon is closed or not. 
The relations between the diagram of the frame and the 
diagram of stress are as follows: 
To every piece in the frame corresponds a line in the 
diagram of stress which represents in magnitude and direction | 
the stress acting on that piece. 
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 two adjacent polygons is such 
that their common side is traced in opposite directions in going 
round the two polygons. 
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 
