408 
But when we are studying the equilibrium of a framework 
composed of such pieces jointed together, in which each piece 
acts only by tension or by pressure between its extremities, it 1s 
not necessary to know whether a particular piece is straight or 
curved or what may be the form of its section. In order, there- 
fore, to exhibit the structure of the frame in the most elemen- 
tary manner we may draw it as a skeleton im which the 
different jomts are connected by straight lines. The tension or 
pressure of each piece may be indicated on such a diagram by 
numbers attached to the line which represents that piece in 
the diagram. ‘The stresses in the frame would thus be in- 
dicated in a way which is geometrical as regards the position 
and direction of the forces, but arithmetical as regards their 
magnitude. ji 
But a purely geometrical representation of a force has been 
made use of from the earliest beginnings of mechanics as a 
science. The force is represented by a straight line drawn 
from the point of application of the force, im the direction 
of the force, and containing as many units of length as there 
are units of force in the force. The end of the line is marked 
by 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 which represents the configuration of 
the system. Such a diagram might be useful as a record of the 
results 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. It would be of less use than the diagram in which 
the magnitudes of the forces were indicated by numbers. 
But we have a geometrical method of testing the equilibrium 
of any set of forces acting at a point by drawing in series a set 
of lines parallel and proportional to these forces. If these lines 
form a closed polygon the forces are in equilibrium. We might 
thus form a set of polygons of forces, one for each joint of the 
frame. But in so doing we give up the principle of always 
