20 PROFESSOR FLEEMING JENKIN’S APPLICATION OF GRAPHIC METHODS 
and direction of this resistance is known, being that shown by the arrow on f/ 
in fig. 17.. The elements are; a, the piston rod and block sliding on the guide 
bars ; 6, the connecting rod ; ¢, the crank, axle, and fly wheel; d, the bed plate 
including the cylinder; ¢, the steam in the cylinder. This element is jointed 
with a and d; the position and direction of the force exerted are in this case 
determinate ; for the cylinder does not oscillate and the piston with its rod are 
subject to no stress that is not axial ; the element @ is in equilibrium under the | 
force due to e, and those due to the joints a) and ad. In fig. 17a link 1 is 
drawn coinciding with the axis of the cylinder, and represents the bearing pres- 
sure produced by ¢ on its joints ; the link 2 may next be drawn tangent to the 
friction circles for ab and be. The third force under which a@ is in equilibrium 
is that due to the joint ad ; the link 5 is drawn through the dynamic joint A, 
‘making the stated angle with the guide bars. This diagram corresponds to an 
engine in which the slide block is as usual fast on the piston rod.* 
We next observe that element ¢ has three joints—first at c/, secondly at be, 
and lastly at cd. The resisting link must, in order that the machine may be 
coniplete, abut at its other end against the bed plate d; it may be due to actual 
friction, as when the fly wheel is, for experimental purposes, fastened between 
two friction blocks secured to. d. We know, by hypothesis, the place and direc- 
tion of its application, and therefore the position and direction of link 6. The 
intersection of 6 and 2 gives the dynamic joint C; the third force acting on ¢ 
must pass through this joint, and make the stated angle at the joint cd; we 
therefore draw link 3 from C tangent to the friction circle for cd. Lastly, we 
observe that the element d is in equilibrium under the following forces :—I1st 
that due to the joint ed, equal and opposite to that on ae; 2d, that due to the 
joint ad; 3d, that due to the resisting link f; 4th, that due to the joint ed. 
We have already on the fig: 17a, the position and direction of all these forces. 
They do not, however, all meet in one joint, and we must therefore, to complete 
the dynamic frame, add a link which shall receive the equal and opposite 
resultants of the forces compounded in two pairs; this we may do by joining 
the intersection between links 5 and 6 with that between 1 and 3, giving the 
complete diagram of fig. 17a. The diagram fig. 17c will help to. explain the 
significance of the several links. The element d, which is the frame, is here shown 
by itself; it is in equilibrium under four external forces, indicated by arrows 
numbered as the links in the frame are numbered; and as this plate 
is itself in equilibrium, the resultant of 1 and. 3 will be opposite and equal 
to the resultant of 5 and 6. The forces at the joints may therefore be repre- 
* Tf, however, there were a joint between these parts, such that the pressure from the guide bars 
must pass very near the centre of the pin at that joint, then links 5 and 2 would be first drawn, and 
link 1 drawn cutting their dynamic joint ; this arrangement would cause the effort exerted by the piston 
to pass a little way on the axis of the cylinder, as shown in fig. 170. 
