TO THE DETERMINATION OF THE EFFICIENCY OF MACHINERY. 27 
drives the pinion which is part of g; the spur-wheel of g drives a pinion which © 
is part of h. A pulley, which is also part of h, drives a belt J, which, in 
its turn, drives a pulley m; a second pulley, also part of m, drives a 
second belt and pulley » and o. A piece of wood, forming part of 0, is 
being turned by a tool which forms part of d. We have here three 
complete machines—Ist, the engine; 2d, the machine gh d, driven by two 
transmitting joints and gdcg, and driving a transmitting link 7; 3d, the 
machine mnod, driven by the transmitting link 7 and the joint md, and overcom- 
ing the useful resistance at the joint od. All these machines have the element din 
common. The dynamic frame of the compound machine is shown in fig. 29a, 
and the reciprocal figure for that frame in fig. 296. The driving element of the first 
machine is the steam which abuts against d, the bed-plate or support. The resist- 
ing element is the whole series of driven machines, in the last of which a resist- 
ance is overcome between an element of the machine and the bed-plate d. The 
resisting element is not complete unless we take into account the force it exerts 
at both ends ; the one end of the resisting link of the first machine pushes up 
the periphery of the fly-wheel c, the other end pushes down the element d; 
this is precisely the action we should have, if the first machine had been com- . 
pleted by a single resisting link ; the circuit must in either case be completed, 
so that the resisting lnk may abut against the common element d, against 
which the first driving link also abuts. The driving link of the second machine 
ghd is in the line of the resisting link of abcde. The direction of this link is 
for both machines determined by the transmitting joint cg, 7.e., by the form of 
the teeth of the wheels. The driving link of the machine mod, is in the line 
of the resultant tension due to the band /, which is here a transmitting element. 
The driving or resisting link of each successive machine, if taken by itself, 
would abut against the common element d. The first driving and last trans- 
_ mitting element do abut against this common element. In any machine it will 
be found easy to analyse the series of parts so as to divide the whole structure 
into a series of complete machines, each joined to its neighbour by a transmit- 
ting joint or link. Each machine can then be treated as a separate whole. 
We see in the example given that the dynamic frame consists of three distinct 
quadrilaterals with diagonals. The connecting links may be considered as double 
links in each case. Thus we may consider the joint C, fig. 29a, as connected by 
one link with the joint G which it drives, while at the same time the joint D, is 
connected by a link with D,. Thus, when the reciprocal figure for the whole 
frame is drawn, as in fig. 29), it forms one connected whole. The stress 
corresponding to each connecting link is used twice as in all reciprocal figures. 
In fig. 295 each link is numbered from 1 to 6 for each successive machine. 
The length of the first line 1 corresponds to the driving effort. The length of 
the last small link 6 corresponds to the resistance which that effort can over- 
