6 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
to lengthen or shorten the element in a definite direction. The two forces in 
this case tend to separate or draw together the other elements with which the 
first is jointed, as a straight elastic link would do if extended or compressed so 
that its line of action coincided with the direction of the forces exerted by the 
driving element. We may therefore conceive an actual driving element as 
replaced by an ideal elastic link producing the same force at the above named 
joints. Some machines have no material driving element, but are actuated by 
an attraction or repulsion between two of their elements, as, for example, when 
a machine is driven by a weight. In this case, as in the former case, we may 
conceive the machine as driven by an ideal elastic link between two elements. 
This link is as well suited to replace the equal and opposite forces due to gra- 
vitation as the equal and opposite forces due to steam. If the two opposite and 
equal forces exerted by a driving element do not lie in one straight line, these 
forces exert a couple between the elements with which the driving element is 
jointed; a similar couple may be exerted by the forces of attraction or repulsion 
between two elements. In either case, the machine may be considered as: 
actuated by an ideal couple due to the elastic reactions of two links. "What 
has been said of the driving power applies mutatis mutandis to the useful work 
done by a machine. In some cases the work is actually done in lengthening or 
shortening a separate resisting element, as when a bale of cotton is compressed. 
In other cases an attraction or repulsion is overcome between two elements, 
as when a weight is lifted. In both these cases we may conceive the resistance 
as represented by an ideal elastic link exerting definite, equal, and opposite 
forces in a definite position and direction. This ideal resisting link is equally 
suited to express the resistance by which cohesion, friction, or inertia opposes 
the relative motion of two elements. When the resisting element, or the resist- 
ance due to the united action of two elements, gives rise to a resisting couple, 
this resistance may be represented by two ideal links between two elements. 
Thus, we see that in every machine where there is only one source of power, 
we may represent that source by one ideal link (or two ideal links) connecting 
two elements, and acting on these elements as one member (or two members) 
of a strained frame acts on the rest of the structure. The name of driving link 
will be given to ideal links of this kind. The name of resisting link will 
similarly be given to ideal links used to represent the useful resistance in a 
machine. In all cases the cause of motion and the useful resistance must be 
considered as an action between two elements. We cannot properly speak of 
a driving point or resisting point, but only of driving or resisting links. . 
§7. Links—Dynamic Frame——Any actual material element might at any 
instant be removed from a machine without altering the stresses on the other 
elements, if at each joint thus laid bare, a force could be applied corresponding 
in position, magnitude, and direction with the pressure supplied at that instant, 
