THE POLYGON OF FORCES 37 
P, Q, R, 5, and T are supposed to act. In the case under consideration 
(Fig. 32) it is obvious that the bars A, B, C, D, and E are subjected to 
tension. Consider the point 2. Here there are three forces acting 
which balance one another, viz. the force P and the tensions in the bars 
A and B, and these three forces are represented in magnitude and 
direction by the three sides of the triangle abo. Again, the three forces 
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acting at the point 3 are represented by the sides of the triangle dco, also 
the three forces acting at the point 4 are represented by the sides of the 
triangle cdo; and the three forces at 5 by the sides of the triangle deo. 
Now in order that the tensions in the bars E and A may be balanced by 
the force T, the force T must act at the point of intersection of the bars 
Eand A. The point 1 is therefore a point in the line of action of T. 
The polygon 12345 is called the funicular polygon, the link polygon 
or the equilibrium polygon of the forces P, Q, R, 8, and T with reference 
to the point 0, which is called the pole. 
Since the pole o may have an infinite number of positions, there are 
an infinite number of funicular polygons to any system of balanced forces. 
Fig. 32. Fia. 33. 
If the diagrams (F) and (/) (Fig. 32) be compared it will be seen 
that each line on the one is parallel to a corresponding line on the other. 
Also, if a system of lines on the one meet at a point, the corresponding 
lines on the other form a closed nee From these properties the 
diagrams (F) and are called reciprocal figures. 
No hi el yet been made to Fig. 33, but all that has been 
said with reference to Fig. 32 will also apply to Fig. 33, where the given 
forces are parallel to one another, except that the bars E and A are in 
compression, the remaining bars B, C, and D being in tension. 
An examination of Figs. 32 and 33 will show that the simple rule to 
be remembered in drawing the funicular polygon is, that any side of that 
lygon has its extremities on the lines of action of two of the forces, 
and that that side is parallel to the line which joins the pole to the point 
of intersection of the lines which represent these two forces on the polygon 
of forces. 
Referring to Figs. 32 and 33, it may be noted that the equilibrant of 
