DIAGRAMS. 653 



The hodograph was invented and used with great success by Sir W. K. 

 Hamilton as a method of studying the motions of bodies. 



DIAGRAMS OF STRESS. 



Graphical methods are peculiarly applicable to statical questions, because 

 the state of the system is constant, so that we do not need to construct a 

 series of diagrams corresponding to the successive states of the system. 



The most useful of these applications relates to the equilibrium of plane 

 framed structures. Two diagrams are used, one called the diagram of the 

 frame and the other called the diagram of stress, 



The structure itself consists of a number of separable pieces or links jointed 

 together at their extremities. In practice these joints have friction, or may 

 be made purposely stiff, so that the force acting at the extremity of a piece 

 may not pass exactly through the axis of the joint ; but as it is unsafe to 

 make the stability of the structure depend in any degree upon the stiffness 

 of joints, we assume in our calculations that all the joints are perfectly smooth, 

 and therefore that the force acting on the end of any link passes through the 

 axis of the joint. 



The axes of the joints of the structure are represented by points in the 

 diagram of the frame. 



The link which connects two joints in the actual structure may be of 

 any shape, but in the diagram of the frame it is represented by a straight 

 line joining the points representing the two joints. 



If no force acts on the link except the two forces acting through the 

 centres of the joints, these two forces must be equal and opposite, and their 

 direction must coincide with the straight line joining the centres of the joints. 



If the force acting on either extremity of the link is directed towards 

 the other extremity, the stress on the link is called pressure and the link is 

 called a strut. If it is directed away from the other extremity, the stress 

 on the link is called tension and the link is called a tie. 



In this case, therefore, the only stress acting in a link is a pressure or 

 a tension in the direction of the straight line which represents it in the 

 diagram of the frame, and all that we have to do is to find the magnitude 

 of this stress. 



In the actual structure, gravity acts on every part of the link, but in 



