26 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
will be called transmitting joints. They do not themselves belong to either 
machine. Distinct elements may be introduced between the two machines, as 
in the typical example, fig. 28. Here the second machine is tied to the first 
by two links, each lettered / and ¢. These elements, which must represent 
forces in one straight line, may be considered as equivalent to the driving 
element of the second machine, and the resisting element of the first. In the 
example given it would be necessary to make / a tie, so that the machine, as 
drawn, would only work when element ¢ was expanding. In another case, one 
part of the link # might be omitted as between bc and a,b,, and replaced by a 
transmitting joint between 6 and }, as above. An element placed between two 
machines and serving to transmit the power, will be called a transmitting element. 
We see then that the communication of power can be made from one complete 
machine to another, either by two joints, by two elements, or by a joint and 
element. We may, with perfect propriety, give the name of complete machine 
to any one of a series, each of which drives its successor ; for we may regard 
the driving system simply as a more or less complex driving element, and the 
driven system as a more or less complex resisting element. We are not con- 
cerned with the complex play of forces which produces the driving or resisting 
effort, but, so far as each complete machine is concerned, only with the fact 
that its elements are driven or resisted in a manner which may be represented 
by a single driving or resisting link. 
§ 24. Compound Machines with one common element—The compound 
machines described in the last paragraph have no elements common to two 
simple machines, but we may have compound machines in which either one or 
two elements are common to two successive machines. The examples most 
commonly met with in engineering practice are those in which there is one 
common element, namely, the framework or support which is continuous and 
common to a series of successive complete machines. The common element is 
necessarily in equilibrium under the whole series of stresses to which it is subject, 
but this equilibrium is not a matter of great interest. The driving link of the 
first machine usually abuts at one end against the common element. If the first 
simple machine stood alone, one end of its resisting link would abut against 
the same element ; when it drives a series of machines, the resisting link of 
each must be so placed that in each case, if that particular machine were the 
last of the series, the resisting link would also abut against the common element. 
The common element takes the place of one transmitting joint or one trans- 
mitting link in the types given in the last paragraph. A practical example 
will serve to show the connection between successive complete machines, having 
one element in common. In fig. 29 a horizontal engine is shown driving a train 
of machinery. The engine consists of the elements abcde. The element d 
is a fixed frame; the element c comprises a fly-wheel and spur-wheel, which 
