DIAGRAMS. 



This determine* whether the stress of the link is a pressure or a tension. 



If w know whether the stress of any one link is a pressure or a tension, 

 this determines the cyclical order of the sides of the two polygons corresponding 

 to the end* of the links, and therefore the cyclical order of all the polygons, 

 and the nature of the stress in every link of the frame. 



Definition of Reciprocal Diagrams. 



When to every point of concourse of the lines in the diagram of stress 

 corresponds a dosed polygon in the skeleton of the frame, the two diagrams 

 are said to be reciprocal. 



The first extensions of the method of diagrams of forces to other cases 

 than that of the funicular polygon were given by Rankine in his Ap^il 

 Mechanics (1857). The method was independently applied to a large number 



rises by Mr W. P. Taylor, a practical draughtsman in the office of the 

 well-known contractor Mr J. B. Cochrane, and by Professor Clerk Maxwell in 

 his lectures in King's College, London. In the Phil. Mag. for 1864 the latter 

 [x'inted out the reciprocal properties of the two diagrams, and in a paper on 

 "Reciprocal Figures, Frames, and Diagrams of Forces," Trans. R. S. Edinburgh, 

 Vol. xxvi. (1870), he shewed the relation of the method to Airy's function of 

 stress and to other mathematical methods. 



Professor Fleeming Jenkin has given a number of applications of the method 

 to practice (Trans. R. S. Edin., Vol. xxv.). 



Cremona (Le figure reciproche nella statica grafica, Milan, 1872) has deduced 

 the construction of reciprocal figures from the theory of the two components 

 of a wrench as developed by Mobius. 



Culmann, in his Graphische Statik, makes great use of diagrams of forces, 

 some of which, however, are not reciprocal. 



M. Maurice Levy in his Statique Graphique (Paris, 1874) has treated the 

 whole subject in an elementary but copious manner. 



Mr R. H. Bow, C.E., F.R.S.E., in his work on The Economics of Constiiiction 

 in relation to Framed Structures, 1873, has materially simplified the process of 

 drawing a diagram of stress reciprocal to a given frame acted on by a system 

 f equilibrating external forces. 



Instead of lettering the joints of the frame, as is usually done, or the 

 links of the frame, as was the writer's custom, he places a letter in each of 



