30 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
pressure will no longer be directly opposite, or in the same straight line, but will 
intersect in a point on the line which indicates the resultant of the forces due to 
the weight and inertia of the element. Let the resultant of all the forces 
exerted on a given element other than those exerted at the joints be called the 
load on the element. This includes the equilibrant of the force producing 
acceleration. Then the action of an element with two joints, as in fig. 34, 
might be supplied -by three forces represented by three half links 1, 2, and 
3, fig. 34, showing in position and direction the bearing pressures at the joints, 
and the load on the element ; this mode of representing a loaded element is 
commonly in use where the equilibrium of arches is discussed. The load 3 is 
here called a half link, for in the complete self-contained machine an equal and 
opposite load necessarily exists in some other element. This equal and opposite 
load is in general supplied by the reaction of the foundations, or more strictly 
by the reaction due to the mass of the earth. 
Where an element has more than two joints, it will be found that the 
arrangement or form of the joints is generally, if not always, such as to render 
determinate the single joimt or pair of joints by which it is supported. The 
effect of the load in modifying the direction of the bearing pressure can for 
these cases be as easily taken into account as in the simple case just cited. 
Let us now consider the effect of four loads, L, L, L, and L,, on the four 
elements abcd of the elementary machine, fig. 35. We may, for the present, 
suppose the driving and resisting element to have no weight or inertia; the 
effect of these elements may then be treated as equivalent to the effect of four 
external forces, la 18, and 6a 68. The dynamic frame for this case will be a 
polygon of eight sides, fig. 35, 2a 26, 3a 38, 4a 48, 5a 58, having its angles on 
the lines of load, and so inclined as to be in equilibrium under these loads. 
The stresses in each link are the pressures at each joint. The reciprocal 
figure for this frame is shown in fig. 35a. The inclinations of the links are 
no longer independent of the magnitudes of the forces acting in the elements e 
and /, as was the case when we neglected weight and inertia. The effort in 
e or the resistance in# must therefore be given, as well as the loads, before 
the frame can be drawn. Let the effort in ¢ or in link 1 be known, the frame 
and its reciprocal may then be drawn as follows, so as to solve the problem of 
finding the resistance which a given effort in ¢ will overcome in /, neglecting 
the effect of friction, but taking into account the weight and inertia of the parts. 
We know the position of four of the angles of the polygon, viz., the 
centres of the pins at the four corners of the machine. Let the loads be 
referred to these four points in the manner practised for the distributed loads 
on the actual rafters of a roof or members of a bridge ; that is to say, let each 
load be replaced by two components acting at these four points. These com- 
ponents are lettered /, /’,, 1, /,, &c. The stress in element / will be the same 
