3 i4 APPLIED SCIENCE 



could from this obtain F 2 , etc. 2FW, the weight which can 

 be raised. The result is after a few turns to reduce F n to nil, 

 after which no more plies can be of any service. The gradually 

 diminishing efficiency of successive pulleys is very well shown 

 by the diagram, Fig. 33. 



27. Loaded Dynamic Frame without Friction. Let us now 

 consider the effect of the mass and weight of the elements of a 

 machine. We may feel sure that the effect of weight and 

 inertia may be shown by means of a dynamic frame, for this 

 frame consists of lines indicating bearing pressures at the joints, 

 and the direction and magnitude of these bearing pressures are 

 always determinate. In the case of a material element sup- 

 ported by two joints, the lines of bearing pressure will no longer 

 be directly opposite, or in the same straight line, but will inter- 

 sect in a point on the line which indicates the resultant of the 

 forces due to the weight and inertia of the element. Let the 

 resultant of all the forces exerted on a given element other than 

 those exerted at the joints be called the load on the element. 

 This includes the equilibrant of the force producing accelera- 

 tion. Then the action of an element with two joints, as in Fig. 

 34, might be supplied by three forces represented by three half 

 links 1, 2, and 3, Fig. 34, showing in position and direction the 

 bearing pressures at the joints, and the load on the element ; 

 this mode of representing a loaded element is commonly in use 

 where the equilibrium of arches is discussed. The load 3 is 

 here called a half link, for in the complete self-contained machine 

 an equal and opposite load necessarily exists in some other ele- 

 ment. This equal and opposite load is in general supplied by 

 the reaction of the foundations, or more strictly by the reaction 

 due to the mass of the earth. 



Where an element has more than two joints, it will be found 

 that the arrangement or form of the joints is generally, if not 

 always, such as to render determinate the single joint or pair of 

 joints by which it is supported. The effect of the load in modi- 

 fying the direction of the bearing pressure can for these cases 

 be as easily taken into account as in the simple case just cited. 



Let us now consider the effect of four loads L a L 6 L c and L d , on 

 the four elements abed of the elementary machine, Fig. 35. W<- 

 may, for the present, suppose the driving and resisting element 



