'tt METHOD OF DRAWING I'lAi.KAMS IN URAPHICAL 8TATIC8. 



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

 a closed polygon in the skeleton of the frame, the two diagrams 



are aaki 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 Applied 



Ifafcmtw (1857). 



The method was indejwndently applied to a large number of cases by 

 Mr W. P. Taylor, a practical draughtsman in the office of the well-known con- 

 tractor Mr J. B. Cochrane. I pointed out the reciprocal properties of the 

 diagram in 1864, and in 1870 shewed the relations of this method to Airy's 

 function of stress and other mathematical methods. 



Prof. Fleeming Jenkin has given a number of applications of the method 

 practice. Trans. R. S. K, Vol. xxv. 



Cremona* has deduced the construction of the reciprocal figures from the 

 theory of the two linear components of a wrench. 



Cul ma nn in his Graphiscfie Statik makes great use of diagrams of forces, 

 some of which, however, are not reciprocal 



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

 whole subject in an elementary and complete manner. 



Mr R. H. Bow, C.E., F.R.S.E., in a recent work On the Economics of 

 Construction in relation to Framed Structures (Spon, 1873), has materially 

 simplified the process of drawing a diagram of stress reciprocal to a given frame 

 acted on by any system of equilibrating external forces. 



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

 pieces of the frame as was my own custom, he places a letter in each of 

 the polygonal areas enclosed by the pieces of the frame, and also in each of 

 the divisions of the surrounding space as separated by the lines of action of 

 the external forces. 



When one piece of the frame crosses another, the point of intersection is 

 treated as if it were a real joint, and the stresses of each of the intersecting 

 pieces are represented twice in the diagram of stress, as the opposite sides of the 

 parallelogram which represents the forces at the point of intersection. Thus 

 the point V in figures 1 and 3, p. 495, is represented by the parallelogram 

 BDCE in figure 2, and the point A in figure 2 is represented by the 

 parallelogram PRQS in figures 1 and 3. 



* L figure reciproche nella sfatica grafica (Milano, 1872). 



