TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 25 
the pulley } in equilibrium are shown in position and direction at the joint B. 
Similarly, the forces which balance ¢ are shown at C, but the driving and 
resisting links, as well as link 6, appear as if under compression. Before pro- 
ceeding to draw the frame with friction, it may be well to show how the 
stiffness of the belt may be taken into account. In fig. 26 the arrows show 
the direction of the motion of the belt. The pulley 6 at the lower side has to 
exert a force P in the direction of the arrow on the belt, and also a right- 
handed couple m to bend the belt ; the resultant of this force and couple is an 
equal force shifted to the left or downwards by a distance o ; we might, there- 
fore, represent the actual belt by a perfectly flexible belt placed as shown by 
the dotted line d, d,. The effect of the stiffness of the belt at the other places 
where it is bent and unbent, is also to shift the line of application of the force 
as shown by the dotted lines d; d,, d;d,, d;d,. Thus the resultants of the forces 
due to the tension of the belt on each pulley will not be opposite each other ; 
the resultant will be shifted outwards on the driving pulley, and inwards on 
follower, or disadvantageously in both places. The actual amount of shifting 
cannot be ascertained until P and P,, the tensions on the belt, are known ; but . 
the nature of the change is easily apprehended, and is therefore included in the 
dynamic frame, fig. 266. This frame is drawn as for the case without friction. 
§ 23. Compound Machines.—It is evident that the resisting link of one 
complete simple machine may be used as the driving link of another simple 
machine. This combination gives rise to what may be called a compound 
machine. If the two machines have no element in common, they must be 
connected by two joints in the manner of which fig. 27 gives a typical example. 
In this figure the lines may be considered to represent either the links of a 
dynamic frame, or the axes ofa series of material elements, jointed without 
friction. The contraction of element e¢ would cause an expansion of the line 
joining the joint dc with da. This line would indicate the position of the 
resisting link of the machine abcde, if this machine were a simple one. 
This same line lies between the joints 0, a, and d, ¢, in the position required to 
enable the effort produced by the first machine ubcd to drive the second 
ad, b, ¢, d, f;. In fact, the whole first machine may be considered as a somewhat 
complex driving element, relatively to the second machine ; or the whole of 
the second machine may be looked on as a rather complex resisting element, 
relatively to the first machine. The two machines may obviously be treated as 
entirely separate. Let the first machine drive the second by contact between 
the elements 6 and 6, and between d and d,. Then it is necessary that at these 
joints the directions of the lines of bearing pressure shall be in one straight 
line. This line is the direction of the resisting link for one machine, and the driv- 
ing link for the next. The joints 50,, and ¢e,, between two successive machines, 
VOL. XXVIII. PART I. G 
